JP5156329B2 - Parametric multiobjective optimization apparatus, parametric multiobjective optimization method, and parametric multiobjective optimization program - Google Patents

Description

  The present invention relates to a parametric multi-objective optimization device, a parametric multi-objective optimization method, and a parametric multi-objective optimization program for optimizing an optimization target parameter (decision variable) whose objective function changes depending on conditions.

  In this specification, the optimization means obtaining an optimum solution or a solution close to the optimum (suboptimal solution).

  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. 28 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 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. 29 is a diagram for explaining the Pareto optimal solution. FIG. 29 shows an example of _two objective functions f ₁ and 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 an fitness function, and the value of the fitness function is called 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: see, for example, Non-Patent Document 3) has been proposed. In particular, NSGA-II and SPEA2 are known as excellent multi-objective evolutionary algorithms.
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

  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. 30 is a view for explaining engine adaptation.

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 FIG. 30, the values of the condition variables w ₁ and w ₂ are selected, the multi-objective optimization of the objective functions f ₁ and f ₂ is performed on the values of the selected condition variables w ₁ and w ₂ , and the decision variables 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 means solving a multi-objective optimization problem that searches for control parameters (decision variables) that satisfy multiple conflicting evaluation criteria (objective functions) for each operating condition (condition variable) required for map control. It is.

  Thus, the multi-objective optimization problem characterized by the condition variable is called a parametric multi-objective optimization problem (PMOP). FIG. 31 is a diagram showing a conceptual diagram of the parametric multi-objective optimization problem.

Here, the condition numbers w ₁ and w ₂ are integrated and represented by a condition variable w. Further, the value of the condition variable w is represented by w ¹ , w ² , w ³ ,. The objective functions f ₁ and f ₂ are characterized by the value of the condition variable w, and the landscape of the objective functions f ₁ and f ₂ changes as the value of the condition variable w changes. As the landscape of the objective functions f ₁ and f ₂ changes, the Pareto optimal solution set also changes.

For example, in the case of engine optimization, if the engine speed that is the condition variable w ₂ is increased, the fuel consumption that is the value of the objective function f ₂ increases, and the decision variables x ₁ and x ₂ that give optimum fuel consumption. The fuel injection timing and ignition timing are different.

  Solving the parametric multi-objective optimization problem is defined as obtaining a Pareto optimal solution set for all values of the condition variables.

  FIG. 32 is a diagram showing how a multi-objective optimization problem for a plurality of values of condition variables is solved. As shown in FIG. 32, in parametric multi-objective optimization, multi-objective optimization is performed using an initial solution set randomly generated for each condition variable value to obtain a Pareto optimal solution. Therefore, a great amount of time is required for optimization.

  By the way, as a problem class similar to the parametric multi-objective optimization problem, there is a problem class called a dynamic multi-objective optimization problem (DMOP). This is a problem that the multi-objective optimization problem changes depending on time.

  For example, Zhou et al. Have proposed an initialization strategy for when the problem has changed over time (Non-Patent Document 4). This initialization strategy predicts a Pareto optimal individual set one hour later from a Pareto optimal individual set one hour before and a Pareto optimal individual set at the current time, and uses this as the initial individual set.

  However, since the above initialization strategy always estimates the future Pareto optimal individual set from the past Pareto optimal individual set, it cannot be applied to parametric multi-objective optimization problems such as engine optimization.

  An object of the present invention is to provide a parametric multi-objective optimization apparatus, a parametric multi-objective optimization method, and a parametric multi-objective optimization program capable of efficiently optimizing a decision variable to be optimized whose objective function changes depending on conditions in a short time. Is to provide.

(1) A parametric multi-objective optimization device according to a first invention is a parametric multi-objective optimization device for optimizing an optimization target in which a plurality of objective functions change depending on a condition variable, the optimization target A condition variable selection unit that selects values of the condition variables in a preset order, an initial solution set generation unit that generates an initial solution set for multi-objective optimization, and a condition variable selected by the condition variable selection unit by performing multi-objective optimization using the initial solution set generated by the initial solution set generation unit for each value, for each value of the conditional variable, multipurpose optimal for obtaining respectively a Pareto optimal solution set of decision variables for a plurality of objective functions And a storage unit that stores a solution set obtained for each value of the condition variable by multi-objective optimization by the multi-objective optimization unit. The initial solution set for one value of the selected condition variable is generated based on the solution set obtained in the multi-objective optimization process for the other value of the condition variable stored in the storage unit.

In the parametric multi-objective optimization apparatus, the condition variable selection unit selects the value of the condition variable to be optimized in a preset order. An initial solution set for multi-objective optimization is generated by the initial solution set generation unit. Further, multi-objective optimization is performed by the multi-objective optimization unit using the initial solution set generated by the initial solution set generation unit for each value of the condition variable selected by the condition variable selection unit. Thus, for each value of the conditional variable, Pareto optimal solution set of decision variables for a plurality of objective functions are obtained, respectively. A solution set obtained for each condition variable value by multi-objective optimization by the multi-objective optimization unit is stored in the storage unit. In this case, the initial solution set for one value of the condition variable selected by the condition variable selection unit is based on the solution set obtained in the multi-objective optimization process for the other value of the condition variable stored in the storage unit. Generated by the initial solution set generation unit.

  Since the initial solution set generated in this manner is closer to the Pareto optimal solution set than the randomly generated initial solution set, the Pareto optimal solution set can be obtained with a smaller number of optimizations. Therefore, it is possible to efficiently optimize a decision variable to be optimized whose objective function changes depending on conditions in a short time.

  In addition, since the condition variable selection order by the condition variable selection unit can be set so that the convergence of the search for the Pareto optimal solution is improved, the Pareto optimal solution can be obtained in a shorter time.

  (2) The initial solution set generation unit includes a plurality of solution sets for a plurality of other values of the condition variable stored in the storage unit as an initial solution set for one value of the condition variable selected by the condition variable selection unit. You may obtain | require by mixing.

  In this case, since the initial solution set is obtained by mixing a plurality of solution sets, an initial solution set close to the Pareto optimal solution set can be obtained by simple processing. Therefore, the time required for optimization can be greatly shortened.

  (3) The initial solution set generation unit selects and selects a plurality of values of the condition variable based on a distance in the condition variable space between one value of the condition variable and another value of the condition variable stored in the storage unit Select multiple Pareto optimal solution sets for the selected multiple values, and calculate the distance in the condition variable space between the selected multiple values of the condition variable and the similarity between the selected multiple Pareto optimal solution sets The relationship between the distance and the similarity is calculated by statistical processing using the distance in the condition variable space as the explanatory variable, the similarity as the explained variable, and the condition variable stored in the storage unit. Selecting a plurality of values of the condition variable based on the distance in the condition variable space with the value of the value, and a solution set obtained in the multi-objective optimization process and a Pareto optimal solution set for each of the selected values of the condition variable, Similarity of Calculate and correspond to multiple selected values of a conditional variable based on the distance in the conditional variable space between one value of the conditional variable and multiple selected values of the conditional variable and the relationship calculated by statistical processing A solution set having a similarity closest to the estimated similarity among the solution sets obtained in the multi-objective optimization process for each of a plurality of selected values of the condition variable, An initial solution set for one value of a condition variable may be generated by mixing the solution set obtained in the multi-objective optimization process for a plurality of selected values of the variable at a ratio based on the distance in the condition variable space .

  In this case, the calculation of the relationship between the distance between the condition variable values in the condition variable space and the similarity between a plurality of Pareto optimal solution sets, the selection of a plurality of condition variable values, the similarity corresponding to the selected values The initial solution set close to the Pareto optimal solution set can be obtained by estimating the degree, selecting the solution set having the closest similarity to the estimated similarity, and mixing the solution sets obtained in the multi-objective optimization process . Therefore, the time required for optimization can be greatly shortened.

(4) A parametric multi-objective optimization method according to a second invention is a parametric multi-objective optimization method for optimizing an optimization target in which a plurality of objective functions change depending on a condition variable, and is optimized by a computer. selecting a value of the condition variables of interest in a predetermined order, the computer and generating an initial solution set for multi-objective optimization, generated for each value of the condition variable computer is selected By performing multi-objective optimization using the initial solution set, a step for obtaining a Pareto optimal solution set of decision variables for multiple objective functions for each condition variable value, and for each condition variable value by the computer using multi-objective optimization Storing the solution set obtained in the storage unit in the storage unit, and generating the initial solution set includes: The method includes a step of generating an initial solution set of values based on a solution set obtained in the multi-objective optimization process for other values of the condition variables stored in the storage unit.

According to the parametric multi-objective optimization method, the value of the condition variable to be optimized is selected in a preset order. An initial solution set for multi-objective optimization is generated. Further, multi-objective optimization is performed using the initial solution set generated for each value of the selected condition variable. Thus, for each value of the conditional variable, Pareto optimal solution set of decision variables for a plurality of objective functions are obtained, respectively. A solution set obtained for each condition variable value by multi-objective optimization is stored in the storage unit. In this case, the initial solution set for one value of the condition variable selected by the condition variable selection unit is based on the solution set obtained by multi-objective optimization for the other value of the condition variable stored in the storage unit. Generated by the set generation unit.

  Since the initial solution set generated in this manner is closer to the Pareto optimal solution set than the randomly generated initial solution set, the Pareto optimal solution set can be obtained with a smaller number of optimizations. Therefore, it is possible to efficiently optimize a decision variable to be optimized whose objective function changes depending on conditions in a short time.

  In addition, since the selection order of the condition variables can be set so that the convergence of the search for the Pareto optimal solution is improved, the Pareto optimal solution can be obtained in a shorter time.

(5) A parametric multi-objective optimization program according to a third invention is a parametric multi-objective optimization program that causes a computer to execute an optimization method for optimizing an optimization target in which a plurality of objective functions change depending on condition variables. A program that selects condition variable values to be optimized in a preset order, generates an initial solution set for multi-objective optimization, and generates each selected condition variable value by performing multi-objective optimization using the initial solution set, which is, for each value of the conditional variable, and processing for determining each Pareto optimal solution set of decision variables for a plurality of objective functions, each value of the conditional variable by multi-objective optimization The process of storing the solution set obtained in step (b) in the storage unit is executed by the computer, and the process of generating the initial solution set is performed for one value of the selected condition variable. This includes processing for generating all initial solution sets based on solution sets obtained in the multi-objective optimization process for other values of the condition variables stored in the storage unit.

According to the parametric multi-objective optimization program, the value of the condition variable to be optimized is selected in a preset order. An initial solution set for multi-objective optimization is generated. Further, multi-objective optimization is performed using the initial solution set generated for each value of the selected condition variable. Thus, for each value of the conditional variable, Pareto optimal solution set of decision variables for a plurality of objective functions are obtained, respectively. A solution set obtained for each condition variable value by multi-objective optimization is stored in the storage unit. In this case, the initial solution set for one value of the condition variable selected by the condition variable selection unit is based on the solution set obtained by multi-objective optimization for the other value of the condition variable stored in the storage unit. Generated by the set generation unit.

  Since the initial solution set generated in this manner is closer to the Pareto optimal solution set than the randomly generated initial solution set, the Pareto optimal solution set can be obtained with a smaller number of optimizations. Therefore, it is possible to efficiently optimize a decision variable to be optimized whose objective function changes depending on conditions in a short time.

  In addition, since the selection order of the condition variables can be set so that the convergence of the search for the Pareto optimal solution is improved, the Pareto optimal solution can be obtained in a shorter time.

  According to the present invention, a Pareto optimal solution set can be obtained with a smaller number of optimizations. Therefore, it is possible to efficiently optimize a decision variable to be optimized whose objective function changes depending on conditions in a short time.

  In addition, since the selection order of the condition variables can be set so that the convergence of the search for the Pareto optimal solution is improved, the Pareto optimal solution can be obtained in a shorter time.

  Hereinafter, a parametric multi-objective optimization apparatus (hereinafter abbreviated as 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 optimal individual set of a multi-objective optimization problem using a multi-objective evolutionary 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 or a simulator 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. The simulator is, for example, an engine simulator or a motor simulator. In the present embodiment, the optimization target 6 is an engine testing machine.

  The multi-objective optimization apparatus 1 includes a condition variable planning unit 2, an individual set initialization unit 3, a multi-objective evolution type algorithm unit 4, and a search history storage unit 5.

  The condition variable planning unit 2, the individual set initialization unit 3, and the multi-objective evolution algorithm unit 4 are realized by a CPU 101 (FIG. 2) described later executing a parametric multi-objective optimization program. The search history storage unit 5 includes an external storage device 106 (FIG. 2) described later.

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

Multiple fitness functions include fuel consumption (fuel consumption), torque, concentration of components such as CO (carbon monoxide), HC (hydrocarbon), and NO _x (nitrogen oxide) contained in engine exhaust gas, etc. A plurality of them are set.

Here, the trade-off relationship includes torque and fuel consumption, torque and CO concentration, torque and HC concentration, fuel consumption and NO _x concentration, CO concentration and NO _x concentration, HC concentration and NO _x concentration, and the like. In the example described later, two fitness functions f ₁ and f ₂ are set, the fitness function f ₁ is, for example, NO _x concentration, and the fitness function f ₂ is, for example, fuel consumption.

In addition, a condition variable representing the condition of the multi-objective optimization problem is set. In the example described later, a combination of _two condition variables w ₁ and w ₂ is referred to as a condition variable w. That is, the condition variable w is a two-dimensional vector. In this case, w = (w ₁ , w ₂ ). The condition variable w is, for example, an engine operating condition, the condition variable w ₁ is, for example, a load torque, and the condition variable w ₂ is, for example, an engine speed. When the condition variables w ₁ and w ₂ each have V values, the condition variable w has V ² sets of values.

The condition variable w may consist of an N-dimensional vector having three or more dimensions. In this case, the condition variable w consists of U condition variables w ₁ , w ₂ ,..., W _U.

  Furthermore, a plurality of decision variables are set as adjustable values. The decision variable is a control parameter of the optimization target 6, for example. 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 has a plurality of sets of decision variables and a plurality of fitness values. The fitness is a value of the fitness function (objective function value). Hereinafter, an individual of a multipurpose genetic algorithm is simply referred to as an individual.

  The multi-objective optimization apparatus 1 obtains a decision variable that optimizes the fitness at each value of the condition variable. Here, obtaining a decision variable that optimizes the fitness at each value of the condition variable is referred to as evaluation of each value of the condition variable.

  The condition variable planning unit 2 determines the evaluation order of the condition variable set composed of a plurality of values of the condition variable, and sets the values of the condition variables to be evaluated to the individual set initialization unit 3, the search history storage unit 5, and the optimization target 6. Output to. The value of the condition variable output from the condition variable planning unit 2 is particularly called a required condition variable value. Details will be described later.

  The individual set initialization unit 3 searches for the Pareto optimal individual set for the value of the unevaluated condition variable from the midway individual set and the Pareto optimal individual set stored in the search history storage unit 5 for each value of the condition variable. Generate an initial population of. Here, the midway individual set is an individual set obtained in the process of searching for the Pareto optimal individual set for each value of the condition variable. The mid-generation population of the final generation is the Pareto optimal population. Details will be described later.

  The multi-objective evolution type algorithm unit 4 uses the initial individual set generated by the individual set initialization unit 3 for the multi-objective optimization problem determined by each value of the conditional variable output from the conditional variable planning unit 2. Search for. In the present embodiment, the multi-objective evolution type algorithm unit 4 generates individuals according to the multi-objective evolution type algorithm for each value of the condition variable, performs a multipoint search, and evaluates the fitness function with Pareto optimality. Find the Pareto optimal population. Further, the multi-objective evolution type algorithm unit 4 presents the obtained Pareto optimal individual set to the user.

  The multi-objective evolution type algorithm unit 4 gives values of a plurality of decision variables to the optimization target 6 and receives the fitness output from the optimization target 6. Further, the multi-objective evolution type algorithm unit 4 gives the halfway individual set or the Pareto optimal individual set together with the fitness to the search history storage unit 5. Details will be described later.

  The search history storage unit 5 stores the midway individual set and the Pareto optimal individual set obtained by the multi-objective evolution type algorithm unit 4 for each value of the condition variable.

  The optimization target 6 outputs the fitness based on the condition variable value output from the condition variable planning unit 2 and the decision variable value provided from the multi-objective evolution type algorithm unit 4.

(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.

  The recording medium 109 records a parametric multipurpose optimization program (hereinafter referred to as a multipurpose optimization program). 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 set of fitness output from the optimization target 6 to the external storage device 106, and gives the set of individual decision variables generated by the multi-objective optimization program to the optimization target 6.

  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. In this example, the decision variables are the fuel injection timing and the ignition timing. 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. In this example, the condition variables w ₁ and w ₂ are the load torque and the engine speed. 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.

Measuring device 63 includes an exhaust gas analyzer, the combustion analyzer and a fuel flow meter, and analyzing components in the exhaust gas from the engine 61, and outputs the concentration of NO _x and fuel efficiency in multi-objective optimization apparatus 1 as fitness .

(4) Search History FIG. 4 is a diagram showing an example of a search history of the Pareto optimal individual set using the initial individual set. 4A shows the configuration of the individual set stored in the search history storage unit 5, and FIG. 4B shows how the initial individual set converges to the Pareto optimal individual set by the multi-objective evolution type algorithm.

As shown in FIG. 4A, the individual set includes values of decision variables x ₁ and x ₂ and values of fitness functions f ₁ and f ₂ with respect to a certain value of the condition variable w. In FIG. 4B, the t-th generation and the t + 1-th generation represent generations between the initial generation and the final generation. In the initial generation, an intermediate individual set is obtained using an initial individual set generated by a method described later. A midway population is obtained for each generation, and a Pareto optimal population is obtained for the final generation.

  FIG. 5 is a diagram illustrating an example of a search history stored in the search history storage unit 5 from the initial generation to the final generation.

In FIG. 5, w ^{1 to} w ⁴ indicate different values of the condition variable w. In the case of the condition variable w = (w ₁ , w ₂ ), w ¹ = (w ₁ ¹ , w ₂ ¹ ), w ² = (w ₁ ² , w ₂ ² ), w ³ = (w ₁ ³ , w ₂ ³ ) and w ⁴ = (w ₁ ⁴ , w ₂ ⁴ ).

In the example of FIG. 5, for the condition variable value w ¹ , the midway population obtained in the initial generation, the t generation and the t + 1 generation, and the Pareto optimal individual set obtained in the final generation are stored in the search history storage unit 5. Has been. Further, the midway individual set obtained in the initial generation and the t-th generation with respect to the condition variable value w ² is stored in the search history storage unit 5.

  In this way, the halfway individual set and the Pareto optimal individual set obtained by the search for each value of the condition variable are stored in the search history storage unit 5.

(5) Concept of generating an initial population In this embodiment, an initial population is generated by mixing intermediate populations obtained for a plurality of other values of a conditional variable for some values of a conditional variable. The Here, the midway population includes the initial population of the last generation (Pareto optimal population).

  FIG. 6 is a conceptual diagram for explaining generation of an initial population by mixing halfway populations.

By mixing the midway population for the condition variable value w ^{1 and} the midway population for the condition variable value w ⁴ , an initial population for the condition variable value w ² is generated. Initial population of individuals is generated for values w ³ of a condition variable by mixing middle individual set of the values w ⁴ of middle individual set and condition variables for the value w ² in the condition variable.

In this way, the search for the Pareto optimal individual set for the condition variable value w ² and the search for the Pareto optimal individual set for the condition variable value w ³ are made efficient.

(6) Overall Processing of Multipurpose Optimization Device FIG. 7 is a flowchart showing the overall processing of the multipurpose optimization device 1 of FIG.

  First, the condition variable planning unit 2 selects a condition variable value (step S1). A method for selecting the value of the condition variable will be described later.

  Next, the search history storage unit 5 stores the value of the condition variable selected by the condition variable planning unit 2 (step S2). The individual set initialization unit 3 determines whether or not the number of condition variable values stored in the search history storage unit 5 is equal to or greater than a predetermined number (step S3).

  When the number of condition variable values stored in the search history storage unit 5 is smaller than a predetermined number, the individual set initialization unit 3 randomly generates an initial individual set for the selected condition variable values. (Step S4).

  When the number of condition variable values stored in the search history storage unit 5 is equal to or greater than a predetermined number, the individual set initialization unit 3 performs intermediate processing for a plurality of condition variable values stored in the search history storage unit 5. By mixing the individual sets, an initial individual set for the value of the selected condition variable is generated (step S5).

  Next, the multi-objective evolution type algorithm unit 4 searches for the Pareto optimal individual set by the multi-objective evolution type algorithm using the initial individual set generated for the value of the selected condition variable (step S6). The search history storage unit 5 stores the midway individual set obtained by the search (step S7).

  The multipurpose evolutionary algorithm unit 4 determines whether or not the search has been completed up to the final generation for the value of the selected condition variable (step S8). If the search has not been completed up to the final generation, the process returns to step S6, and the processes of steps S6 to S8 are repeated. The last generation midway individual set is stored in the search history storage unit 5 as a Pareto optimal individual set.

  When the search has been completed up to the final generation, the multi-objective evolution type algorithm unit 4 determines whether or not the search for the Pareto optimal individual set has been completed for all values of the condition variables (step S9).

  If the search for the Pareto optimal population has not been completed for all values of the condition variable, the process returns to step S1. Thereby, the condition variable planning unit 2 selects the value of the next condition variable.

  When the search for the Pareto optimal individual set is completed for all values of the condition variables, the multi-objective optimization is ended. In this case, the Pareto optimal individual set for all values of the condition variable is stored in the search history storage unit 5.

(7) Condition Variable Selection Method by Condition Variable Planning Unit 2 The condition variable planning unit 2 determines the evaluation order of the condition variable values, and sequentially outputs the value of the condition variable to be evaluated. The value of the condition variable output from the condition variable planning unit 2 is called a request condition variable value.

FIGS. 8A and 8B are diagrams illustrating an example of a condition variable selection method. In this example, the condition variable w is composed of a two-dimensional vector (w ₁ , w ₂ ). FIG. 8 (a), the the horizontal axis represents the value of the condition variable w ₁ of (b), the vertical axis is the value of the condition variable w _2.

  In the example of FIG. 8A, the value of the condition variable is sequentially selected from the outside in the two-dimensional vector space. In the example of FIG. 8B, the values of the condition variables that are close in the two-dimensional vector space are selected in order.

  The selection order of the condition variable values is not limited to the example of FIG. 8, and can be selected in various orders according to the order or number of the condition variables.

(8) Multi-objective evolution type algorithm FIG. 9 is a schematic diagram for explaining a multi-objective evolution type algorithm. FIG. 10 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. 9A, the multipurpose evolution type algorithm unit 4 generates a child individual set Q from the parent individual set P in the t generation (step S11 in FIG. 10).

  Next, as shown in FIG. 9B, the multi-objective evolution type algorithm unit 4 performs non-dominant sorting on the union R of the parent individual set P and the child individual set Q (step S12 in FIG. 10). . 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. 9B, the union R is rearranged into ranks 1 to 4.

  Next, as shown in FIGS. 9C and 9D, the multipurpose evolutionary algorithm unit 4 performs congestion degree sorting for each rank of the union R (step S13 in FIG. 10). 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 It is a method of changing (sorting). Details of the congestion degree sorting will be described later.

  Next, the multipurpose evolutionary algorithm unit 4 leaves the top p (= | P |) individuals as the next-generation (t + 1 generation) parent individual set P (step S14 in FIG. 10). Here, | P | represents the number of parent individual sets. In the example of FIG. 9, rank 4 individuals are deceived, and some of the rank 3 individuals are deceived.

  Thereafter, the multipurpose evolutionary algorithm unit 4 determines whether or not the number of generations has reached a predetermined end condition (step S15 in FIG. 10).

  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 multi-objective evolution type algorithm unit 4 presents the parent individual set P generated in step S15 to the user as a Pareto optimal individual set, and ends the process.

(9) Non-dominant ranking FIG. 11 is a schematic diagram for explaining non-dominant ranking. FIG. 11 shows an individual set of fitness space.

  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. 11, 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.

(10) Congestion degree sort FIG. 12 is a diagram for explaining the congestion degree sort. FIG. 12 shows an individual set of the fitness space.

  In the congestion degree sort, for each target individual of the same rank, a rectangle whose diagonal is a line connecting two adjacent individuals is assumed, and the total degree of the vertical and horizontal sides of the rectangle is the congestion degree (congestion distance) 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. 12, the degree of congestion 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. 13 is a flowchart showing the congestion degree sorting process by the multipurpose evolutionary algorithm unit 4.

  First, the multi-objective evolution type algorithm unit 4 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 4 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 multi-purpose evolutionary algorithm unit 4 sorts the individuals in 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.

(11) Individual set similarity Next, the concept of similarity between individual sets will be described. FIG. 14 is a schematic diagram for explaining the similarity of an individual set.

  FIG. 14 shows two individual sets P1 and P2 in the decision variable space. The individual set P1 includes individuals p11 to p15. The individual set P2 includes individuals p21 to p25. The distances from the individuals p11 to p15 in the individual set P1 to the closest individuals p21 to p24 in the individual set P2 are indicated by arrows a1 to a5, respectively. Further, the distances from the individuals p21 to p25 in the individual set P2 to the closest individuals p11 to p15 in the individual set P1 are indicated by arrows c1 to c5.

  The similarity between the two individual sets P1, P2 is defined by the following equation.

Similarity α = (L ₁₂ + L ₂₁ ) / 2
In the above equation, L ₁₂ is the average value of the distance from each individual in the individual set P1 to the closest individual in the individual set P2, and L ₂₁ is the closest in the individual set P1 from each individual in the individual set P2. This is the average distance to the individual.

(12) Method for generating initial population by mixing midway populations As described above, the population set initialization unit 3 mixes midway populations for a plurality of values of the conditional variable w to provide a certain value of the condition variable w. Generate an initial population for. Next, a method for generating an initial population by mixing halfway populations will be described.

  15 to 23 are schematic diagrams for explaining a method for generating an initial population by mixing a plurality of midway populations. FIG. 24 is a flowchart showing an algorithm for obtaining an initial population by mixing a plurality of midway populations.

Here, it is assumed that an initial individual set for the required condition variable value w ^q output from the condition variable planning unit 2 is generated.

First, using the k-NN method (k-nearest-Neighbor Method) in the condition variable space, a condition variable value (neighboring set) near the required condition variable value w ^q is selected (step S31 in FIG. 24). FIG. 15 shows the required condition variable value w ^q in the condition variable space and the values w ¹ , w ² , w ³ , and w ^{4 of the} plurality of condition variables w. In the example of FIG. 15, condition variable values w ² , w ³ , w ⁴ (neighboring sets) in the vicinity of the required condition variable value w ^q are selected.

  Next, the distance between the values of the selected condition variable w and the similarity between the Pareto optimal individual sets are calculated (step S32 in FIG. 24).

FIG. 16A shows the selected values w ² , w ³ , w ⁴ of the condition variable w in the condition variable space. The distance between the values w ² and w ^{3 of} the condition variable w is dc ₁ , the distance between the values w ³ and w ^{4 of} the condition variable w is dc ₂ , and between the values w ² and w ^{4 of} the condition variable w The distance is dc ₃ . FIG. 16B shows the Pareto optimal individual set for the selected values w ² , w ³ , and w ⁴ of the condition variables in the decision variable space. The similarity between the Pareto optimal individual sets for the values w ² and w ³ of the condition variable w is α ₁ , and the similarity between the Pareto optimal individual sets for the values w ₃ and w ₄ of the condition variable w is α ₂ Yes, the similarity between the Pareto optimal individual sets for the values w ₂ and w ₄ of the condition variable w is α ₃ .

  Next, linear regression is performed using the distance between the values of the selected condition variable w as an explanatory variable, the similarity between the Pareto optimal individual sets for the value of the selected condition variable w as an explained variable, and the regression coefficient is Obtained (step S33 in FIG. 24).

  As a result, as shown in FIG. 17, a straight line F indicating the relationship between the distance dc between the values of the condition variable w and the similarity α between the Pareto optimal individual sets is obtained.

  Next, for each of the selected condition variable values, the similarity between the Pareto optimal individual set and the midway individual set of each generation is calculated (step S34 in FIG. 24). In the upper part of FIG. 18, halfway individual sets in the first generation, the second generation, the third generation, and the final generation for one value of the condition variable are indicated by black circles, and the Pareto optimal individual sets are indicated by white circles. Similarity between first generation midway population and Pareto optimal population, second generation midway population and Pareto optimal population, and third generation midway population and Pareto optimal population Is calculated. Since the middle generation individual set in the final generation is a Pareto optimal individual set, the similarity is zero. The lower part of FIG. 18 shows the relationship between the generation and the similarity α. The horizontal axis is the generation, and the vertical axis is the similarity.

Next, the value of the condition variable w near the request condition variable value w ^q is selected, and the distance between the request condition variable value w ^q and the value of the nearby condition variable w is calculated (step S35 in FIG. 24). FIG. 19 shows the selected values w ² and w ³ and the required condition variable value w ^q of the condition variable w in the decision variable space. The distance between the request condition variable value w ^q and the value w ² of the condition variable w is d1, and the distance between the request condition variable value w ^q and the value w ³ of the condition variable w is d2.

  Further, the estimated similarity corresponding to each distance is calculated from the distance between the required condition variable value wq and the value of the nearby condition variable using the above regression coefficient (step S36 in FIG. 24). FIG. 20 shows a straight line F indicating the relationship between the distance dc and the similarity α. The estimated similarity α1 is calculated from the distance d1, and the estimated similarity α2 is calculated from the distance d2.

Next, for each value of the condition variable w, a midway individual set having a similarity close to the estimated similarity is selected using the relationship between the generation and the similarity calculated in FIG. 18 (step S37 in FIG. 24). FIG. 21A shows the relationship between the generation for the value w ² of the condition variable w and the similarity α, and FIG. 21C shows the generation for the value w ³ of the condition variable w. The relationship with the similarity α is shown. Using the relationship shown in FIG. 21A, as shown in FIG. 21B, a midway individual set having a similarity close to the estimated similarity α1 is selected. Further, as shown in FIG. 21D, a midway individual set having a similarity close to the estimated similarity α2 is selected using the relationship shown in FIG.

Next, based on the distance between the required condition variable value w ^q and the selected value of the condition variable w in the decision variable space, a mixture ratio of a plurality of midway individual sets is determined, and a plurality of midway individual sets are determined based on the ratio. Mix (step S38 in FIG. 24). In the example of FIG. 22, the weighting function FW determined based on the distances d1 and d2 between the required condition variable value w ^q in the decision variable space and the selected values w ² and w ³ of the condition variable w is shown. . Using this weight function, the mixing ratio of a plurality of midway populations is determined. In this case, the ratio is set smaller as the distance increases. The selected mid-population population is mixed at the determined ratio. That is, a large number of individuals in the midway individual set are mixed with respect to the value of the condition variable w whose distance from the required condition variable value w ^q is small. In this way, an initial population for the requirement variable value w ^q is obtained.

(13) Effects of the Embodiment In the multi-objective optimization apparatus 1 according to the present embodiment, the initial individual set for a plurality of values of the conditional variable w is an intermediate individual set for the other values of the conditional variable w. Produced by mixing. As a result, an appropriate Pareto optimal population can be efficiently obtained with a small number of generations. Accordingly, even when the number of condition variables is large, the time required for parametric multi-objective optimization can be significantly reduced.

  In addition, the condition variable planning unit 2 can arbitrarily set the evaluation order of the value of the condition variable w so as to improve the convergence of the search for the Pareto optimal individual set, so that the Pareto optimal individual set can be obtained more efficiently. Is possible.

(14) Examples In the following examples, the effect of reducing the number of evaluations by the multi-objective optimization apparatus 1 according to the above embodiment was examined by numerical experiments.

  In this embodiment, NSGA-II is used as the multi-objective evolutionary algorithm, the parent individual set size | P | is set to 100, and the child individual set size | Q | is also set to 100. As crossover operation, UNDX (Unimodal Normal Distribution Crossover) is used at a crossover rate of 1.0, and mutation operation is not used.

FIGS. 25A and 25B are diagrams showing the value of the condition variable w and the evaluation order thereof in the embodiment. The horizontal axis of FIG. 25 shows the value of a condition variable w _1, the vertical axis represents the value of a condition variable w _2.

As shown in FIG. 25A, the values of the condition variables w ₁ and w ₂ are all 0.0, 0.25, 0.5, 0.75, and 1.0. In this case, the value of the condition variable w is 25 sets.

  The experimental procedure is as follows. First, the evaluation order of the value of the condition variable w is determined. In this embodiment, the value of the condition variable w is evaluated in the order indicated by numbers in the circles in FIG.

When the value of the condition variable w stored in the search history storage unit 5 is less than k, the generation number T is optimized using a randomly generated initial individual set, and an intermediate individual set (from the last generation) The search history storage unit 5 stores the individual set obtained in the previous generation) and the Pareto optimal individual set (individual set obtained in the last generation). If the value of the condition variable w becomes k or more, the value of a plurality of condition variables w is selected from the condition variables w stored in the search history storage unit 5 by the k-NN method. Then, a mixture of middle individual set of the values of the selected condition variables w, implementing the following optimization mixed with middle individual set as an initial population of individuals for the requirements variable w ^q.

  In this embodiment, T = 100 and k = 4. Further, in this example, in order to confirm the effect of the multi-objective optimization apparatus 1 of the above-described embodiment, optimization is performed up to the T + 1 generation without terminating the search halfway. Therefore, a Pareto optimal individual set with good quality can be used to generate the initial individual set.

  However, in practice, the search is terminated under a predetermined termination condition. For example, the search is terminated when the rate of change in similarity is equal to or less than a predetermined value ε. Here, the similarity is the similarity between the current generation individual set and the previous generation individual set. In this case, the individual set when the predetermined end condition is satisfied becomes the Pareto optimal individual set.

  As a test function, the following two-condition two-objective n-variable problem is used.

Here, −2 ≦ x ₁ ≦ 2, −2 ≦ x ₂ ≦ 2, 0 ≦ w ₁ ≦ 1, 0 ≦ w ₂ ≦ 1, and n = 20.

  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 the example, in order to evaluate the average performance of the multi-objective optimization apparatus of the above-described embodiment, an average value of 30 optimization results is obtained.

  On the other hand, in the comparative example, a search is performed using an initial individual set that is randomly generated for all values of the condition variable w.

  Next, the similarities of all the generations in the example are normalized using the similarities obtained in the final generation (101st generation) in the comparative example. Then, the number of generations when the normalized similarity is 1 or less is obtained. Thereby, it can be known how many generations can be reduced in the embodiment.

FIG. 26 is a diagram showing experimental results. The horizontal axis of FIG. 26 shows the value of a condition variable w _1, the vertical axis represents the value of a condition variable w _2. The numbers in each square in FIG. 26 indicate the number of generations when the normalized similarity is 1 or less.

  The four sets of values of the condition variable in the lower left of FIG. 26 are optimized using a randomly generated initial individual set, so that the same degree of similarity as in the comparative example is obtained in the 101st generation. For each other value of the condition variable w, an initial individual set is generated by mixing the midway individual sets for the other values of the condition variable w. Accordingly, it can be seen from the results of FIG. 26 that similarities to the comparative example are obtained in the 20th to 82nd generations, and the same similarity as the comparative example is obtained in about 50 generations on average. Therefore, in this embodiment, it can be said that the total search time can be reduced to about ½.

  As described above, it can be seen that the multi-objective optimization device according to the above-described embodiment can significantly reduce the time required for optimization by the multi-objective evolutionary algorithm.

(15) Other Embodiments (a) In the above embodiment, NSGA-II is used as a multi-objective 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) Application to three or more objectives In the above embodiment, two-purpose optimization has been described as an example. However, the present invention can be similarly applied to optimization of three or more objectives. . In this case, three or more fitness functions having a trade-off relationship are set.

  (C) In the above embodiment, the conditional variable planning unit 2, the individual set initialization unit 3, the multipurpose evolution type algorithm unit 4 and the search history storage unit 5 are realized by the CPU 101 and the program. Part or all of the individual set initialization unit 3, the multipurpose evolution type algorithm unit 4 and the search history storage unit 5 may be realized by hardware such as an electronic circuit.

  (D) Other optimization algorithms may be used instead of the multi-objective evolution type algorithm.

  FIG. 27 is a block diagram showing an example of a multi-objective optimization apparatus using another optimization algorithm.

  27, a solution set initialization unit 30 is used instead of the individual set initialization unit 3 shown in FIG. 1, and a multi-objective optimization unit 40 is used instead of the multi-object evolution algorithm unit 4 shown in FIG. A search history storage unit 50 is used instead of the search history storage unit 5 of FIG.

  The solution set initialization unit 30 searches for the Pareto optimal solution set for the value of the unevaluated condition variable from the halfway solution set and the Pareto optimal solution set stored in the search history storage unit 50 for each value of the condition variable. Generate an initial solution set of. Here, the halfway solution set is a set of solutions obtained in the search process of the Pareto optimal solution set for each value of the condition variable.

  The multi-objective optimization algorithm unit 40 uses the initial solution set generated by the solution set initialization unit 30 for the multi-objective optimization problem determined by each value of the conditional variable output from the conditional variable planning unit 2. Search for. In this example, the multi-objective optimization algorithm unit 40 performs a multipoint search according to an optimization algorithm for each value of the condition variable, and obtains a Pareto optimal solution set by evaluating the objective function with Pareto optimality. The multi-objective optimization algorithm unit 40 presents the obtained Pareto optimal solution set to the user.

  The multi-objective optimization algorithm unit 40 gives values of a plurality of decision variables to the optimization target 6 and receives an objective function value output from the optimization target 6. Further, the multi-objective optimization algorithm unit 40 gives the halfway solution set or Pareto optimal solution set to the search history storage unit 50 together with the objective function value.

  The search history storage unit 50 stores the halfway solution set and Pareto optimal solution set obtained by the multi-objective optimization algorithm unit 40 for each value of the condition variable.

  The optimization target 6 outputs an objective function value based on the condition variable value output from the condition variable planning unit 2 and the decision variable value provided from the multi-objective optimization algorithm unit 40.

  In the multi-objective optimization apparatus 1 of this example, an initial solution set for a plurality of values of a condition variable is generated by mixing an intermediate solution set for other values of the condition variable. Thereby, an appropriate Pareto optimal solution set can be efficiently obtained with a small number of optimizations. Accordingly, even when the number of condition variables is large, the time required for parametric multi-objective optimization can be significantly reduced.

(16) 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 conditional variable planning unit 2 is an example of a conditional variable selection unit, the individual set initialization unit 3 or the solution set initialization unit 30 is an example of an initial solution set generation unit, and the search history storage unit 5 Alternatively, the search history storage unit 50 is an example of a storage unit, and the multi-purpose evolution type algorithm unit 4 or the multi-purpose optimization algorithm unit 40 is an example of a multi-purpose optimization unit.

  In addition, the initial individual set is an example of the initial solution set, the Pareto optimal individual set is an example of the Pareto optimal solution set, the Pareto optimal individual is an example of the Pareto optimal solution, and the regression process by the least square method is a statistical process It is an example.

  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 which shows an example of the search history of the Pareto optimal individual set using an initial individual set. It is a figure which shows an example of the search history memorize | stored in a search history memory | storage part from the initial generation to the last generation. It is a conceptual diagram for demonstrating the production | generation of the initial population by the interpolation of a Pareto optimal population. It is a flowchart which shows the whole process of the multi-objective optimization apparatus of FIG. It is a figure which shows the example of the selection method of a condition variable. 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 schematic diagram for demonstrating the similarity of an individual set. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a schematic diagram for demonstrating the production | generation method of the initial population by mixing a some middle population. It is a flowchart which shows the algorithm for calculating | requiring an initial population by mixing of a some middle population. It is a figure which shows the value of the condition variable in an Example, and its evaluation order. It is a figure which shows an experimental result. It is a block diagram which shows the example of the multi-objective optimization apparatus using another optimization algorithm. 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 figure which shows the conceptual diagram of a parametric multiobjective optimization problem. It is a figure which shows a mode that the multiobjective optimization problem about the several value of a condition variable is solved.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Multiobjective optimization apparatus 2 Condition variable plan part 3 Individual set initialization part 4 Multiobjective evolution type algorithm part 5 Search history memory | storage part 6 Optimization object 30 Solution set initialization part 40 Multiobjective optimization algorithm part 50 Search history memory | storage part 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 b1~b5 branch c1~c5 arrow f _{1, f 2} fitness function I1~I10 individual p11~p15, p21~p25 individuals P1, P2 individual set w, w ₁ , w ₂ conditional variables w ¹ , w ² , w ³ , w ⁴ conditional variable values w ^q required conditional variable values x ₁ , x ₂ decision variables

Claims (5)

A parametric multi-objective optimization device for optimizing an optimization target in which a plurality of objective functions change depending on a condition variable,
A condition variable selection unit for selecting values of the condition variables to be optimized in a preset order;
An initial solution set generator for generating an initial solution set for multi-objective optimization;
By performing multi-objective optimization using the initial solution set generated by the initial solution set generation unit for each value of the condition variable selected by the condition variable selection unit , the plurality of objectives for each value of the condition variable a multi-objective optimization section for determining each Pareto optimal solution set of decision variables for the function,
A storage unit that stores a solution set obtained for each condition variable value by multi-objective optimization by the multi-objective optimization unit;
The initial solution set generation unit obtains an initial solution set for one value of the condition variable selected by the condition variable selection unit in a multi-objective optimization process for another value of the condition variable stored in the storage unit. A parametric multi-objective optimization device, characterized in that the parametric multi-objective optimization device is generated based on a set of solutions. The initial solution set generator generates an initial solution set for one value of the condition variable selected by the condition variable selection unit, and a plurality of solution sets for other values of the condition variable stored in the storage unit The parametric multi-objective optimization apparatus according to claim 1, wherein the parametric multi-objective optimization apparatus is obtained by mixing. The initial solution set generation unit includes:
Selecting a plurality of values of the condition variable based on a distance in the condition variable space between the one value of the condition variable and another value of the condition variable stored in the storage unit; Choose the Pareto optimal solution set of
Calculating a distance in the condition variable space between the selected values of the condition variable and a similarity between the selected Pareto optimal solution sets;
Using the distance in the condition variable space as an explanatory variable, and calculating the relationship between the distance and the similarity by statistical processing using the similarity as an explained variable,
Selecting a plurality of values of the condition variable based on a distance in the condition variable space between the one value of the condition variable and another value of the condition variable stored in the storage unit; For each value of, calculate the similarity between the solution set obtained in the multi-objective optimization process and the Pareto optimal solution set,
The selected plurality of values of the condition variable based on a distance in the condition variable space between the one value of the condition variable and the selected plurality of values of the condition variable and the relationship calculated by the statistical processing Estimate the similarity corresponding to
Selecting a solution set having a similarity closest to the estimated similarity among solution sets obtained in the process of multi-objective optimization for each of the selected plurality of values of the condition variable;
An initial solution set for the one value of the condition variable is mixed by mixing a solution set obtained in the process of multi-objective optimization for the selected plurality of values of the condition variable at a ratio based on the distance in the condition variable space. The parametric multi-objective optimization apparatus according to claim 1 or 2, wherein the parametric multi-objective optimization apparatus is generated. A parametric multi-objective optimization method for optimizing an optimization target in which a plurality of objective functions change depending on a condition variable,
A computer selecting values of the condition variables to be optimized in a preset order;
The computer generating an initial solution set for multi-objective optimization;
The computer performs multi-objective optimization using the generated initial solution set for each value of the selected conditional variable, so that the Pareto optimal solution of the decision variable for the plurality of objective functions is obtained for each value of the conditional variable. Obtaining each set, and
Storing the solution set obtained by the computer for each condition variable value in the multipurpose optimization in a storage unit,
In the step of generating the initial solution set, an initial solution set for one value of the selected condition variable is obtained in a multi-objective optimization process for another value of the condition variable stored in the storage unit. A parametric multi-objective optimization method comprising the step of generating based on: A parametric multi-objective optimization program for causing a computer to execute an optimization method for optimizing an optimization target in which a plurality of objective functions change depending on a condition variable,
A process of selecting values of the condition variables to be optimized in a preset order;
Processing to generate an initial solution set for multi-objective optimization;
Each By performing multi-objective optimization using the initial solution set said generated for each value of the selected condition variables, for each value of the condition variable, the Pareto optimal solution set of decision variables for said plurality of objective functions The required processing,
Storing a solution set obtained for each condition variable value by the multi-objective optimization in a storage unit;
Causing the computer to execute,
The process of generating the initial solution set includes: an initial solution set for one value of the selected condition variable and a solution set obtained in a multi-objective optimization process for another value of the condition variable stored in the storage unit A parametric multi-objective optimization program characterized in that it includes processing to be generated on the basis of.

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