JP2010152851A - Apparatus, method and program for multiobjective optimization - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus, method and program for multiobjective optimization, enabling optimization of a determination variable for an optimization target having a restriction condition, with high accuracy in short time. <P>SOLUTION: A restriction violation flag indicative of whether or not a determination variable value, which is evaluated by a multiobjective evolutionary algorithm unit 2, an adaptation degree which is output from an optimization target 6, and a restriction variable value which is output from the optimization target 6, violate the restriction condition is stored into a search history memory 3 in a related manner as a search history. Upon decision of a determination variable value to be evaluated, a predetermined number of determination variable values, whose evaluations are completed and which are nearer to an unevaluated determination variable value, are selected from the search history stored in the search history memory 3. It is decided whether or not the unevaluated determination variable value is to be evaluated, based on whether or not the restriction violation flag, corresponding to the predetermined number of selected determination variable values, indicates the violation of the restriction condition. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a multi-objective optimization device, a multi-objective optimization method, and a multi-objective optimization program for optimizing parameters (decision variables) to be optimized having constraints.

  Conventionally, there is a problem class called a multi-objective optimization problem. For example, when considering the problem of minimizing the cost of a product and maximizing performance, this becomes a multi-objective optimization problem of two objective functions. In this case, cost and performance are two objective functions. Generally, there is not a single solution for the multi-objective optimization problem because there is a trade-off relationship that lowering the cost degrades the performance and increasing the performance increases the cost.

FIG. 30 is a diagram showing an example in which the multi-objective optimization problem is applied to engine optimization. When the multi-objective optimization problem is applied to engine fuel efficiency and torque optimization, the fuel efficiency and torque are two objective functions f ₁ and f ₂ . In this case, the values of the objective functions f ₁ and f ₂ are optimized by adjusting parameters such as the fuel injection amount and the ignition timing.

  The solution A has better fuel efficiency than the solution B, but the torque is inferior to the solution B. As described above, since the engine fuel efficiency and the engine torque have a trade-off relationship, there are a plurality of optimum solutions. The user can select a solution suitable for the purpose from a plurality of optimum solutions. For example, the solution A is selected for an engine used for a motorcycle suitable for sports driving, and the solution B is selected for an engine used for a motorcycle suitable for long touring.

  In general, the multi-objective optimization problem is defined as a problem of minimizing the values of M objective functions for N parameters within the range of the constraint condition of each parameter. When maximizing the value of the objective function, a negative sign is added to the objective function to convert it into a problem that minimizes the value of the objective function.

  Such a multi-objective optimization problem generally does not have a single optimal solution, but has an optimal solution set defined by a concept called a Pareto optimal solution. Here, the Pareto optimal solution is a solution in which the value of at least one other objective function must be altered in order to improve the value of a certain objective function, and is defined as follows: (For example, refer nonpatent literature 1).

[Definition 1] For two solutions x1, x2εF of a certain number of p objective functions f _k (k = 1,..., P), f _k (x1) ≦ f _k (x2) (） _k = 1 ,..., P) ∧f _k (x1) <f _k (x2) (∃k = 1,..., P), x1 is said to dominate x2. Here, F is a set of solutions.

  [Definition 2] When a solution x0 dominates all other solutions xεF, x0 is an optimal solution.

  [Definition 3] When there is no solution xεF superior to a solution x0, x0 is a Pareto optimal solution (or non-inferior solution).

  Obtaining the Pareto optimal solution set results in obtaining an optimal solution set with respect to the objective function trade-off.

FIG. 31 is a diagram for explaining the Pareto optimal solution. Figure 31 shows two examples of the objective function _f 1, _{f 2.} The value _f 1 of the objective function _{f 1} for solution a (a) the value _f 1 of the objective function _{f 1} for solutions b (b) less than, the value _f 2 of the objective function _{f 2} for Solution a (a) Is smaller than the value f ₂ (b) of the objective function f ₂ for the solution b. Therefore, the solution a is superior to the solution b.

  Similarly, the solution a dominates the solutions c and d. There is no solution superior to solution a. Similarly, there is no solution superior to the solutions e and f. Accordingly, the solutions a, e, and f are Pareto optimal solutions.

  The solution g is a weak Pareto optimal solution. The weak Pareto optimal solution is a Pareto solution that is not superior to the Pareto optimal solution only for a certain objective function. The weak Pareto optimal solution is not a rational solution and is a solution that does not need to be originally obtained.

  Many solutions for multi-objective optimization problems have been proposed. Recently, there has been a multiobjective evolutionary algorithm (MOEAs).

The biggest feature of this method is that the Pareto optimal solution set is obtained at a time using the multi-point search of the evolutionary algorithm. The obtained Pareto optimal solution set is used for decision making to find a solution that matches the purpose from among them, or for obtaining knowledge from the shape of the Pareto optimal solution set (Pareto boundary).

  There have been many studies on applying genetic algorithms (GA) as multi-objective optimization problems as evolutionary algorithms. Genetic algorithms are computational methods that mimic the adaptive evolution of organisms. In a genetic algorithm, a solution candidate is called an individual. The objective function is called a fitness function, and the value of the fitness function is called a fitness.

  This genetic algorithm is based on the process of natural evolution (chromosome selection, crossover and mutation) as a hint. This is an algorithm proposed by Holland. The design variable is regarded as a gene, an initial design individual set is randomly generated, and the fitness of each individual is evaluated. Parents are selected so that individuals with better fitness are more likely to be selected as parents. And offspring are created by crossover (gene replacement) and mutation (random change of gene). Furthermore, generations are repeated through evaluation, selection, crossover, and mutation to search for an optimal solution.

Specifically, Fonseca et al. MOGA (Multiobjective Genetic Algorithm: see, for example, Non-Patent Document 1), Deb et al. NSGA-II (Non-Dominated Sorting Genetic Algorithm-II, see, for example, Non-Patent Document 2), Zitzler et al. SPEA2 (Strength
Pareto Evolutionary Algorithm 2: For example, see Non-Patent Document 3). In particular, NSGA-II and SPEA2 are known as excellent multi-objective evolutionary algorithms.
JP 2008-045476 A CMfonseca, pJFlemimg: genetic algorithms for multiobjective optimization: formation, discussion and generalization, of the 5th international conference on genetic algorithms, pp.416-423 (1993) K. Deb, S. Agrawal, A. Pratab, and T. Meyarivan: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II, KanGAL report 20001, Indian Institute of Technology, Kanpur, India (20OO ) E.Zitzler, M. Laumanns, L. Thiele: SPEA2: Improving the Performance of the Strength Pareto Evolutionary A1gorithm, Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001) A.Zhou et al .: Prediction-based Population Re-initialization for Evolutionary Dynamic Multi-objective Optimization, Proc. Of EMO2007 U. Bazarsuren, M. Knaak, S. Schaum, and C. Guhmann, “Determining Adjustment Ranges for Model-based Approaches Using Support Vector Machines,” Proc. Of CCA 2006, pp. 2066-2071, 2006 H. Kaji, and H. Kita, “Acceleration of Experiment-Based Evolutionary Multi-objective Optimization of Internal-Combustion Engine Controllers using Fitness Estimation,” Proc. Of CEC 2007, pp. 1777-1784, 2007

  In recent automobile engines, various electronic control devices such as fuel injection devices are installed to reduce harmful components contained in exhaust gas and improve power performance while addressing environmental problems. Control is taking place.

  Since the engine is a control target with strong nonlinearity, feedforward control called map control is the mainstream as engine control by the electronic control unit. In the map control, for example, control parameters of the electronic control device set for each operation condition such as load torque and engine speed are used. The control parameters for map control are determined by conducting preliminary experiments for each operating condition. This task is called calibration.

Conventional adaptation is performed by a technician manually adjusting an engine connected to an engine tester. However, such adaptation is harmful components of exhaust gas (CO concentration, HC concentration and NO _x concentration) becomes a multi-purpose evaluation of such fuel efficiency and output torque, it is related generally a trade-off. Furthermore, the number of electronic control units and their control parameters tends to increase. For this reason, manual optimization has become increasingly difficult.

  FIG. 32 is a view for explaining adaptation of the engine.

For engine adaptation, values of operating conditions (condition variables w ₁ and w ₂ ) such as load torque and engine speed are selected. The fuel injection timing and ignition timing (control parameters (determined variables x ₁ , x ₂ )) that optimize the NO _x concentration and fuel consumption (values of the objective functions f ₁ , f ₂ ) under the selected operating conditions Explore.

In Figure 32, select the value of the condition variable _w 1, _{w 2,} performs multi-objective optimization of the objective function _f 1, _{f 2} for the selected condition variables _w 1, _{w 2} value, the decision variable _x 1, obtaining a Pareto optimal solution x _2. Thereafter, a suitable solution is selected from the Pareto optimal solution, a map M1 showing the relationship between the value of the decision variable x ₁ corresponding to the solution and the value of the condition variables w ₁ and w ₂ , and the decision variable corresponding to the solution to create a map M2 indicating the value of the relationship between the value and condition variables _w 1, _{w 2} of x _2.

In order to complete the maps M1 and M2, it is necessary to repeat multi-objective optimization on the values of the conditional variables w ₁ and w ₂ corresponding to the number of grids of the maps M1 and M2.

  Engine adaptation is a control parameter value that satisfies multiple conflicting evaluation criteria (objective functions) within the given limits (constraints) for each operating condition (condition variable) required for map control. It is to solve a multi-objective optimization problem that searches for a set of (decision variable values). A range in which a set of control parameter values satisfying the constraint condition is called an executable area, and the other range is called an inexecutable area.

  Conventionally, when trying to optimize the control parameters of the optimization target, the optimization target is modeled based on the laws of physics, etc., and the result is an optimization problem, resulting in a gradient method such as a quasi-Newton method or a genetic algorithm. Apply representative metaheuristics. And the approach of applying the obtained optimal solution to an actual optimization object is taken. On the other hand, in the case of an optimization target for which it is difficult to construct a theoretical model, optimization is performed through experiments.

  When optimization is performed through experiments, the objective function to be optimized and the value of the item to be restricted (constraint function) may be the actual output of the optimization target. An approach called response surface methodology is widely applied to such optimization targets. In the response surface method, first, an objective function value and a constraint function value, which are outputs to be optimized, for a set of control parameter values determined based on an experimental design method are obtained. Next, an approximation model of the objective function and constraint function to be optimized is obtained using a statistical method such as a polynomial or an artificial neural network. Then, in this approximate model, a set of control parameter values that optimizes the objective function value within the range of the constraint condition given by the constraint function by the gradient method or metaheuristics on the computer, that is, in the executable region, is obtained.

  On the other hand, with the recent development of measurement and control environment, an approach in which an optimization method is directly applied to an actual optimization target is becoming realistic. Hereinafter, this approach is referred to as experiment-based optimization. Experiment-based optimization does not require experiment design or model selection, and does not require modeling errors in the approximate model.

  As described above, the computer can freely change the control parameter value of the electronic control unit regardless of whether the response surface methodology or the experiment-based optimization is used, but there are certain restrictions on the combinations that can actually be operated. is there. Here, the constraint condition is that when the control parameter value is set in the electronic control unit, the engine cannot be started, the optimization target and the malfunction of the measuring instrument due to the exhaust gas concentration being too high, or the temperature This refers to physical constraints for avoiding problems such as engine damage due to excessively high values.

  When the constraint condition is expressed as a function of the control parameter by a mathematical expression, before the control parameter value is evaluated by the actual machine, the control parameter value is input to the mathematical expression, and whether or not the calculation result violates the constraint condition. You can investigate.

  However, as mentioned above, some constraints are observed through experiments. In this case, it is determined whether or not the constraint condition is violated only after the control parameter value is set in the electronic control device and the engine is operated.

  In the response surface method, a set of control parameter values to be measured is determined by an experimental design method. In a method called orthogonal design, central composite design, or D-optimal design used in this case, approximation of a statistical model is performed in the entire space (control parameter space or decision variable space) formed by a set of control parameter values to be searched. In order to increase accuracy, a set of control parameter values is determined so as to be widely distributed in the control parameter space. Therefore, there may be a set of control parameter values that violate the constraint conditions.

  For example, methods disclosed in Non-Patent Documents 4 and 5 have been proposed as methods for setting a constraint condition for a set of control parameter values in the response surface methodology. These methods are generally performed as follows.

  FIG. 33 is a conceptual diagram for explaining a method of setting a constraint condition for a set of control parameter values in the response surface methodology.

  In FIG. 33, first, a set of control parameter values that is known to be safe in advance is set as an initial parameter value IP, and an internal dividing point between the initial parameter value IP and a set of control parameter values LA1 to LA8 set by the experimental design method. Are evaluated discretely or continuously in order from the initial parameter value IP toward the set control parameter values LA1 to LA8. When a constraint condition is violated when evaluating a certain control parameter value (for example, when the exhaust gas temperature exceeds a predetermined threshold value), the control parameter value is changed from the control parameter value to the previous control parameter value. Returning, the control parameter values are determined as the limit parameter values LP1 to LP8.

  In FIG. 33, control parameter values at which no constraint condition violation occurs are indicated by white circles, and control parameter values at which the constraint condition violation occurred are indicated by black circles.

  An approximation model of an executable region indicated by a dotted line is created by creating a two-class classifier using a convex hull or a support vector machine for all the limit parameter values LP1 to LP8 determined in this way. The approximate model of the feasible region obtained in this way is also called a boundary model.

  However, in the above method, it is difficult to express a boundary of a complicated shape because the boundary of an executable region is estimated using very few points. As shown in FIG. 33, the true executable region and the estimated executable region may greatly differ.

  Therefore, when a true Pareto optimal solution exists outside the boundary model, the Pareto optimal solution cannot be found. Further, when the boundary model includes a true infeasible region, there is a possibility that a part of the obtained Pareto optimal solution set violates an actual constraint condition. Furthermore, when the Pareto optimal solution set exists near the center of the boundary model, the effort for obtaining the boundary model is wasted.

  On the other hand, in the experiment-based optimization using the multi-objective evolutionary algorithm, the search area can be changed adaptively, and thus the above problem is avoided. However, because individuals are generated stochastically, there is a possibility that individuals will be generated in the infeasible region by the crossover operator or the mutation operator, particularly when the Pareto optimal individual set exists near the boundary of the feasible region. Get higher. As a result, there is a possibility that the evaluation of the individual in a state where the constraint condition is violated may increase.

  As described above, if an individual is evaluated in a state where the constraint condition is violated, there is a possibility that the optimization target or the measuring instrument may be broken or damaged.

  An object of the present invention is to provide a multi-objective optimization apparatus, a multi-objective optimization method, and a multi-objective optimization program that can optimize a decision variable to be optimized having a constraint condition in a short time with high accuracy.

(1) A multi-objective optimization apparatus according to a first invention is a multi-objective optimization apparatus that optimizes a decision variable to be optimized having a plurality of objective functions within a range of constraint conditions, and evaluates the multi-objective optimization apparatus in multi-objective optimization. Determine the value of the power decision variable, give the value of the decision variable determined to be evaluated to the optimization target, and perform multi-objective optimization using the value of the objective function output from the optimization target to optimize The multi-objective optimization unit that obtains the Pareto approximate solution set of the decision variable within the range where the constraint function value output from the target satisfies the constraint condition, and the value of the decision variable evaluated by the multi-objective optimization unit and output from the optimization target A multi-objective optimization unit including a storage unit that associates and stores, as a search history, constraint violation information indicating whether or not the value of the objective function and the value of the constraint function output from the optimization target violate the constraint condition Is When determining the value of the decision variable to be valued, it is selected from the search history stored in the storage unit by selecting the value of the decision variable that is closer to the value of the unevaluated decision variable and has been evaluated a predetermined number. Whether or not the value of the unevaluated decision variable should be evaluated is determined based on whether or not the constraint violation information corresponding to the predetermined number of decision variable values indicates violation of the constraint condition.

  In the multi-objective optimization apparatus, the value of the decision variable to be evaluated in the multi-objective optimization is determined by the multi-objective optimization unit. The value of the decision variable determined to be evaluated is given to the optimization target, and the multi-objective optimization unit performs multi-objective optimization using the value of the objective function output from the optimization target. A Pareto approximate solution set of the decision variable is obtained in a range where the value of the output constraint function satisfies the constraint condition.

  Constraint violation information indicating whether the value of the decision variable evaluated by the multi-objective optimization unit, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violate the constraint condition Are associated with each other as a search history and stored in the storage unit.

  When determining the value of the decision variable to be evaluated, the value of the decision variable that is closer to the value of the unevaluated decision variable and that has been evaluated is selected and selected from the search history stored in the storage unit. It is determined whether or not the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the predetermined number of decision variable values indicates a violation of the constraint condition.

  Thereby, the possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target violates the constraint condition is reduced. Therefore, it is possible to obtain a Pareto approximate solution set with high accuracy while avoiding violation of constraint conditions.

  (2) The predetermined number is 1, and when the multipurpose optimization unit determines the value of the decision variable to be evaluated, the value of the one evaluated decision variable closest to the value of the unevaluated decision variable If the constraint violation information corresponding to the value of one selected decision variable that has been evaluated does not indicate a violation of the constraint condition, it is determined that the value of the unevaluated decision variable should be evaluated and selected. When the constraint violation information corresponding to one evaluated decision variable value indicates violation of the constraint condition, it may be determined that the value of the unevaluated decision variable should not be evaluated.

  In this case, there is a possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target by a simple method may violate the constraint condition, and the value of the decision variable that does not violate the constraint condition in the vicinity of the Pareto optimal solution. The possibility of not being evaluated can be reliably reduced.

  (3) The predetermined number is k (k is a natural number of 2 or more), and the multi-objective optimization unit is closer to the value of the unevaluated decision variable and k pieces when determining the value of the decision variable to be evaluated. The value of a decision variable that has been evaluated is selected, and an unevaluated decision is made by majority decision whether or not the constraint violation information corresponding to the selected k evaluation variable values that have been evaluated indicates violation of the constraint condition It may be determined whether the value of the variable should be evaluated.

  In this case, there is a possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target by a simple method may violate the constraint condition, and the value of the decision variable that does not violate the constraint condition in the vicinity of the Pareto optimal solution. The possibility of not being evaluated can be reliably reduced.

  (4) The multi-objective optimization unit may select a predetermined number of evaluation variable values that are closer to the unevaluated determination variable value in the determination variable space and based on the Euclidean distance.

  In this case, it is possible to accurately select a predetermined number of evaluated decision variable values that are closer to the unevaluated decision variable value by a simple method.

  (5) The multi-objective optimization unit, in the decision variable space, determines the Euclidean distance and the unevaluated decision between the value of the unevaluated decision variable and the value of the number of decided decisions that indicate that the constraint violation information does not violate the constraint condition. Weight each Euclidean distance between the value of the variable and the value of the number of decisions that have been evaluated to indicate that the constraint violation information violates the constraint condition, and the value of the unevaluated decision variable based on the weighted Euclidean distance The value of a decision variable that is closer and a predetermined number of evaluated variables may be selected.

In this case, it is possible to adjust the range of values of the decision variable to be evaluated by adjusting the weight. Thereby, it is possible to adjust the range of the value of the decision variable evaluated in the vicinity of the Pareto optimal solution, and to adjust the error between the Pareto approximate solution set and the Pareto optimal solution set to be obtained.

  (6) The multi-objective optimization unit may generate an unevaluated decision variable value by a multi-objective evolutionary algorithm. In this case, a Pareto approximate solution set can be efficiently obtained.

  (7) A multi-objective optimization method according to the second invention is a multi-objective optimization method for optimizing a decision variable to be optimized having a plurality of objective functions within a range of constraints, and is evaluated in the multi-objective optimization. Determine the value of the power decision variable, give the value of the decision variable determined to be evaluated to the optimization target, and perform multi-objective optimization using the value of the objective function output from the optimization target to optimize A step for obtaining a Pareto approximate solution set of decision variables within a range in which the value of the constraint function output from the target satisfies the constraint conditions, the value of the evaluated decision variable, the value of the objective function output from the optimization target, and the optimization A step of obtaining a Pareto approximate solution set, comprising associating constraint violation information indicating whether or not a constraint function value output from a target violates a constraint condition as a search history in a storage unit When determining the value of the decision variable to be evaluated, select the value of the decision variable that is closer to the value of the unevaluated decision variable and has been evaluated a predetermined number from the search history stored in the storage unit, and select And determining whether or not the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the predetermined number of decision variable values indicates a violation of the constraint condition.

  In the multi-objective optimization method, the value of a decision variable to be evaluated in multi-objective optimization is determined. The value of the decision variable determined to be evaluated is given to the optimization target, and multi-objective optimization is performed using the value of the objective function output from the optimization target, and the constraint function output from the optimization target A Pareto approximate solution set of decision variables is obtained in the range where the value of satisfies the constraint condition.

  The constraint violation information indicating whether the value of the evaluated decision variable, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violates the constraint condition is the search history. Correspondingly stored in the storage unit.

  When determining the value of the decision variable to be evaluated, the value of the decision variable that is closer to the value of the unevaluated decision variable and that has been evaluated is selected and selected from the search history stored in the storage unit. It is determined whether or not the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the predetermined number of decision variable values indicates a violation of the constraint condition.

  Thereby, the possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target violates the constraint condition is reduced. Therefore, it is possible to obtain a Pareto approximate solution set with high accuracy while avoiding violation of constraint conditions.

  (8) A multi-objective optimization program according to a third invention is a multi-objective optimization program for causing a computer to execute a multi-objective optimization method for optimizing a decision variable to be optimized having a plurality of objective functions within a range of constraint conditions. Therefore, the value of the decision variable to be evaluated in multi-objective optimization is determined, the value of the decision variable determined to be evaluated is given to the optimization target, and the value of the objective function output from the optimization target is used. Multi-objective optimization and obtaining a Pareto approximate solution set of decision variables within the range where the constraint function values output from the optimization target satisfy the constraint conditions, and the evaluated decision variable values and output from the optimization target Processing that stores constraint violation information that indicates whether or not the value of the objective function that has been set and the value of the constraint function that is output from the optimization target violates the constraint condition as a search history and stores it in the storage unit The processing for obtaining the Pareto approximate solution set includes a search history stored in the storage unit, when determining the value of the decision variable to be evaluated, closer to the value of the unevaluated decision variable and a predetermined number of evaluations. The value of the decision variable that has already been selected and the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the selected number of decision variable values indicates a violation of the constraint condition. This includes processing for determining whether or not

According to the multi-objective optimization method, the value of the decision variable to be evaluated in the multi-objective optimization is determined. The value of the decision variable determined to be evaluated is given to the optimization target, and multi-objective optimization is performed using the value of the objective function output from the optimization target, and the constraint function output from the optimization target A Pareto approximate solution set of decision variables is obtained in the range where the value of satisfies the constraint condition.

  The constraint violation information indicating whether the value of the evaluated decision variable, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violates the constraint condition is the search history. Correspondingly stored in the storage unit.

  When determining the value of the decision variable to be evaluated, the value of the decision variable that is closer to the value of the unevaluated decision variable and that has been evaluated is selected and selected from the search history stored in the storage unit. It is determined whether or not the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the predetermined number of decision variable values indicates a violation of the constraint condition.

  Thereby, the possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target violates the constraint condition is reduced. Therefore, it is possible to obtain a Pareto approximate solution set with high accuracy while avoiding violation of constraint conditions.

  According to the present invention, the possibility that the value of the constraint function corresponding to the value of the decision variable given to the optimization target violates the constraint condition is reduced. Therefore, it is possible to obtain a Pareto approximate solution set with high accuracy while avoiding violation of constraint conditions.

  Hereinafter, a multi-objective optimization apparatus according to an embodiment of the present invention will be described with reference to the drawings.

(1) Functional Configuration of Multi-Objective Optimization Device FIG. 1 is a block diagram showing a functional configuration of a multi-purpose optimization device according to an embodiment of the present invention.

  In the present embodiment, the multi-objective optimization apparatus 1 calculates a Pareto approximate individual set of a multi-objective optimization problem using a multi-objective evolutionary algorithm. The Pareto approximate individual set is an approximate Pareto optimal individual set obtained by a multi-objective evolution type algorithm, and specifically, an individual set obtained in the final generation of multi-objective optimization by a multi-objective evolution type algorithm. For example, a multipurpose genetic algorithm (GA) is used as a multipurpose evolutionary algorithm.

  This multi-objective optimization apparatus 1 is connected to an optimization target 6. The optimization target 6 is an evaluation system that evaluates the performance of the device. The evaluation system is an evaluation device that evaluates an actual system. The actual system is, for example, an engine or a motor, and the evaluation device is, for example, an engine evaluation device or a motor evaluation device. In the present embodiment, the optimization target 6 is an engine testing machine.

  The multi-objective optimization apparatus 1 includes a multi-objective evolution type algorithm unit 2 and a search history storage unit 3.

  The multi-objective evolution type algorithm unit 2 is realized by a CPU 101 (FIG. 2) described later executing a multi-objective optimization program. The search history storage unit 3 includes an external storage device 106 (FIG. 2) described later.

  In the multi-objective optimization apparatus 1, a plurality of decision variables, one or more condition variables, a plurality of fitness functions (objective functions), and one or a plurality of constraint functions are set.

  The decision variable is an adjustable value (control parameter) of the optimization target 6. A conditional variable is a variable that represents a condition of a multi-objective optimization problem. The fitness function and the constraint function are functions having a decision variable as an input. The output of the fitness function for the value of the specific decision variable is called fitness (objective function value), and the output of the constraint function for the value of the specific decision variable is called the constraint function value. A condition that the constraint function value should satisfy is called a constraint condition.

  Examples of the decision variable include fuel injection amount, fuel injection timing, ignition timing, throttle opening, and the like. The decision variable is called a gene in the genetic algorithm. An individual of a multi-objective genetic algorithm is a candidate for a solution of a multi-objective optimization problem, and consists of a set of values of a plurality of decision variables. Hereinafter, an individual of a multipurpose genetic algorithm is simply referred to as an individual.

The fitness function includes, for example, fuel consumption (fuel consumption), torque, CO (carbon monoxide) concentration, HC (hydrocarbon) concentration, NO _x (nitrogen oxide) concentration, SOF (possible) in engine exhaust gas. Soluble organic component) amount, soot amount and the like.

Here, the relation of trade-off, torque and fuel economy, torque and CO concentrations, torque and HC concentration, fuel efficiency and concentration of NO _x, CO concentration and concentration of NO _x, HC concentration and concentration of NO _x, concentration of NO _x and soot amount Etc.

The constraint function, for example, the amount of torque fluctuation, the presence or absence of abnormal injection, CO concentration in the exhaust gas of the engine, HC concentration, NO _x concentration, SOF amount, and soot amount, and the like. Examples of the condition variable include load torque, engine rotation speed, and the like.

  The multi-objective evolution type algorithm unit 2 generates individuals according to the multi-objective evolution type algorithm for each value of the condition variable, performs multipoint search, and evaluates the fitness with Pareto optimality. Find a Pareto approximated population within a satisfactory range. Further, the multi-objective evolution type algorithm unit 2 presents the obtained Pareto approximate individual set to the user.

  Specifically, the multi-objective evolution type algorithm unit 2 gives the individual (a set of values of a plurality of decision variables) and the condition variable to the optimization target 6 and a plurality of fitness levels output from the optimization target 6. And the Pareto optimality of the fitness set corresponding to the individual whose constraint function value satisfies the constraint condition. In addition, the multi-objective evolution type algorithm unit 2 provides the search history storage unit 3 with an individual (values of a plurality of decision variables), a fitness set corresponding to the individual, and a constraint violation flag corresponding to the individual. Details will be described later.

  The search history storage unit 3 includes an individual (a set of values of a plurality of decision variables) given from the multi-objective evolution type algorithm unit 2, a fitness set corresponding to the individual, a constraint violation flag corresponding to the individual, and a Pareto approximation. Memorize the population. Hereinafter, the individual stored in the search history storage unit 3, the fitness set corresponding to the individual, and the constraint violation flag corresponding to the individual are referred to as a search history. An individual stored in the search history storage unit 3 is called a search history individual.

  Hereinafter, when the multi-objective evolution type algorithm unit 2 gives an individual to the optimization target 6 and receives the fitness output from the optimization target 6 is referred to as individual evaluation.

(2) Hardware Configuration of Multipurpose Optimization Device FIG. 2 is a block diagram showing a hardware configuration of the multipurpose optimization device 1 of FIG.

  The multi-objective optimization apparatus 1 includes a CPU (Central Processing Unit) 101, a ROM (Read Only Memory) 102, a RAM (Random Access Memory) 103, an input device 104, a display device 105, an external storage device 106, and a recording medium driving device 107. And an input / output interface 108.

  The input device 104 includes a keyboard, a mouse, and the like, and is used for inputting various commands and various data. The ROM 102 stores a system program. The recording medium driving device 107 includes a CD (compact disk) drive, a DVD (digital versatile disk) drive, a flexible disk drive, and the like, and reads / writes data from / to a recording medium 109 such as a CD, DVD, or flexible disk.

  A multipurpose optimization program (hereinafter referred to as a multipurpose optimization program) is recorded on the recording medium 109. The external storage device 106 includes a hard disk device or the like, and stores a multipurpose optimization program and various data read from the recording medium 109 via the recording medium driving device 107. The CPU 101 executes the multipurpose optimization program stored in the external storage device 106 on the RAM 103.

  The display device 105 includes a liquid crystal display panel, a CRT (cathode ray tube), and the like, and displays various images such as a midway individual set and a Pareto optimal individual set. The optimization target 6 is connected to the input / output interface 108 by wireless communication or wired communication. The input / output interface 108 transfers the fitness set output from the optimization target 6 to the external storage device 106, and the individual (set of decision variable values) generated by the multipurpose optimization program is optimized 6 To give.

  As the recording medium 109 for recording the multipurpose optimization program, various recording media such as a semiconductor memory such as a ROM and a hard disk can be used. Alternatively, the multipurpose optimization program may be downloaded to the external storage device 106 via a communication medium such as a communication line and executed on the RAM 103.

Here, as long as the recording medium 109 is a computer-readable recording medium, the recording medium 109 includes an electronic reading method, a magnetic reading method, an optical reading method, or any other reading method. For example, in addition to the above-mentioned CD, DVD and flexible disk, optical reading type recording medium such as CDV (compact disk video), semiconductor recording medium such as RAM and ROM, magnetic recording type recording medium such as hard disk, MO (magneto-optical) A magnetic storage type / optical reading type recording medium such as a disk) can be used.

(3) Configuration of Optimization Target FIG. 3 is a block diagram showing an example of the configuration of the optimization target 6. The optimization target 6 in FIG. 3 is an engine evaluation device.

  The optimization target 6 includes an engine 61, an ECU (engine control unit) 62, a measuring device 63, a control computer 64, and an ultra-low inertia dynamometer 65. The ECU 62, the measuring device 63, the control computer 64, and the ultra-low inertia dynamometer 65 constitute an engine testing machine. According to this engine testing machine, the evaluation can be performed in the same manner as when the engine 61 is mounted on an actual vehicle using the engine 61 alone.

  The ultra-low inertia dynamometer 65 is connected to the crankshaft of the engine 61 and controls the load torque applied to the engine 61 in real time. The engine 61 has an electronic control unit for controlling the fuel injection timing and the ignition timing.

  The ECU 62 receives the value of the decision variable as a control parameter from the multipurpose optimization device 1. The decision variables are fuel injection timing, ignition timing, and the like. The ECU 62 controls the fuel injection timing and ignition timing of the engine 61 based on the value of the decision variable.

  Further, the control computer 64 receives the value of the condition variable as the operation condition from the multipurpose optimization apparatus 1. Condition variables are load torque, engine speed, and the like. The control computer 64 is equipped with a drive system model and a vehicle model. The control computer 64 controls the load torque applied to the engine 61 by the ultra-low inertia dynamometer 65 based on the value of the condition variable. The control computer 64 controls the rotational speed of the engine 61.

The measuring device 63 includes an exhaust gas analysis device, a combustion analysis device, and a fuel flow meter, analyzes the components in the exhaust gas from the engine 61, and optimizes the NO _x concentration, the SOF amount, the soot amount, etc. as the fitness. Output to device 1.

(4) Constraint Conditions FIG. 4 is a diagram for explaining the constraint conditions. The horizontal axis in FIG. 4 is time, and the vertical axis is the constraint function value.

  As described above, when an individual is input to the optimization target 6, fitness and constraint function values are output from the optimization target 6. The fitness obtained at the end of the evaluation time in FIG. 4 is adopted as the final fitness.

  In FIG. 4, the fatal constraint condition is a condition in which the optimization target 6 is immediately damaged or conforms to it when the constraint function value exceeds the lower limit value of the condition. Examples of fatal constraints are above the critical rotational speed at which the engine breaks or above the critical oil temperature. In the multi-objective optimization, the constraint function value is not allowed to exceed the lower limit value of the critical constraint condition, but the critical constraint condition cannot be known unless the optimization target 6 is damaged. Therefore, the fatal constraint condition is a conceptual condition.

  There is no problem in the risk constraint condition that the constraint function value exceeds the lower limit value of the condition for a short time, but when the constraint function value exceeds the lower limit value of the condition for a long time, the optimization target 6 is adversely affected. It is a condition. An example of the risk constraint condition is a range that is equal to or higher than the upper limit value of the engine rotation speed or oil temperature set to be operable in the test and lower than the lower limit value of the fatal constraint condition. Normally, even if the constraint function value exceeds the lower limit value of the risk constraint condition, the optimization target 6 is not immediately damaged, but the value of the decision variable is set so that the constraint function value does not exceed the lower limit value of the risk constraint condition as much as possible. Is set.

  The safety constraint condition is a condition in which the optimization target 6 is not affected even if the constraint function value exceeds the lower limit value of the condition for a long time. An example of a safety constraint is a legally acceptable noise tolerance or exhaust gas tolerance.

  In the multi-objective optimization apparatus 1 according to the present embodiment, the decision variable is adjusted in a range where the constraint function value satisfies the safety constraint condition while adjusting the value of the decision variable in a range where the constraint function value does not exceed the upper limit value of the risk constraint condition. Optimize the value of.

  In the following explanation, when the constraint function value is less than or equal to the lower limit value of the risk constraint condition, it is said that the constraint function value satisfies the constraint condition, and when the constraint function value exceeds the lower limit value of the risk constraint condition, Violates the constraints. An individual whose constraint function value is less than or equal to the lower limit value of the risk constraint condition is called an individual that satisfies the constraint condition, and an individual whose constraint function value exceeds the lower limit value of the risk constraint condition is called an individual that violates the constraint condition.

(5) Search History Individual Next, a search history individual stored as a search history in the search history storage unit 3 will be described.

  The search history H is expressed as follows:

^{H = {(h 1, C} (h 1)), ..., (h L, C (h L))}
Here, L is a natural number, and h ¹ ,..., H ^L are L search history individuals. ^{Also, C (h 1), ...} , C (h L) Each search history individuals ^h 1, ..., a L-number of constraint violations flag vector corresponding to ^{h L.}

Here, if each of the search history individuals h ¹ ,..., H ^L is h, the search history individual h is represented by the following equation.

h = [h ₁ ... h _n ] ^T
As shown in the above equation, the search history individual h is an n-dimensional decision variable vector composed of a set of _n decision variables h ₁ ,..., H _n . n is a natural number.

Each of constraint violation flag vectors C (h ¹ ),..., C (h ^L ) is represented by C (h ), The constraint violation flag vector C (h) is expressed by the following equation.

C (h) = [C ₁ (h),..., C _P (h)] ^T
In the above equation, C ₁ (h),..., C _P (h) are p constraint violation flags indicating whether or not the p constraint function values violate the constraint conditions. p is a natural number.

i = 1,. . . , When p, constraint violation flag _C i (h) is expressed by the following equation.

C _i (h) ε {0,1}
Each constraint violation flag C _i (h) is “0” when the constraint function value corresponding to the search history individual h satisfies the risk constraint condition, and the constraint function value corresponding to the search history individual h is the risk constraint condition. It is set to “1” when violated.

  When an individual is given to the optimization target 6, it is desirable to stop the fitness evaluation when the constraint function value obtained from the optimization target 6 violates the risk constraint condition. In this case, since the final fitness cannot be obtained, the worst value is given as the fitness corresponding to the individual.

(6) Multi-objective evolutionary algorithm FIG. 5 is a schematic diagram for explaining a multi-objective evolutionary algorithm. FIG. 6 is a flowchart for explaining the multipurpose evolutionary algorithm.

  In the present embodiment, NSGA-II (Non-Dominated Sorting Genetic Algorithm-II) proposed by Deb et al. Is used (see Non-Patent Document 2).

  First, as shown in FIG. 5A, the multipurpose evolution type algorithm unit 2 generates a child individual set Q from the parent individual set P in the t generation (step S11 in FIG. 6).

  Next, as shown in FIG. 5B, the multi-objective evolution type algorithm unit 2 performs non-dominant sorting on the union R of the parent individual set P and the child individual set Q (step S12 in FIG. 6). . Non-dominant sorting is a method in which individuals are ranked by non-dominant ranking, and an individual set is rearranged (sorted) so that individuals with lower ranks remain as excellent individuals in the next generation. Details of the non-dominant ranking will be described later. In the example of FIG. 5B, the union R is rearranged into ranks 1 to 4.

Next, as shown in FIGS. 5C and 5D, the multi-objective evolution type algorithm unit 2 performs congestion degree sorting for each rank of the union R (step S13 in FIG. 6). Congestion degree sort is to evaluate the sparseness of the individual distribution in order to evaluate the superiority or inferiority of individuals within the same rank, and to arrange the individual sets so that the individuals present in the sparser part are left as excellent individuals in the next generation Change (sort)
Is the method. Details of the congestion degree sorting will be described later.

  Next, the multipurpose evolutionary algorithm unit 2 leaves the top p (= | P |) individuals as the next-generation (t + 1 generation) parent individual set P (step S14 in FIG. 6). Here, | P | represents the number of parent individual sets. In the example of FIG. 5, individuals with rank 4 are deceived, and some lower-order individuals among the individuals with rank 3 are deceived.

  Thereafter, the multipurpose evolutionary algorithm unit 2 determines whether or not the number of generations has reached a predetermined end condition (step S15 in FIG. 6).

  If the number of generations has not reached the predetermined end condition, the process proceeds to step S11. When the number of generations reaches a predetermined end condition, the multipurpose evolutionary algorithm unit 2 presents the parent individual set P generated in step S15 to the user as a Pareto approximate individual set, and ends the process.

(7) Non-dominant ranking FIG. 7 is a schematic diagram for explaining non-dominant ranking. FIG. 7 shows an individual set in the fitness space. 7, the horizontal axis is one fitness function f _1, the vertical axis is the other one fitness function f _2.

  In the non-dominant ranking, the Pareto optimal individual set is obtained based on the ranking of each individual. Each individual is ranked according to the following procedure.

  First, superiority comparison is performed for all individuals based on the definition of superiority comparison, an individual that is not superior to other individuals (non-dominant individual) is selected, and the non-dominant individual is ranked 1. Next, the individual of rank 1 is removed from the individual set, and the same operation is performed on the remaining individual set. The non-dominant individuals in the remaining population are ranked 2. The above operation is repeated until the ranks of all individuals are determined.

  Here, rank 1 is the highest rank, and ranks of higher numerical values become lower ranks as the numerical value increases.

  In the example of FIG. 7, the individuals I1 to I4 are not superior to other individuals. Therefore, the rank of the individuals I1 to I4 is 1.

  In a state where the individuals I1 to I4 are removed, the individuals I5 to I8 are not dominated by other individuals. Therefore, the ranks of the individuals I5 to I8 are 2.

  In a state where the individuals I5 to I8 are removed, the individuals I9 and I10 are not superior to other individuals. Therefore, the rank of the individuals I9 and I10 is 3. The rank of the remaining individual I11 is 4.

(8) Congestion degree sort FIG. 8 is a diagram for explaining the congestion degree sort. FIG. 8 shows an individual set of fitness space.

  In the degree of congestion sort, for each target individual of the same rank, a rectangle whose diagonal is the line connecting two adjacent individuals is assumed, and the degree of congestion (congestion distance) is the sum of the lengths of the vertical and horizontal sides of the rectangle. Represents. The smaller the value of the degree of congestion, the more focused the individual is in the crowded area. Individuals at both ends of the same rank are given maximum congestion.

  In the example of FIG. 8, the congestion degree of the individual I2 is represented by the sum of the length d1 of the horizontal side and the length d2 of the vertical side of the rectangle s1 formed by the adjacent individuals I1 and I3. The congestion degree of the individual I3 is represented by the sum of the length d3 of the horizontal side and the length d4 of the vertical side of the rectangle s2 formed by the adjacent individuals I2 and I4.

  FIG. 9 is a flowchart showing the congestion degree sorting process by the multipurpose evolutionary algorithm unit 2.

  First, the multi-objective evolution type algorithm unit 2 sorts the individual set for each fitness function, and examines two individuals adjacent to each target individual within the same rank for each fitness function (step S21).

Next, the multi-objective evolution type algorithm unit 2 calculates a mathematical distance between two individuals adjacent to each target individual for each fitness function, and sums the mathematical distances in a plurality of fitness functions for each target individual. Is calculated as a congestion degree (step S22). Here, the Euclidean distance is used as the mathematical distance.

  Thereafter, the multipurpose evolutionary algorithm unit 2 sorts the individuals of the individual set of each rank in descending order of the value of the degree of congestion (step S23).

  In this way, a predetermined number of individuals having a higher degree of congestion at a higher rank are selected, and other individuals are deleted. As a result, more excellent individuals are left for the next generation.

(9) Child Individual Sorting Method by the Nearest Neighbor Method FIG. 10 is a flowchart for explaining a child individual sorting method by the multipurpose evolutionary algorithm unit 2 according to the present embodiment. In the present embodiment, it is determined using the nearest neighbor method whether or not the generated child individual is adopted as a child individual in multi-objective optimization.

  First, the multi-purpose evolution type algorithm unit 2 selects a plurality of search history individuals that do not violate all of the constraint conditions from the search history individuals stored in the search history storage unit 3 as parent individuals (step S31).

  Next, the multipurpose evolution type algorithm unit 2 generates a child individual by crossing or mutating a plurality of parent individuals (step S32).

  Further, the multipurpose evolution type algorithm unit 2 selects the search history individual nearest to the child individual generated on the decision variable space (step S33).

  Then, the multi-purpose evolution type algorithm unit 2 determines whether or not at least one of the constraint violation flags corresponding to the selected search history individual is “1” (step S34).

  If at least one of the constraint violation flags corresponding to the selected search history individual is “1”, the multi-objective evolution type algorithm unit 2 rejects the generated child individual (step S35), and the process of step S32 Return to.

  When all the constraint violation flags corresponding to the selected search history individual are “0”, the multi-purpose evolution type algorithm unit 2 adopts the generated child individual (step S36).

  Thereafter, the multipurpose evolutionary algorithm unit 2 determines whether or not the number of crossovers or mutations has reached the upper limit (step S37). If the number of crossovers or mutations has not reached the upper limit, the multipurpose evolutionary algorithm unit 2 returns to the process of step S32 and repeats the processes of steps S32 to S37 until the number of crossovers or mutations reaches the upper limit. . When the number of crossovers or mutations reaches the upper limit, the multipurpose evolutionary algorithm unit 2 determines whether or not the number of adopted child individuals has reached the child individual set size (step S38).

  If the number of adopted child individuals does not reach the child individual set size, the multi-purpose evolution type algorithm unit 2 returns to the process of step S31 until the number of adopted child individuals reaches the child individual set size. The processes in steps S31 to S38 are repeated.

  When the number of adopted child individuals reaches the child individual set size, the multipurpose evolutionary algorithm unit 2 ends the processing.

  In this way, a child individual generated from a parent individual is rejected as a child individual in optimization when at least one of the constraint violation flags corresponding to the nearest search history individual is “1”, and its nearest neighbor When all of the constraint violation flags corresponding to the search history individuals are “0”, they are adopted as child individuals in the multi-objective optimization.

(10) Example of Child Individual Sorting Method by Nearest Neighbor Method FIGS. 11 to 15 are conceptual diagrams showing an example of a child individual sorting method by the nearest neighbor method. 11 to 15 show individuals on a two-dimensional decision variable space made up of two decision variables x ₁ and x ₂ .

  In the decision variable space of FIGS. 11 to 15, an actual boundary RE between a region where a child individual that does not violate the constraint condition and a region where a child individual that violates the constraint condition is generated is indicated by a broken line. Search history individuals that do not violate the constraint conditions are indicated by white circles, and search history individuals that violate the constraint conditions are indicated by black circles.

  Furthermore, among the child individuals generated from the parent individual, the child individuals adopted as the child individuals in the multi-objective optimization are indicated by circles having a diagonal pattern, and the child individuals rejected as the child individuals in the multi-objective optimization are cross-patterned. Indicated by a circle with

In the above nearest neighbor method, a boundary between a region where a search history individual that does not violate a constraint condition and a region where a search history object that violates a constraint condition can be generated is a boundary called a Voronoi boundary. An area where a search history individual that does not violate the constraint condition can be generated is called a Voronoi area. 11 to 15, the region on the right side of the Voronoi boundary is the Voronoi region.

First, as shown in FIG. 11, two search history individuals h ¹ and h ² on the decision variable space are used. A perpendicular bisector connecting the ^two search history individuals h ¹ and h ² is obtained as the Voronoi boundary VE1.

As shown in FIG. 12, three child individuals I ³ , I ⁴ , and I ⁵ are generated. The nearest neighbor of an individual's offspring I ^3, I ⁴ is a search history individual h ^1, which does not violate the constraints. Accordingly, offspring individuals I ³ and I ⁴ are employed in multi-objective optimization. The nearest individual of the child individual I ⁵ is the search history individual h ² that violates the constraint condition. Therefore, the child individual I ⁵ is rejected in the multi-objective optimization.

The child individuals I ³ and I ⁴ are evaluated in the multi-objective optimization, and it is determined whether or not the constraint function value violates the constraint condition.

As shown in FIG. 13, the evaluated child individuals I ³ and I ⁴ are stored in the search history storage unit 3 as search history individuals h ³ and h ⁴ . Search history individual h ^3, h ⁴ is not in violation of the constraints. Furthermore, three child individuals I ⁶ , I ⁷ , and I ⁸ are generated. The nearest individual of the child individuals I ⁶ and I ⁷ is the search history individual h ³ that does not violate the constraint conditions. Accordingly, the offspring I ⁶ and I ⁷ are employed in the multi-objective optimization. The nearest individual of the child individual I ⁸ is the search history individual h ² that violates the constraint condition. Therefore, the child individual I ⁸ is rejected in the multi-objective optimization.

Offspring I ^6, I ⁷ is evaluated in the multi-objective optimization, whether constraint function values violates the constraint condition is determined.

In this case, the vertical bisector connecting the ^two search history individuals h ² and h ³ and the vertical bisector connecting the two search history individuals h ² and h ⁴ are obtained as the Voronoi boundary VE2. It is done.

As shown in FIG. 14, the evaluated child individuals I ⁶ and I ⁷ are stored in the search history storage unit 3 as search history individuals h ⁶ and h ⁷ . The search history individual h ⁶ violates the constraint condition, and the search history individual h ⁷ does not violate the constraint condition. Further, three child individuals I ⁹ , I ¹⁰ , I ¹¹ are generated. The nearest individual of the child individual I ⁹ is the search history individual h ³ that does not violate the constraint conditions. Accordingly, offspring I ⁹ is employed in the multi-objective optimization. The nearest individual of the child individual I ¹⁰ is the search history individual h ⁶ that violates the constraint condition. Accordingly, offspring I ⁹ is rejected in the multi-objective optimization. The nearest individual of the child individual I ¹¹ is the search history individual h ⁴ that does not violate the constraint conditions. Therefore, the child individual I ¹¹ is employed in the multi-objective optimization.

The child individuals I ⁹ and I ¹¹ are evaluated in the optimization, and it is determined whether or not the constraint function value violates the constraint condition.

In this case, a vertical bisector of a line segment connecting two search history individuals h ³ and h ⁶ , a vertical bisector of a line segment connecting two search history individuals h ⁶ and h ^7, and two search history individuals A vertical bisector connecting a line connecting h ² and h ⁷ and a vertical bisector connecting two search history individuals h ² and h ⁴ are obtained as the Voronoi boundary VE3.

As shown in FIG. 15, the evaluated child individuals I ⁹ and I ¹¹ are stored in the search history storage unit 3 as search history individuals h ⁹ and h ¹¹ . The search history individual h ⁹ does not violate the constraint condition, and the search history individual h ¹¹ violates the constraint condition.

In this case, the vertical bisector of the line segment connecting the two search history individuals h ⁶ and h ⁹ , the vertical bisector of the line segment connecting the two search history individuals h ³ and h ^6, and the two search history individuals A vertical bisector connecting a line connecting h ⁶ and h ⁷ , a perpendicular bisector connecting a line connecting two search history individuals h ² and h ^7, and a line connecting two search history individuals h ⁷ and h ¹¹ The vertical bisector of the minute and the perpendicular bisector of the line connecting the two search history individuals h ⁴ and h ¹¹ are obtained as the Voronoi boundary VE4.

  As described above, the Voronoi boundary changes as a new search history individual is generated.

  Hereinafter, an area where a child individual that does not violate the constraint condition can be generated is called an executable area, and an area where a child individual that violates the constraint condition can be generated is called an inexecutable area. In addition, a search history individual that does not violate the constraint condition is called an executable individual, and a search history individual that violates the constraint condition is called an inexecutable individual.

  As described above, multi-objective optimization and executable region specification can be performed simultaneously.

  Here, the generated child individual is expressed by the following equation.

x = [x ₁ ,..., x _n ] ^T
The child individual x is composed of n decision variables x ₁ ,..., X _n . n is a natural number.

  The Voronoi region is expressed by the following equation.

In the above equation, d _E is the Euclidean distance, is expressed by the following equation.

d _E (x, h ⁱ ) = √ {(x−h ⁱ ) ^T (x−h ⁱ )}
Here, i = 1,..., L. As described above, a Voronoi boundary having a complicated shape can be obtained as the number of search history individuals increases.

(11) Nearest neighbor method using weight parameter A weight parameter may be introduced to adjust the feasible region. In this case, using the weighted distance d _M obtained by the following equation instead of the Euclidean distance d _E.

d _M (x, h ⁱ ) = (1 / W ⁱ ) √ {(x−h ⁱ ) ^T (x−h ⁱ )}
In the above equation, W ⁱ is a weight parameter and is expressed by the following equation.

W ⁱ ∈ {W _F , W _I }
Here, i = 1,..., L. W _F is the weight parameter for executable individuals, W _I is the weight parameter of the non-executable individuals.

FIG. 16 is a conceptual diagram showing Voronoi boundaries when weight parameters are introduced. In FIG. 16, an individual on a two-dimensional decision variable space composed of two decision variables x ₁ and x ₂ is shown.

FIG. 16 (a) shows the Voronoi boundary when the weight parameter W _F executable individuals is greater than the weight parameter W _I of infeasible individuals, FIG. 16 (b) the weight parameter W _F executable individuals unexecutable It shows the Voronoi boundary is smaller than the weight parameter W _I individuals.

As shown in FIG. 16 (a), (b) , when one of the weighting parameters W _F and the weighting parameters W _I is greater than the other, the Voronoi boundary is not a straight line, a part of a circle, called the Apollonius circle .

As shown in FIG. 16 (a), if the weighting parameter W _F is greater than the weight parameter W _I, the feasible region is relatively wider than the non-executable region. Weight parameter W _F is referred to as the aggressive approach the nearest neighbor method of is greater than the weight parameter W _I.

Conversely, as shown in FIG. 16 (b), if the weighting parameter W _F is less than the weight parameter W _I, the feasible region is relatively narrow compared to the non-executable region. The nearest neighbor method when the weight parameter W _F is smaller than the weight parameter W _I called a passive approach.

(12) Child individual selection method by the k-NN method Instead of the child individual selection method by the nearest neighbor method, a child individual selection method by the k-NN method (k-nearest-Neighbor Method) may be used. Good. In the selection method of child individuals by the k-NN method, a plurality of search history individuals in the vicinity of each generated child individual are examined, and adoption and rejection of each individual is determined by a majority decision of executable and infeasible individuals.

FIG. 17 is a conceptual diagram showing an example of a child individual selection method by the k-NN method. FIG. 17 shows an individual on a two-dimensional decision variable plane composed of two decision variables x ₁ and x ₂ .

Search history individuals h ¹¹ , h ¹² , h ¹³ that do not violate the constraint conditions and search history individuals h ¹⁴ , h ¹⁵ , h ¹⁶ that violate the constraint conditions exist in the decision variable space of FIG. In this state, three offspring individuals I ¹⁷ , I ¹⁸ , and I ¹⁹ are generated.

Of the three search history individuals h ¹¹ , h ¹³ , h ¹⁴ in the vicinity of the child individual I ^17, the search history individuals h ¹¹ , h ¹³ are executable individuals, and the search history individual h ¹⁴ is an inexecutable individual. Therefore, the child individual I ¹⁷ is adopted as a child individual in the multi-objective optimization, and becomes the search history individual h ¹⁷ .

Of the three search history individuals h ¹³ , h ¹⁴ , h ¹⁵ in the vicinity of the child individual I ^18, the search history individual h ¹³ is an executable individual, and the search history individuals h ¹⁴ , h ¹⁵ are non-executable individuals. Therefore, the child individual I ¹⁸ is rejected as a child individual in the multi-objective optimization and becomes a search history individual h ¹⁸ .

Of the three search history individuals h ¹² , h ¹³ , h ¹⁴ in the vicinity of the child individual I ^19, the search history individuals h ¹² , h ¹³ are executable individuals, and the search history individual h ¹⁴ is an inexecutable individual. Therefore, the child individual I ¹⁹ is adopted as a child individual in the multi-objective optimization, and becomes a search history individual h ¹⁹ .

(13) Effects of the Embodiment According to the multipurpose optimization apparatus 1 according to the present embodiment, the constraint violation flag is stored in the search history storage unit 3 together with the search history individual. The multi-objective evolution type algorithm unit 2 determines each child individual in multi-objective optimization based on whether a predetermined number of search history individuals in the vicinity of each child individual generated from the parent individual are executable individuals or non-executable individuals. It is determined whether or not to adopt as a child individual. Thereby, the possibility that the constraint function value output by the evaluation of the child individual violates the constraint condition is reduced. Therefore, it is possible to obtain a Pareto approximate individual set with high accuracy in a short time while avoiding violation of the constraint conditions.

(14) Example 1
In Example 1 below, the effect of reducing the number of violations of constraint conditions by the multi-objective optimization apparatus 1 according to the above-described embodiment was examined by numerical experiments.

  In the first embodiment, NSGA-II is used as the multi-objective evolution type algorithm, the parent individual set size | P | is 100, the child individual set size | Q | is 100, and the number of generations is 100. Since the initial parent individual set P and the 100th generation child individual set Q are evaluated, the total number of evaluations of the individual is 10100. As crossover operation, UNDX (Unimodal Normal Distribution Crossover) is used at a crossover rate of 1.0, and mutation operation is not used.

  In the comparative example, NSGA-II that does not avoid violation of constraint conditions is used as a multi-purpose evolutionary algorithm. In the comparative example NSGA-II, a constraint condition is handled by a method called a constraint superiority principle.

FIG. 18 is a diagram illustrating a two-condition two-purpose problem used as a test function in the first embodiment. f ₁ and f ₂ are fitness functions, g ₁ and g ₂ are constraint functions, and x ₁ and x ₂ are decision variables.

Since the multi-objective evolutionary algorithm is a probabilistic optimization method, the result differs depending on the arrangement of the initial individual set and the operation by the multiobjective evolutionary algorithm in the search process. Therefore, in Example 1 and the comparative example, in order to evaluate the average performance of the multipurpose optimization apparatus 1 of the above embodiment, an average value of 30 optimization results is obtained. In Example 1, 0.5 (passive technique) as weighting parameter _{W F,} using 1.0 (neutral method) and 1.5 (positive approach). Another weight parameter _{W I} is 1.0.

  As evaluation indexes, GD (Generational Distance) and D1R were used. In addition, the number of offspring individuals that violated the constraints among the evaluated offspring individuals was obtained. As described above, a search history individual that satisfies the constraint condition is called an executable individual, and a search history individual that violates the constraint condition is called an inexecutable individual.

  FIG. 19 is a diagram for explaining GD, and FIG. 20 is a diagram for explaining D1R.

19 and 20 show a Pareto optimal individual set P1 and a Pareto approximate individual set P2 in a fitness space composed of _two fitness functions f ₁ and f ₂ . The Pareto optimal individual set P1 includes individuals p11 to p17, and the Pareto approximate individual set P2 includes individuals p21 to p27.

  In FIG. 19, the distances from the individuals p21 to p27 in the Pareto approximate individual set P2 to the closest individuals p11 to p13, p15, and p16 in the Pareto optimal individual set P1 are indicated by arrows. GD is the average value of the shortest distance from the Pareto approximate individual set P2 to the Pareto optimal individual set P1.

In FIG. 20, the distances from the individuals p11 to p17 in the Pareto optimal individual set P1 to the closest individuals p22 and p23 to p27 in the Pareto approximate individual set P2 are indicated by arrows. D1R is an average value of the shortest distances from the Pareto optimal individual set P1 to the Pareto approximate individual set P2.

  FIG. 21 is a diagram showing GD, D1R, and the number of unexecutable individuals in Example 1 and Comparative Example. In FIG. 21, the average value and standard deviation of GD in 30 optimization results, the average value and standard deviation of D1R in 30 optimization results, and the number of infeasible individuals per generation in 30 optimization results Average values and standard deviations of (NoV) are shown.

  As shown in FIG. 21, GD and D1R in Example 1 are hardly deteriorated compared to GD and D1R in the comparative example. On the other hand, the infeasible number per generation (NoV) in Example 1 is significantly smaller than the infeasible number per generation (NoV) in the comparative example. That is, according to Example 1, it can be seen that the number of inexecutable individuals can be reduced without deteriorating the search performance as compared with the comparative example.

FIG. 22 is a diagram showing the distribution in the decision variable space of executable individuals and non-executable individuals in the search history of the comparative example. FIG. 23 to FIG. 25 are diagrams showing distributions of executable individuals and non-executable individuals in the decision variable space in the search history of the first embodiment. The horizontal axis in FIGS. 22 to 25 is one of the decision variables x _1, the vertical axis represents the decision variable x ₂ of the other one.

22 to 25 show results when the TNK function is used. Figure 23 shows the case weight parameter _{W F} is 0.5 (passive technique), FIG. 24 shows a case where the weighting parameter _{W F} is 1.0 (neutral method), Figure 25 is the weighting parameter _{W F} is 1 The case of .5 (proactive method) is shown. In Comparative Example and Example 1, the total number of individuals is 10100.

In the comparative example of FIG. 22, the number of non-executable individuals is 5690. On the other hand, in Example 1 (W _F = 0.5) in FIG. 23, the number of infeasible individuals is 288, and in Example 1 (W _F = 1.0) in FIG. 24, the number of infeasible individuals is 527. Thus, in Example 1 (W _F = 1.5) in FIG. 25, the number of non-executable individuals was 1251.

From the results of FIGS. 23 to 25, by changing the weighting parameter W _F, it can be seen that adjusting the number of infeasible individuals. Moreover, it can be seen from the results of FIGS. 22 to 25 that according to the first embodiment, the number of inexecutable individuals can be reduced as compared with the comparative example.

(15) Example 2
In Example 2 below, a case where the multipurpose optimization apparatus 1 according to the above embodiment is applied to multistage injection parameter optimization of a parallel 4-cylinder common rail diesel engine will be described.

  In a diesel engine, a common rail system, which is a high-pressure direct injection system, allows multiple fuel injections (multistage injection) during one combustion cycle. This multi-stage injection greatly contributes to the purification of exhaust gas, but since there are a large number of decision variables (control parameters) to be adapted, it is difficult to manually obtain appropriate combinations of decision variables.

  Therefore, in the second embodiment, a multi-objective optimization problem with three objectives and seven variables is set, and an engine for three-stage injection is optimized on an experimental basis.

NSGA-II combined with the “Pre-selection” algorithm (Non-Patent Document 5 above), which is a technique for reducing the number of evaluations as a multi-objective evolutionary algorithm, with a parent individual set size | P | The child individual set size | Qc | was set to 100, and the child individual set size | Q | was set to 4. The weight parameter _{W F} and 1.0, and a weight parameter _{W I} also 1.0. Local weighted regression (LWR) was used as an approximate modeling technique for the “Pre-selection” algorithm.
FIG. 26 is a conceptual diagram illustrating the injection timing and the injection amount in the second embodiment.

  As shown in FIG. 26, the three-stage injection includes a pilot injection Pi, a pre-injection Pr, and a main injection Mi. In FIG. 26, the MI timing is the energization start timing of the main injection Mi as viewed from the top dead center (TDC) in the advance direction. The Pre-MI interval is an interval between the energization start timing of the pre-injection Pr and the energization start timing of the main injection Mi. The Pil-Pre interval is an interval between the energization start timing of the pilot injection Pi and the energization start timing of the pre-injection Pr.

In Example 2, as three fitness functions (objective function), NO _x concentration in the exhaust gas, soluble organic component (SOF) amount and use of soot amount. Further, the SOF amount in the exhaust gas, the soot amount in the exhaust gas, the HC concentration in the exhaust gas, the engine torque fluctuation, and the presence or absence of abnormal injection are used as the constraint function. SOF and soot are components of an exhaust gas component called particulate matter (PM).

  Seven decision variables (control parameters) include MI timing, Pre-MI interval, Pil-Pre interval, pilot injection amount (Pil Quantity), pre-injection amount (Pre Quantity), intake air amount (Fresh Air Mass), and Use fuel pressure. The pilot injection amount is a fuel injection amount at the time of pilot injection, and the pre-injection amount is a fuel injection amount at the time of pre-injection. The intake air amount is the amount of intake air controlled by an EGR (exhaust gas recirculation device) valve or the like. The fuel pressure is the fuel pressure of the common rail.

  The experiment of Example 2 was performed under conditions of constant engine speed and constant torque. A decision variable (control parameter) expressed as an individual of NSGA-II is transmitted to the ECU 62 of FIG. The measurement function 63 measures the fitness function value and the constraint function value for a predetermined time.

  In Example 2, 210 evaluations of the decision variable were performed. Here, the reevaluation of the parent individual set P is not performed.

FIG. 27 is a diagram showing the distribution of the last generation individual set (Pareto approximate individual set). Since the second embodiment is a three-objective optimization, the Pareto approximate individual set is distributed in the three-dimensional fitness space. FIG. 28 shows a Pareto approximation individual set by projecting the NO _x concentration, the SOF amount, and the soot amount onto six two-dimensional fitness planes. 27, the vertical axis of the fitness planes D1, D2 is the concentration of NO _x, the horizontal axis represents the respective SOF amount and the soot amount. The vertical axis of fitness plane D3, D4 is the amount SOF, the horizontal axis is the concentration of NO _x and soot amount, respectively. The vertical axis of fitness plane D5, D6 are weight soot, the horizontal axis is the concentration of NO _x and SOF amount, respectively. Concentration of NO _x, the values of the SOF amount and the soot quantity are normalized.

  In each of the fitness planes D1 to D6, the lower left direction is the direction of optimization. The fitness plane D1 and the fitness plane D3 have their vertical and horizontal axes interchanged, and the fitness plane D2 and the fitness plane D5 have their vertical and horizontal axes interchanged, and the fitness plane D4. In the fitness plane D6, the vertical axis and the horizontal axis are interchanged.

In fitness plane D1, D3, as is well known in the diesel engine, a trade-off is clearly seen between the concentration of NO _x and soot amount.

  FIG. 28 shows the distribution of search history individuals. In FIG. 28, executable individuals, non-executable individuals, and Pareto approximation individuals are shown on 42 two-dimensional decision variable planes.

  The vertical axis of the six decision variable planes in the first stage is the MI timing, the vertical axis of the six decision variable planes in the second stage is the Pre-MI interval, and the six decision variable planes in the third stage. , The vertical axis of the six decision variable planes in the fourth stage is the Pil-Pre interval, and the vertical axis of the six decision variable planes in the fifth stage is the pilot injection quantity. The vertical axis of the six decision variable planes in the sixth stage is the intake air amount, and the vertical axis of the six decision variable planes in the seventh stage is the fuel pressure.

  The horizontal axis of the six decision variable planes in the first column is the MI timing, the horizontal axis of the six decision variable planes in the second column is the Pre-MI interval, and the six decision variable planes in the third column The horizontal axis is the pre-injection amount, the horizontal axis of the six decision variable planes in the fourth row is the Pil-Pre interval, and the horizontal axis of the six decision variable planes in the fifth row is the pilot injection amount The horizontal axis of the six decision variable planes in the sixth stage is the intake air amount, and the horizontal axis of the six decision variable planes in the seventh row is the fuel pressure.

  In FIG. 28, dark circles indicate executable individuals, slightly dark circles indicate inexecutable individuals, and light circles indicate Pareto approximate individuals.

  In regions where search history individuals are sparse, infeasible individuals are concentrated, but in regions where search history individuals are densely present, executable individuals and Pareto approximation individuals are concentrated. The biased distribution of search history individuals in FIG. 28 indicates that child individuals are generated so as to avoid violation of the constraint conditions.

FIG. 29 is a diagram showing the transition of the number of non-executable individuals obtained from an actual engine. In the evaluation of the initial population (0 generation evaluation), 45 individuals out of 50 individuals were infeasible individuals. Thereafter, the actual engine was evaluated with 4 individuals per generation. As a result, it can be seen that the number of unexecutable individuals is 2 or less until the 12th generation. Since then, it can be seen that the number of infeasible individuals has increased slightly. This suggests that the Pareto optimal population exists near the boundary of the feasible region. In particular, in the “Pre-selection” algorithm, since promising individuals close to the Pareto optimal individual set are positively evaluated, it is considered that the possibility of violating the constraint condition slightly increases as the final generation is approached.

  It was confirmed that the characteristics of the Pareto approximate population obtained in Example 2 were valid as the characteristics of the diesel engine used in the experiment. Therefore, according to the multi-objective optimization apparatus 1 according to the above-described embodiment, it has been found that a Pareto approximate individual set can be obtained with high accuracy in a short time while avoiding violation of constraint conditions.

(16) Other Embodiments (a) In the above embodiment, NSGA-II is used as a multi-purpose evolutionary algorithm. However, the present invention is not limited to this, and instead of NSGA-II, SPEA2 (Non-patent Document 3) is used. A calculation method based on a similar idea such as) may be used.

  (B) In the above embodiment, the multi-purpose evolutionary algorithm unit 2 is realized by the CPU 101 and a program. However, a part or all of the multi-purpose evolutionary algorithm unit 2 may be realized by hardware such as an electronic circuit.

  (C) Other optimization algorithms may be used instead of the multi-objective evolutionary algorithm.

  (D) In order to generate an initial search history individual, an executable region may be estimated by the method shown in FIG. In this case, since the search history individual can be generated near the boundary of the estimated executable region, the search efficiency can be improved.

(17) Correspondence between Claim Component and Each Part of Embodiment The following describes an example of correspondence between each component of the claim and each part of the embodiment, but the present invention is not limited to the following example. .

  In the above embodiment, the multipurpose evolution type algorithm unit 4 is an example of a multipurpose optimization unit, and the search history storage unit 5 is an example of a storage unit. A Pareto approximate individual set is an example of a Pareto approximate solution set, and a constraint violation flag is an example of constraint violation information.

  As each constituent element in the claims, various other elements having configurations or functions described in the claims can be used.

  The present invention can be used for optimizing a decision variable to be optimized whose objective function changes depending on conditions.

It is a block diagram which shows the functional structure of the multi-objective optimization apparatus which concerns on one embodiment of this invention. It is a block diagram which shows the hardware constitutions of the multi-objective optimization apparatus of FIG. It is a block diagram which shows an example of a structure of the optimization object. It is a figure for demonstrating a constraint condition. It is a schematic diagram for demonstrating a multipurpose evolution type algorithm. It is a flowchart for demonstrating a multipurpose evolution type algorithm. It is a schematic diagram for demonstrating a non-dominant ranking. It is a figure for demonstrating congestion degree sort. It is a flowchart which shows the process of the congestion degree sort by a multipurpose evolution type algorithm part. It is a flowchart for demonstrating the production | generation method of the child individual by the multipurpose evolution type algorithm part which concerns on this Embodiment. It is a conceptual diagram which shows an example of the selection method of the child individual by the nearest neighbor method. It is a conceptual diagram which shows an example of the selection method of the child individual by the nearest neighbor method. It is a conceptual diagram which shows an example of the selection method of the child individual by the nearest neighbor method. It is a conceptual diagram which shows an example of the selection method of the child individual by the nearest neighbor method. It is a conceptual diagram which shows an example of the selection method of the child individual by the nearest neighbor method. It is a conceptual diagram which shows the Voronoi boundary at the time of introducing a weight parameter. It is a conceptual diagram which shows an example of the selection method of the child individual by k-NN method. It is a figure which shows the 2 conditions 2 objective problem used as a test function in Example 1. FIG. It is a figure for demonstrating GD, It is a figure for demonstrating D1R. It is a figure which shows GD, D1R, and an unexecutable individual number in Example 1 and a comparative example. It is a figure which shows distribution on the decision variable space of the executable individual | organism | solid and non-executable individual | organism | solid in the search log | history of a comparative example. It is a figure which shows distribution on the decision variable space of the executable individual | organism | solid and non-executable individual | organism | solid in the search log | history of Example 1. FIG. It is a figure which shows distribution on the decision variable space of the executable individual | organism | solid and non-executable individual | organism | solid in the search log | history of Example 1. FIG. It is a figure which shows distribution on the decision variable space of the executable individual | organism | solid and non-executable individual | organism | solid in the search log | history of Example 1. FIG. It is a conceptual diagram which shows the injection timing and injection quantity in Example 2. FIG. It is a figure which shows distribution of the individual set (Pareto approximate individual set) of the last generation. It is a figure which shows distribution of search log | history individual | organism | solid. It is a figure which shows transition of the number of non-executable individuals obtained from an actual engine. It is a figure which shows the example which applied the multi-objective optimization problem to engine optimization. It is a figure for demonstrating a Pareto optimal solution. It is a figure for demonstrating the adaptation of an engine. It is a conceptual diagram for demonstrating the method of setting the constraint condition of the group of control parameter values in a response surface method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Multi-objective optimization apparatus 2 Multi-objective evolution type algorithm part 3 Search history memory | storage part 6 Optimization object 61 Engine 62 ECU
63 Measuring device 64 Control computer 65 Ultra-low inertia dynamometer 101 CPU
102 ROM
103 RAM
104 input device 105 display device 106 an external storage device 107 recording medium drive 108 output interface 109 recording medium D1~D6 fitness plan d1~d4 length ^{h 1, h 2, h 3} , h 4, h 6, h 7 , H ¹¹ , h ¹² , h ¹³ , h ¹⁴ , h ¹⁵ , h ¹⁶ , h ¹⁷ , h ¹⁸ , h ¹⁹ search history individuals I1 to I11 individuals I ³ , I ⁴ , I ⁵ , I ⁶ , I ⁷ , I ^{8, I 9, I 10,} I 11, I 17, I 18, I 19 children individuals P parents set P1 Pareto-optimal population of individuals P2 individual set p11~p17, p21~p27 individual s1, s2 rectangular VE1~VE4 Voronoi boundary W _{F, W I} weighting parameters x _{1, x 2} decision variables

Claims (8)

A multi-objective optimization device for optimizing a decision variable to be optimized having a plurality of objective functions within a range of constraints,
Determine the value of the decision variable to be evaluated in multi-objective optimization, give the value of the decision variable determined to be evaluated to the optimization target, and use the value of the objective function output from the optimization target A multi-objective optimization unit that performs multi-objective optimization and obtains a Pareto approximate solution set of decision variables in a range in which a value of a constraint function output from the optimization target satisfies the constraint condition;
Whether the value of the decision variable evaluated by the multi-objective optimization unit, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violate the constraint condition. A storage unit that associates and stores the constraint violation information shown as a search history,
When the multi-objective optimization unit determines the value of the decision variable to be evaluated, the search variable stored in the storage unit is closer to the value of the unevaluated decision variable and is a predetermined number of evaluated decision variables. Whether or not the value of the unevaluated decision variable should be evaluated based on whether or not the constraint violation information corresponding to the selected predetermined number of decision variable values indicates violation of the constraint condition Multipurpose optimization device that determines whether The predetermined number is 1, and the multi-objective optimization unit determines the value of one evaluated decision variable closest to the value of the unevaluated decision variable when determining the value of the decision variable to be evaluated. Selecting and determining that the value of the unevaluated decision variable should be evaluated when the constraint violation information corresponding to the selected decision variable value that has been evaluated does not indicate violation of the constraint condition; The constraint violation information corresponding to the selected value of the one evaluated decision variable indicates that the value of the unevaluated decision variable should not be evaluated if the constraint violation information indicates a violation of the constraint condition. The multipurpose optimization device according to 1. The predetermined number is k (k is a natural number of 2 or more), and the multi-objective optimization unit is closer to the value of the unevaluated decision variable and determines k values when determining the value of the decision variable to be evaluated. The value of the decision variable that has been evaluated is selected, and the unevaluated state is determined by a majority decision whether or not the constraint violation information corresponding to the selected k evaluated value of the decision variable indicates violation of the constraint condition. The multi-objective optimization apparatus according to claim 1, wherein it is determined whether or not the value of the decision variable should be evaluated. The multi-objective optimization unit selects the value of the predetermined number of decision variables that are closer to the value of the unevaluated decision variable based on the Euclidean distance in the decision variable space and that is the predetermined number of evaluated variables. Multipurpose optimization device as described in 1. The multi-objective optimization unit, in the decision variable space, the Euclidean distance between the value of the unevaluated decision variable and the value of the number of decision cases already evaluated indicating that the constraint violation information does not violate the constraint condition Each of the Euclidean distances between the value of the variable and the value of the number of evaluated decisions indicating that the constraint violation information violates the constraint condition is weighted, and based on the weighted Euclidean distance, The multi-objective optimization apparatus according to claim 1, wherein the multi-objective optimization apparatus selects a value of the decision variable that is closer to the value and that is the predetermined number of evaluated variables. The multi-objective optimization device according to claim 1, wherein the multi-objective optimization unit generates an unevaluated decision variable value by a multi-objective evolutionary algorithm. A multi-objective optimization method for optimizing a decision variable to be optimized having a plurality of objective functions within a range of constraints,
Determine the value of the decision variable to be evaluated in multi-objective optimization, give the value of the decision variable determined to be evaluated to the optimization target, and use the value of the objective function output from the optimization target Performing multi-objective optimization and obtaining a Pareto approximate solution set of decision variables in a range in which a value of a constraint function output from the optimization target satisfies the constraint condition;
Constraint violation information indicating whether the value of the evaluated decision variable, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violate the constraint condition And associating it as a search history and storing it in the storage unit,
In the step of obtaining the Pareto approximate solution set, when determining the value of the decision variable to be evaluated, the search history stored in the storage unit is closer to the value of the unevaluated decision variable and a predetermined number of evaluated variables have been evaluated. A value of a certain decision variable is selected, and the value of the unevaluated decision variable is evaluated based on whether or not the constraint violation information corresponding to the selected predetermined number of decision variable values indicates violation of the constraint condition A multi-objective optimization method comprising the step of determining whether or not to do so. A multi-objective optimization program for causing a computer to execute a multi-objective optimization method for optimizing a decision variable to be optimized having a plurality of objective functions within a range of constraints,
Determine the value of the decision variable to be evaluated in multi-objective optimization, give the value of the decision variable determined to be evaluated to the optimization target, and use the value of the objective function output from the optimization target A process of performing multi-objective optimization and obtaining a Pareto approximate solution set of decision variables in a range in which a value of a constraint function output from the optimization target satisfies the constraint condition;
Constraint violation information indicating whether the value of the evaluated decision variable, the value of the objective function output from the optimization target, and the value of the constraint function output from the optimization target violate the constraint condition Processing associated with the search history and stored in the storage unit,
When determining the value of the decision variable to be evaluated, the process for obtaining the Pareto approximate solution set is based on the search history stored in the storage unit and is closer to the value of the unevaluated decision variable and a predetermined number of evaluated variables. A value of a decision variable is selected, and the value of the unevaluated decision variable is evaluated based on whether the constraint violation information corresponding to the selected predetermined number of decision variable values indicates violation of the constraint condition A multi-objective optimization program including processing for determining whether or not to perform.

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