JP2008059146A - Search device for state space and search method for state space - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide the search device of a state space for efficiently calculating continuous values to a state, and for efficiently solving the optimization problem of non-linear combination. <P>SOLUTION: The optimization of continuous values is operated by a secondary planning method using an interior point method with respect to a focusing state by a focusing state evaluation part 2, and the optimal solution is stored in an optimal solution storage database 8. Then, an adjacent state is created from the focusing state, and the optimization of the continuous values is operated by the secondary planning method using an active-set method by using the optimal solution stored in the optimal solution storage database 8 as an initial value with respect to the adjacent state, and the adjacent state is evaluated by an adjacent state preparation/evaluation part 3, and stored in an adjacent state database 9. Then, the most satisfactory evaluation function value among the adjacent states stored in the adjacent state database 9 is defined as the next focusing state by a state transition part 4, and processing by the focusing state evaluation part 2 and the adjacent state preparation/evaluation part 3 and the state transition part 4 is repeated and the optimal state is searched. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a state space search apparatus and a state space search method for obtaining an optimal solution of a nonlinear combination.

As a conventional combinatorial optimization technique, for example, Non-Patent Document 1 describes a technique using a tabu search method.
The nonlinear combinatorial optimization problem is generally handled as a double optimization problem in which continuous variables in each state in the combinatorial optimization problem are determined by a continuous system optimization method. As shown in Non-Patent Document 1, a tabu search method and a quadratic programming method using an interior point method as a continuous system optimization method are employed.

2000 Annual Conference of the Institute of Electrical Engineers of Japan, No. 268, Toshiyuki Sawa, et al., “Weekly operation plan of power plant using tabu search method”

  However, in a realistic nonlinear combinatorial optimization problem, for one state (a set of discrete variables and continuous variables), the number of adjacent states obtained by changing one or more locations of the combination (discrete variables) is In general, there are several tens to several hundreds, and the number of continuous variables that should be optimized by a continuous optimization method for one state is typically thousands to tens of thousands, or more. In the conventional technique that applies the quadratic programming method using the above as a method for optimizing continuous variables for all states, it takes a lot of processing time to calculate continuous variables for individual states. There was a problem that the search range was limited.

  The present invention has been made to solve the above-described problems, and can efficiently calculate a continuous value (continuous variable) with respect to a state and efficiently solve an optimization problem of a non-linear combination. It is an object of the present invention to obtain a state space search device and a state space search method.

  In the state space search device according to the present invention, a state space consisting of a state having both a combination of a plurality of discrete values and a continuous value determined corresponding to the combination of the discrete values is determined from the initial state of interest. The state space in which the evaluation function value is searched for is determined by sequentially repeating the process of determining the state to be transitioned from the adjacent states obtained by changing the combination of the target states and setting the next target state. In the search device, the target state evaluation unit that optimizes the continuous value by the quadratic programming method using the interior point method for the target state, and the continuous value optimization by the target state evaluation unit for the adjacent state As an initial value, an adjacent state creation / evaluation means for optimizing continuous values by a quadratic programming method using the Active-set method is provided.

  As described above, the present invention starts from an initial state of interest in a state space consisting of a state having a combination of a plurality of discrete values and a continuous value determined corresponding to the combination of discrete values. , A state space search device that sequentially repeats the process of determining the state to be transitioned from adjacent states obtained by changing the combination of the target states and setting the next target state, and searching for the state with the best evaluation function value In the target state evaluation means that optimizes the continuous value by the quadratic programming method using the interior point method for the target state and the continuous value optimization by the target state evaluation means for the adjacent state. As an initial value, the adjacent state creation / evaluation means that optimizes the continuous value by the quadratic programming method using the Active-set method is provided, so that the state continuation can be performed at high speed without reducing the accuracy of the solution. Seeking a value Possible and it is possible to explore the broader state space in a limited processing time.

Embodiment 1 FIG.
FIG. 1 is a block diagram showing a state space search apparatus according to Embodiment 1 of the present invention, and shows a state space search apparatus 200 using the tabu search method.
In FIG. 1, information necessary for performing a state space search in the state space search apparatus 200 is input as input information 100 to the state creation database 7 through a communication means such as a LAN or a GUI (Graphical User Interface). Is done.
The state creation data reading unit 1 is a mechanism that initially sets a state serving as a starting point for the search of the state space as a state of interest, and extracts data necessary for creating a state from the state creation database 7. The initial value of the initial attention state and the evaluation function value of the best state are set, and the initial setting of the iteration number counter L in the subsequent iterative processing from the attention state evaluation unit 2 to the search continuation determination unit 5 is performed.
Here, the state space is composed of a state having both a combination of a plurality of discrete values and a continuous value determined corresponding to the combination of the discrete values. For example, when the discrete value is the number of facilities, the continuous value is the fuel cost of the facility, and the continuous value is determined as the fuel cost of each facility corresponding to the combination of the entire facilities. The search of the state space is a search for a state where the overall fuel cost is minimum, that is, a state where the overall evaluation function value is minimum.

The focused state evaluation unit 2 (focused state evaluation means, first procedure) optimizes the continuous values in the focused state by the quadratic programming method using the interior point method (determining individual continuous values corresponding to the overall combination) ) And the evaluation of the state of interest (determining an evaluation function value), and the result of the optimization of the continuous value is used in the adjacent state creation / evaluation unit 3 and the state transition unit 4 described later in Active- The initial value of the quadratic programming method using the set method is stored in the Active-set method initial value database 9.
If the evaluated state of interest has the best evaluation function value among the states of interest searched so far, the state of interest is stored in the best solution storage database 8 as the best state.

  The adjacent state creation / evaluation unit 3 (adjacent state evaluation means, second procedure) refers to the tabu list database 11 and prohibits creation by the tabu list from adjacent states having a combination different from the state of interest by one or more places. This is a mechanism that creates an adjacent state that has not been performed, optimizes the continuous value of the adjacent state using the initial value stored in the active-set method initial value database 9, and evaluates the adjacent state The adjacent state database 10 stores state change information such as the adjacent state type and combination change location necessary for state transition from the target state to the adjacent state, and the evaluation function value of the adjacent state.

The state transition unit 4 is a mechanism that sets the adjacent state having the best evaluation function value among the adjacent state data stored in the adjacent state database 10 as the next state of interest. In addition, the state change information such as the adjacent state type and the combination change portion necessary for transition from the target state to the next target state is stored in the tabu list database 11 and the tabu list stored in the previous search is stored. Update.
The search continuation determination unit 5 determines whether or not the number of repetitions L in the iterative processing from the focused state evaluation unit 2 to the search continuation determination unit 5 exceeds the maximum number of repetitions LMAX.
The optimum state output unit 6 extracts the best state obtained from the iterative processing from the state-of-interest evaluation unit 2 to the search continuation determination unit 5 from the best solution storage database 8 and outputs it to the output information 101 as the optimum solution.

FIG. 2 is a flowchart showing processing of the state creation data reading unit of the state space search apparatus according to Embodiment 1 of the present invention.
FIG. 3 is a flowchart showing the processing of the focused state evaluation unit of the state space search apparatus according to Embodiment 1 of the present invention.
FIG. 4 is a flowchart showing processing of the adjacent state creation / evaluation unit of the state space search apparatus according to Embodiment 1 of the present invention.
FIG. 5 is a flowchart showing processing of the state transition unit of the state space search apparatus according to Embodiment 1 of the present invention.
FIG. 6 is a flowchart showing processing of the search continuation determination unit of the state space search apparatus according to Embodiment 1 of the present invention.
FIG. 7 is a flowchart showing processing of the optimum state output unit of the state space search apparatus according to Embodiment 1 of the present invention.

FIG. 8 is a diagram showing a physical image of the state space search apparatus according to Embodiment 1 of the present invention.
In FIG. 8, the storage medium 202 has 7 to 11 databases. The CPU 201 has 1 to 6 programs and is connected to the storage medium 202.

Next, processing of the state creation data reading unit 1 will be described with reference to the flowchart of FIG.
In step S11, data for searching is input. In step S12, an initial state of interest is set based on the data input in step S11. Next, in step S13, the evaluation function value of the best solution is initialized (a sufficiently large value is set for a minimization problem and a sufficiently small value is set for a maximization problem). Next, in step S14, an iterative counter L in the iterative process from the focused state evaluation unit 2 to the search continuation determination unit 5 is initialized.

Next, the focused state evaluation unit 2 will be described with reference to the flowchart of FIG.
In step S21, individual continuous values are determined corresponding to the combination of the state of interest by the quadratic programming method using the interior point method. In step S22, the solution obtained by the quadratic programming method using the interior point method is stored as an initial value of the quadratic programming method using the Active-set method.

Here, the interior point method and the Active-set method will be described.
First, the interior point method will be described. The interior point method handles the following standard form of optimization problems:

Min f (x) (Formula 1)
s. t. g (x) = 0 (Formula 2)
x + s−ω = 0 (Formula 3)
x ≧ 0 (Formula 4)
s ≧ 0 (Formula 5)
However,
s _i : slack variable introduced to convert upper limit constraint of element x _i of x into equality constraint ω: upper limit value of x

The above standard form does not include functional inequality constraints, but by introducing slack variables, functional inequality constraints can be converted into functional inequality constraints, as shown below. The standard format does not lose generality.

h _min ≦ h (x) ≦ h _max → h (x) −s = 0, h _min ≦ s ≦ h _max

In the standard form problem, the range of x is 0 ≦ x ≦ ω (the same applies to s). This can be realized by moving the coordinate origin of the variable to x _min and expanding / contracting the variable. Therefore, generality is not lost. In the optimal solution of the above problem, the following KKT (Karush-Kuhn-Tucker) condition needs to be satisfied.

g (x) = 0 (Formula 7)
x + s−ω = 0 (Formula 8)
x _i λ _xi = 0 (Equation 9)
s _i λ _si = 0 (Formula 10)
x ≧ 0 (Formula 11)
s ≧ 0 (Formula 12)
λ _x ≧ 0 (Formula 13)
λ _s ≧ 0 (Formula 14)
However,
μ: Lagrange multiplier corresponding to g (x) = 0 ν: Lagrange multiplier corresponding to x + s−ω = 0 λ _x : Lagrange multiplier corresponding to the lower limit constraint of x λ _s : Lagrange multiplier corresponding to the lower limit constraint of s

The interior point method simultaneously satisfies (Expression 6), (Expression 7), (Expression 8), (Expression 9), and (Expression 10) while keeping the variables x, s, λ _x , and λ _s in a non-negative region. This method solves x, μ, ν, λ _x , and λ _s and obtains an optimal solution. There is no need to give an approximate value of the optimal solution as an initial value. For large problems exceeding tens of thousands of variables, dozens of times In order to converge, it is generally the most convenient optimization method.

Subsequently, the Active-set method will be described.
In the Active-set method, the optimization problem of the standard format shown in the following (Formula 15) is handled.

Min f (x) (Formula 15)
s. t. gi (x) = 0, i = 1,..., I
x _min ≤ x ≤ x _max

The above standard form does not include functional inequality constraints, but as described above, by introducing slack variables, functional inequality constraints can be converted to functional equality constraints. Does not lose sex. In the standard format, upper and lower limits are given to the control variable x. However, if there is no limit, it is possible to give a sufficiently small _xmin or a sufficiently large _xmax. Does not lose generality. In the optimal solution of the above problem, the following KKT condition needs to be satisfied.

_{∇f + Σμ i ∇g i + λ} U - λ L = 0 ( Equation 16)
g _i (x) = 0 (Formula 17)
x _min ≦ x ≦ x _max (Formula 18)
λ _U ≧ 0 (Equation 19)
λ _L ≧ 0 (Formula 20)
However,
λ _U : A vector that stores a Lagrangian multiplier relating to the upper limit constraint of x, has a non-negative element at the element position of x where the upper limit constraint is active in the optimal solution, and the other elements are zero.
λ _L : A vector that stores a Lagrangian multiplier relating to the lower limit constraint of x, has a non-negative element at the element position of x where the lower limit constraint is active in the optimal solution, and the other elements are zero. Since the upper limit constraint and the lower limit constraint of x are not active at the same time, (λ _U −λ _L ) can be collectively expressed as λ. In this case, the lower limit constraint is related to the active element. Will have a non-positive value. When (Equation 16) is represented by λ, it is as follows.
∇f + Σμ _i ∇g _i + λ = 0 (Formula 16a)

  The Active-set method assumes inequality constraints that are active in the optimal solution (elements of the variable x in which the upper and lower limit constraints are active in the optimal solution since the standard form optimization problem is handled), and under that assumption (expression If x, μ, and λ that simultaneously satisfy 16a) and (Expression 17) are solved and inequality constraints ((Expression 18), (Expression 19), and (Expression 20)) that x and λ must satisfy are satisfied, If the inequality constraint that becomes active in the optimal solution can be predicted fairly accurately by an optimization method that reviews the assumption of the inequality constraint that is active in the optimal solution and repeats the process again It becomes effective.

The number of iterations of the Active-set method is approximately the number of different parts of the inequality constraints that are active between the optimal solution of the basic problem and the optimal solution of the optimization problem that is slightly different from the basic problem (variables attached to the upper and lower limits). The number of differences).
Further, since the Active-set method assumes a variable that sticks to the upper and lower limits (becomes a fixed value and is not a variable), the processing time per iteration in the Active-set method is substantially reduced. ^{It doubled} approximately (the number of number / variable variables not adhere Zhang above lower limit) of the processing time per iteration.
Since the number of iterations in the interior point method is generally about 40, assuming that half of the variables handled in the Active-set method are variables that stick to the upper and lower limits, the difference in the inequality constraints that are active as described above The Active-set method is advantageous in terms of processing time compared to the interior point method for the problem that the number (the number of differences between the variables attached to the upper and lower limits) is 160 or less.

Returning to FIG. 3, step S23 is a step of calculating an evaluation function value for the state of interest from the state of interest and the continuous value for the state of interest determined in step S21.
Step S24 determines whether or not the evaluation function value of the state of interest is better than the evaluation function value of the best solution stored in the previous search (small for a minimization problem / large for a maximization problem). If the evaluation function value of the target state is better than the evaluation function value of the best solution, the process proceeds to step S25. If not, the process branches to end the process of the target state evaluation unit 2. In step S25, the state of interest and its evaluation function value are stored as the best solution.

Next, the adjacent state creation / evaluation unit 3 will be described with reference to the flowchart of FIG.
In step S31, initialization of the counter J for counting the number of adjacent states is performed. In step S32, a transition from the target state to the adjacent state is prohibited by searching whether the adjacent state to be created or state change information for transition from the target state to the adjacent state is registered in the tabu list. Determine whether it is not done. If transition is prohibited, the process proceeds to step S37. If transition is possible, the process branches to step S33.
In step S33, one or more combinations are changed from the state of interest to create an adjacent state. In step S34, the continuous value for the adjacent state is optimized by performing quadratic programming using the active-set method using the initial value stored in step S22. In step S35, the evaluation function value of the adjacent state is calculated from the combination of adjacent states and the continuous value calculated in step S34. In step S36, state change information necessary for transition from the state of interest to the adjacent state and the evaluation function value of the adjacent state are stored.
In step S37, after the counter J for the number of adjacent states has been incremented by one, it is determined in step S38 whether or not the processing for all adjacent states has been completed. The process of the creation / evaluation unit 3 is ended. If it has not ended, the process returns to step S32 to branch to continue the process.

Next, the state transition unit 4 will be described using the flowchart of FIG.
In step S41, the state with the best evaluation function value among the adjacent states stored in the adjacent state creation / evaluation unit 3 is set as the next state of interest. In step S42, the state change information such as the adjacent state type and the state change part necessary for the transition from the target state to the next target state is stored in the tabu list, and the information already stored in the tabu list is updated. .

Next, the search continuation determination unit 5 will be described with reference to the flowchart of FIG.
In step S51, it is determined whether or not the iteration count L regarding the iteration process from the focused state evaluation unit 2 to the search continuation determination unit 5 is smaller than the iteration count upper limit LMAX. If L is smaller than LMAX, the process proceeds to step S52. If L is greater than or equal to LMAX, the iterative process from the focused state evaluation unit 2 to the search continuation determination unit 5 is terminated, and the process proceeds to the optimum state output unit 6. Branch. In step S52, the number of repetitions L is incremented by one.

Next, the optimum state output unit 6 will be described with reference to the flowchart of FIG.
In step S 61, the best solution obtained by the processing from the state creation data reading unit 1 to the search continuation determination unit 5 is extracted from the best solution storage database 8. In step S62, the extracted best solution is output to the output information 101 as a calculation result.

The output information 101 is an output result obtained by outputting the optimum solution obtained by the mechanism shown in the optimum state output unit 6 from the state creation data reading unit 1 in a form in which the state space search device is required.
This output result indicates that, for example, the power supply equipment and the demand for heat are matched so that the demand and supply amount of power are matched using the power supply equipment such as natural energy, secondary battery, gas engine, etc. Used to control the start / stop of power and the amount of power generation, and to control the start / stop of heat supply equipment and heat output so that the demand and supply of heat match using a heat supply equipment such as a boiler It is done.
In other words, when the state space search device is applied to these systems, the optimal solution is displayed to the operator via the GUI, or the power supply facility or the heat supply facility via the communication means such as LAN. It is used to output control commands such as start / stop commands.

FIG. 8 shows the relationship between the hardware of the state space search apparatus and each function of FIG. 1, and FIG. 8 will be described next.
The state creation data reading unit 1 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, and calls input information 100 necessary for creating a state on the CPU 201 from the state creation database 7. The CPU 201 creates an initial state of interest. Here, the state creation database 7 is formed in a storage medium 202 represented by a hard disk, a memory, or the like.

  The state-of-interest evaluation unit 2 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, and determines a continuous value for the state of interest by quadratic programming using the interior point method, and is obtained at that time The calculation result is stored in the Active-set method initial value database 9 and the evaluation function value of the state of interest is calculated. In addition, the best solution obtained by the previous search is called from the best solution storage database 8 on the CPU 201, and it is determined whether or not the evaluation function value of the state of interest is better than the called evaluation function value of the best solution. If the focused state is a better solution than the best solution, the focused state is stored in the best solution storage database 8. Here, each database of the best solution storage database 8 and the Active-set method initial value database 9 is formed in a storage medium 202 represented by a hard disk, a memory, or the like.

The adjacent state creation / evaluation unit 3 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, calls the tabu list set by the previous search from the tabu list database 11 to the CPU 201, and pays attention to it. It is determined whether or not it can be created as an adjacent state to the state, and if it is a neighboring state that can be created, after creating an adjacent state for the state of interest, an initial value is called from the Active-set method initial value database 9 and Active- By performing quadratic programming using the set method, a continuous value for the adjacent state is determined and an evaluation function value for the adjacent state is calculated.
Further, the created adjacent state, state change information for transitioning from the state of interest to the adjacent state, and the evaluation function value of the adjacent state are stored in the adjacent state database 10. Here, the adjacency state database 10 and the tabu list database 11 are formed in a storage medium 202 represented by a hard disk, a memory, or the like.

  The state transition unit 4 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, and the best evaluation among the adjacent states created by the neighboring state creation / evaluation unit 3 on the CPU 201 from the neighboring state database 10. Call a state with a function value and set it to the next state of interest. Further, the state change information for transitioning from the focused state to the next focused state is stored in the tabu list database 11 and the list information stored in the tabu list database 11 is updated.

  The search continuation determination unit 5 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, and the number of repetitions L regarding the iterative processing from the state-of-interest evaluation unit 2 to the search continuation determination unit 5 is from the repetition number upper limit LMAX. It is determined whether the number is small, and the number of repetitions L is incremented by one.

  The optimum state output unit 6 in FIG. 1 is a program that operates on the CPU 201 of the state space search apparatus, and calls the best solution stored in the best solution storage database 8 and outputs the best solution as a calculation result.

In the above description, the tabu search method has been described. However, the present invention is not limited to the tabu search method, and starts from an initial state of interest such as a problem space search method, a local search method, a genetic algorithm, and simulated annealing. It is possible to apply to a search method in which the state to be transitioned from the adjacent states obtained by changing the combination of these is determined and the next state of interest is sequentially repeated to search for the state with the best evaluation function value.
This is very effective in improving the processing speed, and a wider state space can be searched as compared with the prior art.

  According to the first embodiment, it is possible to obtain a continuous value of a state at high speed without reducing the accuracy of the solution, and it is possible to search a wider state space within a limited processing time.

Embodiment 2. FIG.
FIG. 9 is a block diagram showing a state space search apparatus according to Embodiment 2 of the present invention.
9, the adjacent state creation / evaluation unit 3 is changed to the adjacent state creation / evaluation unit 3 ′ in the configuration shown in FIG. Other configurations are the same as those in FIG.

FIG. 10 is a flowchart showing processing of the adjacent state creation / evaluation unit of the state space search apparatus according to Embodiment 2 of the present invention.
In FIG. 10, steps S31 to S33 and steps S35 to S38 are the same processes as those in FIG. In FIG. 10, processing of steps S341 and S342 is executed instead of step S34 of FIG.

FIG. 11 is an explanatory diagram for explaining the processing of the adjacent state creation / evaluation unit of the state space search apparatus according to Embodiment 2 of the present invention.
In FIG. 11, the number of state change points from the focused state to the adjacent state 2 is 4. An adjacent state 1 is created from the focus state by the adjacent state creation procedure 1, and an adjacent state 2 is created from the adjacent state 1 by the adjacent state creation procedure 2. The number of state change points from the adjacent state 1 to the adjacent state 2 is 2.
Here, the adjacent states 1 and 2 are adjacent states for a certain state of interest. The adjacent state 1 is an adjacent state in which two states are changed from 1 to 2 from the focused state. Adjacent state 2 is a state in which two states are changed from 1 to 2 from the state of interest and are further changed from two states 1 to 0. When determining the continuous value related to the adjacent state 2, the state change from the state of interest to the adjacent state 2 (continuous value upper and lower limit constraint change) than the number of places 4 (continuous value upper and lower limit constraints) Change) Number of places 2 is less.

  In the second embodiment, for example, when adjacent states that change a plurality of locations at the same time as shown in FIG. 11 are sequentially created and the continuous values are determined, the calculation stored when the continuous value of the adjacent state that was created last time is determined. A quadratic programming method using the following Active-set method is performed using the result.

Next, the processing of the adjacent state creation / evaluation unit 3 ′ of FIG. 9 will be described using the flowchart of FIG.
After step S31 to step S33 are executed in the same manner as in FIG. 4, step S341 is the initial value stored in step S22 from the Active-set method initial value database 9 in FIG. 9, or the initial value stored in step S342 described later. A continuous value for the adjacent state is calculated by calling a value, that is, the latest initial value at the time point, and performing quadratic programming using the Active-set method.
That is, for the adjacent state (first adjacent state) created first from the state of interest, a solution obtained by optimizing continuous values by quadratic programming using the interior point method is obtained in step S22. Optimize the continuous value using the saved initial value. In addition, for the adjacent state (second adjacent state) created after the second state from the state of interest, the solution obtained by optimization of the continuous value by the quadratic programming method using the immediately preceding Active-set method is obtained. As an initial value, a continuous value is optimized.
In step S342, the calculation result of the quadratic programming method calculated in step S341 is used as the initial value for performing the quadratic programming method using the next Active-set method in the Active-set method initial value database 9 of FIG. save.
Next, steps S35 to S38 are executed in the same manner as in FIG.

  According to the second embodiment, for example, when sequentially creating adjacent states that simultaneously change a plurality of locations as shown in FIG. 11 and determining the continuous values, the calculation results stored when determining the continuous values of the state of interest It is considered that the calculation result stored when determining the continuous value of the adjacent state created last time is closer to the optimum solution condition than the initial value, and as a result, the result using the Active-set method is used. By reducing the number of iterations of the next programming method, the effect of shortening the processing time can be obtained.

Embodiment 3 FIG.
FIG. 12 is a flowchart showing processing of the adjacent state creation / evaluation unit of the state space search apparatus according to Embodiment 3 of the present invention.
In FIG. 12, steps S31 to S33 and steps S35 to S38 are the same processes as those in FIG. In FIG. 12, the process of step S343 is executed instead of step S34 of FIG.
Hereinafter, the description will be given focusing on the difference from the first embodiment.

  The third embodiment is different from the first embodiment in step S343 in FIG. In step S343, a continuous value for the adjacent state is calculated by performing quadratic programming using the active-set method using the initial value stored in step S22. In the quadratic programming method using the Active-set method, continuous values are optimized by iterative calculation, and the number of iterative calculations in the quadratic programming method using the Active-set method exceeds a predetermined upper limit of the number of iterations. In this case, the continuous value for the adjacent state is calculated by switching to the quadratic programming method using the interior point method.

Assuming that the number of iterations of a general interior point method is approximately 40, solve a derived problem (an optimization problem with slightly different conditions from the basic problem) in a situation where the optimal solution of the basic problem is known. When doing so, the relationship between the number of variables of the basic problem, the number of differences between the variables that stick to the upper and lower limits of the optimal solution of the basic problem and the derived problem, and the number of variables that do not stick to the upper and lower limits (Equation 21) When satisfying the above, it is more advantageous in terms of processing speed to optimize using the Active-set method than to use the interior point method.
However, the number of differences between the variables that stick to the upper and lower limits and the number of variables that do not stick to the upper and lower limits are values that are assumed based on the difference in conditions between the optimal solution of the basic problem and the derived problem. It is necessary to have a likelihood of about 10 to 20% for the number of different parts of the variable that stick to and the number of variables that do not stick to the upper and lower limits.

(Number of differences between variables that stick to upper and lower limits) x (number of variables that do not stick to upper and lower limits / number of variables) ² <40 (Formula 21)

  Further, when the number of repetitions of the Active-set method reaches the number satisfying the condition of (Equation 22), the above assumption is not satisfied, and it is unclear how many iterative calculations are required thereafter. In order to avoid the risk of a significant increase in processing time in such an unexpected situation, when the number of repetitions of the Active-set method satisfies the condition of (Equation 22), the optimization by the Active-set method is stopped. , Switch to optimization by interior point method.

Number of repetitions> 40 × (number of variables / number of variables not sticking to upper and lower limits) ² (Formula 22)

  According to the third embodiment, the configuration as described above can prevent a significant increase in processing time even in the case of an unexpected situation as described above.

Embodiment 4 FIG.
FIG. 13 is a block diagram showing a state space search apparatus according to Embodiment 4 of the present invention.
In FIG. 13, in the configuration of FIG. 1, the adjacent state creation / evaluation unit 3 is changed to an adjacent state distribution unit 3a to an adjacent state aggregation unit 3e. Other configurations are the same as those in FIG.

FIG. 14 is a diagram showing a physical image of the state space search apparatus according to Embodiment 4 of the present invention.
In FIG. 14, 202, 1, 2, 4 to 11 are the same as those in FIG. In FIG. 14, the adjacent state distribution unit 3a, the adjacent state creation / evaluation unit 3b, and the adjacent state aggregation unit 3e are on the CPU 1 (201), and the adjacent state creation / evaluation unit 3c is on the CPU 2 (203). The evaluation unit 3d operates on the CPU 3 (204).
Hereinafter, the description will be given focusing on the difference from the first embodiment.

  The fourth embodiment relates to a state space search apparatus using a tabu search method that operates on hardware having three CPUs 201, 203, 204 and one storage medium 202 as shown in FIG. FIG. 14 relates to the state space search apparatus of FIG. 13 and shows the relationship between hardware and each function of FIG.

Next, each function will be described with reference to FIG.
The state creation data reading unit 1, the target state evaluation unit 2, the state transition unit 4, the search continuation determination unit 5, and the optimum state output unit 6 are the same as those shown in the first embodiment, and on the CPU 1 (201). It is a program that runs.

The adjacent state distribution unit 3a assigns each adjacent state of the CPU 1 (201), CPU 2 (203), or CPU 3 (204) to a plurality of adjacent states obtained by changing one or more combinations with respect to the target state. This is a mechanism for determining which CPU to create and evaluate and assigning to each CPU, and operates on the CPU 1 (201).
The adjacent state creation / evaluation unit 3b is a program that operates on the CPU 1 (201), the adjacent state creation / evaluation unit 3c is a program that operates on the CPU 2 (203), and the adjacent state creation / evaluation unit 3d , A program that operates on the CPU 3 (204), and operates in the same manner as the adjacent state creation / evaluation unit 3 shown in the first embodiment.
The adjacent state aggregation unit 3e is a program that operates on the CPU 1 (201). The adjacent state creation / evaluation unit 3b, the adjacent state creation / evaluation unit 3c, and the adjacent state created by the adjacent state creation / evaluation unit 3d The state change information for transition from the state to the adjacent state and the evaluation function value of the adjacent state are stored in the adjacent state database 10.

  According to the fourth embodiment, by configuring as described above, the same effects as those of the first embodiment can be obtained even when parallel operations are performed by a plurality of CPUs.

  The present invention is applied to various optimization designs such as logistics, LSI optimum wiring determination, generator start / stop problems and system configuration creation in the power system, various optimization plans such as gas and water supply route creation, and optimum control.

It is a block diagram which shows the state space search apparatus by Embodiment 1 of this invention. It is a flowchart which shows the process of the state creation data reading part of the state space search device by Embodiment 1 of this invention. It is a flowchart which shows the process of the attention state evaluation part of the state space search apparatus by Embodiment 1 of this invention. It is a flowchart which shows the process of the adjacent state preparation and evaluation part of the state space search apparatus by Embodiment 1 of this invention. It is a flowchart which shows the process of the state transition part of the state space search apparatus by Embodiment 1 of this invention. It is a flowchart which shows the process of the search continuation determination part of the state space search apparatus by Embodiment 1 of this invention. It is a flowchart which shows the process of the optimal state output part of the state space search apparatus by Embodiment 1 of this invention. It is a figure which shows the physical image of the state space search apparatus by Embodiment 1 of this invention. It is a block diagram which shows the state space search apparatus by Embodiment 2 of this invention. It is a flowchart which shows the process of the adjacent state preparation and evaluation part of the state space search apparatus by Embodiment 2 of this invention. It is explanatory drawing explaining the process of the adjacent state preparation / evaluation part of the state space search apparatus by Embodiment 2 of this invention. It is a flowchart which shows the process of the adjacent state preparation and evaluation part of the state space search apparatus by Embodiment 3 of this invention. It is a block diagram which shows the state space search apparatus by Embodiment 4 of this invention. It is a figure which shows the physical image of the state space search apparatus by Embodiment 4 of this invention.

Explanation of symbols

1 state creation data reading unit, 2 state of interest evaluation unit,
3, 3 ′, 3b, 3c, 3d adjacent state creation / evaluation unit,
3a Adjacent state distribution unit, 3e Adjacent state aggregation unit,
4 state transition unit, 5 search continuation determination unit, 6 optimum state output unit,
7 database for state creation, 8 best solution storage database,
9 Active-set method initial value database,
10 Adjacency state database, 11 Tabu list database,
100 input information, 101 output information, 200 state search device,
201, 203, 204 CPU, 202 Storage medium.

Claims (5)

  Starting from an initial focus state in a state space consisting of a combination of a plurality of discrete values and a continuous value determined corresponding to the discrete value combination, the combination of the focus states is changed. In the state space search device that searches for a state with the best evaluation function value by sequentially determining the next state of interest by determining the state to be transitioned from the adjacent states obtained in the above, for the state of interest , The attention state evaluation means for optimizing the continuous value by quadratic programming using the interior point method, and the solution obtained by the optimization of the continuous value by the attention state evaluation means for the adjacent state A state space search apparatus comprising: an adjacent state evaluation unit that optimizes the continuous value by a quadratic programming method using an Active-set method as an initial value.   The adjacent state evaluation unit is first created from the target state by a quadratic programming method using the Active-set method with the solution obtained by the optimization of the continuous value by the target state evaluation unit as an initial value. The continuous value is optimized for the first adjacent state, and the second adjacent state created after the second state from the state of interest is a second order using the previous Active-set method. 2. The continuous value is optimized by a quadratic programming method using the Active-set method, with a solution obtained by optimization of the continuous value by a programming method as an initial value. State space search device.   The quadratic programming method using the Active-set method of the adjacent state evaluation means optimizes the continuous value by iterative calculation at the time of optimization of the continuous value for the adjacent state, and the number of repeated calculations. However, when the value exceeds a predetermined value, the quadratic programming method using the Active-set method is switched to the quadratic programming method using the interior point method to optimize the continuous value for the adjacent state. The state space search device according to claim 1 or 2, wherein:   The adjacent state evaluation means operates on a CPU, and optimization of continuous values for the plurality of adjacent states is executed in parallel on the plurality of CPUs. The state space search device according to claim 1. Starting from an initial focus state in a state space consisting of a combination of a plurality of discrete values and a continuous value determined corresponding to the discrete value combination, the combination of the focus states is changed. In the state space search method for determining a state with the best evaluation function value by sequentially determining the next state of interest by determining the state to be transitioned from the adjacent states obtained in the above, , A first procedure for optimizing the continuous value by quadratic programming using the interior point method, and a solution obtained by optimizing the continuous value by the first procedure for the adjacent state A state space search method comprising a second procedure for optimizing the continuous value by a quadratic programming method using an Active-set method as an initial value.

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