JP2002288625A - Multipurpose optimization method, program and planning device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a multipurpose optimization method, especially under an non-linear choice function. SOLUTION: This multipurpose optimization method is furnished with (a) a step for providing a neutral network 20, (b) a step for giving a plural number of input data x1 , x2 concerning a multipurpose optimizing problem to the neutral network, (c) a step with which the neutral network learns as a result of (b) and (d) a step for providing the neutral network to approximate the choice functions in the multipurpose optimization problem, as a result of (c).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a multi-objective optimization method, a program, and a plan making device, and more particularly, to a multi-objective optimization method, a program, and a plan making device capable of approximating a nonlinear preference function in the multi-objective optimization. .

[0002]

2. Description of the Related Art In a multi-objective optimization in which a plurality of objectives exist, if only one objective is optimized, the other objectives often become undesired. Therefore, it is necessary to optimize while balancing the objectives. At this time, the solution selected for some reason is called a preferred solution. To achieve this balance some sort of comparison between objectives is required, but comparisons between values determined by different criteria are often difficult.

In order to numerically analyze the preferred solution,
At present, multi-objective problems are formally transformed into single-objective problems because they have to rely on optimization methods for single-objective problems.

[0004] The following preference analysis method has a major difference in how to convert a multi-purpose into a single purpose. (1) weight parameter method; linear utility function method (2) ε constraint method (3) lexicographic array method Lexicographic (4) goal programming method (5) goal reaching method Goal attainment m
method (6) Utility function method (7) Surrogate-Worth method
Trade-off method)

Conventionally, in the multi-objective optimization, a method of adjusting the weights mainly by taking a linear weighted sum of the objective functions and a method of introducing a preference function for integrating (single-objective) the objective functions are often used. Used.

As a preference function, for example, a method using a fuzzy target has been proposed (Sakakazu et al., "Fuzzy Multi-Objective Combination Optimization by Improved Genetic Algorithm",
Journal of the Japanese Fuzzy Association, vol. 6, no. 1, pp. 1
77-186, 1994).

[0007]

However, in the conventional method, since the preference function is assumed to be linear, a nonlinear preference cannot be expressed.

There is a need for a multi-objective optimization method under a nonlinear preference function. There is a need for a multi-objective optimization method under a nonlinear preference function that can flexibly cope with a change in the multi-objective optimization problem itself. There is a need for a plan formulation device that can obtain various plans as a preference solution for multi-objective optimization under a nonlinear preference function.

It is an object of the present invention to provide a multi-objective optimization method under a preference function. Another object of the invention is to provide a multi-objective optimization method, especially under a non-linear preference function. Still another object of the present invention is to provide a multi-objective optimization method under a nonlinear preference function that can flexibly cope with a change in the multi-objective optimization problem itself. Still another object of the present invention is to provide a plan drafting apparatus capable of obtaining various plans as preference solutions of multi-objective optimization under a nonlinear preference function.

[0010]

Means for solving the problem are described as follows. The technical matters corresponding to the claims in the expression are appended with parentheses (), numbers, symbols, and the like. The numbers, symbols, etc. clarify the correspondence / correspondence between the technical matter corresponding to the claim and the technical matter of at least one of the plural forms of implementation. It is not intended to show that technical matters are limited to the technical matters of the embodiments.

The multi-objective optimization method of the present invention comprises: (a) providing a neural network (20);
(B) A plurality of input data (x1, x2) relating to a multi-objective optimization problem are added to the neural network (20).
(C) learning by the neural network (20) as a result of (b); and (d) as a result of (c), approximating a preference function in the multi-objective optimization problem. Obtaining a neural network (20).

In the multi-objective optimization method according to the present invention, in the above (b), the neural network (20)
Are the respective objective evaluation values in the multi-objective optimization problem.

In the multi-objective optimization method according to the present invention, in the above (b), the neural network (20)
Are each a Pareto solution selected from a Pareto solution set in the multi-objective optimization problem.

In the multi-objective optimization method according to the present invention, the Pareto solution is selected based on a result of performing a Pareto solution analysis on the Pareto solution set.

In the multi-objective optimization method according to the present invention, the learning in (c) is supervised learning, and the learning in (b) is performed.
Converts teacher data (z) corresponding to the plurality of input data (x1, x2) into the neural network (20).
The step of providing

In the multi-objective optimization method according to the present invention, the teacher data (z) includes the plurality of input data (x1, x
The preferred solution to 2) by the decision maker for the multi-objective optimization problem.

In the multi-objective optimization method according to the present invention, the step (c) is performed again when the preference criterion of the multi-objective optimization problem changes.

In the multi-objective optimization method according to the present invention, the step (c) is performed again when the multi-objective optimization problem changes.

The multi-objective optimization method of the present invention comprises: (a) providing a neural network (10);
(B) A plurality of input data (x1, x2) relating to a multi-objective optimization problem are added to the neural network (10).
(C) learning by the neural network (10) as a result of (b); and (d) as a result of (c), approximating a preference function in the multi-objective optimization problem. Obtaining a neural network (10), wherein the plurality of input data (x1, x2, y1, y2) are a first input data (x1, x2) and a second input data (y1, y2).
2) and the first input data (x1, x2)
Is an evaluation index of the multi-objective optimization problem, and the second
Are input data (y1, y2) for adjusting the weight of the first input data (x1, x2) as the evaluation index.

The multi-objective optimization method of the present invention comprises: (a) providing a neural network (10);
(B) A plurality of input data (x1, x2) relating to a multi-objective optimization problem are added to the neural network (10).
(C) learning by the neural network (10) as a result of (b); and (d) as a result of (c), approximating a preference function in the multi-objective optimization problem. Obtaining a neural network (10); (e) providing a group of individuals each having fitness for the multi-objective optimization problem; and (f) the individual having the higher fitness from the individual population. (G) performing a solution search using a genetic algorithm that performs a plurality of generations of a natural selection operation so that the selection probability is high; and (g) performing the operation of a single generation of the plurality of generations in the (f). Inputting the result of the execution to the neural network (10) obtained as a result of the above (d); As a result, the step (f) is performed by regarding the individual having a high evaluation (14) output from the neural network (10) as the individual having the high fitness.

The multi-objective optimization method of the present invention includes: (i) providing a plurality of sample data; (j) providing a neural network (20);
(K) In the neural network (20), a plurality of input data (x1, x2) relating to a multi-objective optimization problem selected from the plurality of sample data, and a teacher corresponding to the plurality of input data (x1, x2) Providing data (z); (l) the neural network (20) performing supervised learning as a result of (k); and (m) the neural network (20) as a result of (l). ) And an error between the value output from the plurality of sample data and an evaluation value of the plurality of sample data; (n) a step of executing the above (k) to (m) a plurality of times; As a result,
The plurality of input data (x1, x2) used when the error is small, and the plurality of input data (x1, x2)
(2) using the teacher data (z) corresponding to (2) to train the neural network (20); and (p) approximating a preference function in the multi-objective optimization problem as a result of (o). Obtaining said neural network (20).

In the multi-objective optimization method of the present invention, when the above (n) is performed, a solution search using a genetic algorithm is performed.

In the multi-objective optimization method according to the present invention, said neural network (1) approximating said preference function
0) approximates the nonlinear preference function.

In the multi-objective optimization method according to the present invention, the neural network is an RBF network (1
0).

The program of the present invention is a program for causing a computer to execute each step of the multi-objective optimization method of the present invention.

The plan drafting apparatus of the present invention is a plan drafting apparatus for drafting a plan defined by a multi-objective optimization problem, comprising a neural network (20), wherein the neural network (20) includes A plurality of input data (x1, x
2) is given, and as a result, the neural network (20) learns, and the learned neural network (20) approximates the preference function in the multi-objective optimization problem, and based on the approximated preference function, Output the plan.

In the plan drafting apparatus of the present invention, the plan includes any one of a travel plan, a facility deployment plan, a facility allocation plan, a physical distribution plan, and a design plan.

[0028]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a plan drafting apparatus according to the present invention will be described with reference to the accompanying drawings.

The present embodiment is a plan drafting apparatus capable of obtaining various plans as preference solutions for multi-objective optimization under a nonlinear preference function. Here, the various plans include a travel plan, a facility arrangement plan, a facility allocation plan, a distribution plan, a design (design) plan, a search method plan, and the like.

First, the preferred solution in the multi-objective optimization will be described.

In the Pareto solution set, a particular solution that is introduced as a certain viewpoint (preference criterion) and is regarded as optimal from that viewpoint is referred to as a preference solution (Preference Solution). In conclusion, the preferred solution is the optimal solution when multiple objectives are integrated into a single objective.

However, in the actual situation of a multipurpose problem, the decision maker often does not have a foreseeable and rational value criterion enough to integrate the multipurpose into a single purpose prior to analysis. Therefore, pareto solution analysis is performed, and based on the analysis, some preference criterion is introduced between multipurpose values to make a comparison judgment.

The general preference criterion is yet to be determined and should be carefully determined each time according to the semantics of the planning problem encountered. In other words, in order to obtain a preference solution, the decision maker must determine an appropriate preference criterion by taking in consideration such as value analysis and the results thereof and the results of the Pareto analysis.

The preference criterion in the multi-objective optimization cannot be expressed by a mathematical expression. Also, when trying to express a preference criterion using a plurality of IF statements in programming, an enormous number of IF statements are required.

The preference of a decision maker has a certain distribution or probability. Focusing on this, a neural network is suitable for expressing the distribution. In the neural network, when a user who interactively selects one that matches the preference of the decision maker from a plurality of sample data, the characteristic of the preference of the decision maker can be extracted based on the result of the selection. If the coupling coefficient of the neural network is adjusted so as to reflect the feature, a preference solution reflecting the preference of the decision maker is output. From this, it can be said that the neural network is suitable for realizing the nonlinear preference function in the multi-objective optimization.

By repeatedly selecting, from the plurality of sample data, ones that meet the preference of the decision maker, and repeatedly making the neural network learn the selection result,
A neural network is constructed in which an output (an approximation of a non-linear preference function) reflecting the decision maker's preference is obtained.

The functional characteristics of the neural network are as follows. Taking a hierarchical neural network as an example, a neural network is a circuit network in which simple arithmetic elements called units modeling nerve cells are interconnected by weighted links corresponding to synapses. Each unit performs a product-sum operation in which input data or an input from another unit is multiplied by a weight and added, and the statistical input is converted by a non-linear function and output. The result output in this way is initially random, but the weight coupling (coupling coefficient) between the units is adjusted so as to reduce the error from the desired output (called a teacher signal). Such a process is called learning, and a data pair of an input and a teacher is sequentially given to a neural network, and a correct output is output as learning (load adjustment) is repeated.

The functional features of such a neural network include: a high degree of adaptability based on a learning function.・ Information expression that can tolerate vague / incomplete information. -High parallelism and real-time processing based on it. -Robustness by expressing information in a distributed manner. And the like.

The neural network excels at human-like information processing, such as comprehensive judgment from a large amount of information and high-speed and flexible processing of ambiguous pattern information. Human information processing, more precisely, is right-brain-like processing. That is, it is said that the left brain is good at processing information in an analytical order, and the right brain is good at processing information simultaneously as a whole. A Neumann computer is good at symbol manipulation and logical processing and performs sequential processing, so it is left-brain-like. A neural network is good at pattern processing and makes comprehensive judgments, so it can be considered right-brain-like.

Next, the basic theorem regarding the function approximation ability of the neural network will be described. Here, the function approximation capability of the feedforward neural network will be described.

Any function can be approximated with high accuracy by a feedforward neural network composed of three layers, an input layer, a hidden layer, and an output layer. However, to increase the approximation accuracy, the number of elements in the intermediate layer must be increased.

In general, most of circuit theory and signal theory are directed to linear circuits and linear signal processing systems.
Linear systems can be analyzed by linear algebra theory,
The system behavior can be grasped quantitatively and theoretically. This (analysability) is an advantage of linear systems,
Paradoxically, what can be theoretically analyzed is that the behavior of a linear system is simple, and there is naturally a limit to what can be done with a simple system. If you try to get out of the linearity and do something more sophisticated, you have to use nonlinear systems that are difficult to analyze theoretically. In that case, the method is often constructed by relying on ad hoc and empirical devices.

In a neural network, computational power is enhanced by introducing nonlinearities in a limited manner, while retaining the analyticity that is an advantage of linear systems. The ability to approximate an arbitrary function in a three-layer network is also due to the non-linearity. If the components of the neural network are linear, the function approximation capability is severely limited. For example, the non-linear function sigmoid (z) used in the component is changed to a linear function f
When (z) = az is replaced and the element operates according to the following equation, the ability to approximate an arbitrary function cannot be obtained regardless of the number of elements or the number of layers.

(Equation 1)

(Equation 2)

(Equation 3) Where s is the intracellular potential of the neuron and x
_n is an input signal given to the neuron from another element or the outside, w _n is a weight (coupling coefficient), y is an output from the neuron, and θ is a threshold value.

In the neural network, in the above equation, only the form of the one-variable function f (z) is changed to introduce nonlinearity. For example, in the analog model, f is a sigmoid function. In the discrete model, a step function is used. Both functions are non-linear functions. By introducing nonlinearity in only a part of the whole operation, the neural network has gained the ability to approximate an arbitrary function.

A multivariable function that provides one output for M input variables is written as f (x ₁ , x ₂ ,..., X _M ). There is a three-layer feedforward neural network that approximately realizes an arbitrary given multivariable function. As shown in FIG. 2, M input variables x ₁ ,
x _2, ... each of _{x M,} theta ₁ in the neural network is input to the M non-linear elements θ ₂ ... θ _M. The subsequent stage of the M nonlinear elements is a linear element.

Learning of a neural network is to obtain a set of coupling coefficients that gives an appropriate response according to an input. Neural network learning includes supervised learning,
Unsupervised learn
ing).

In the supervised learning, data is successively given to the input side of the neural network, and at the same time, a value to be output (ie, a model) is given to each input data, and the output from the neural network corresponds to the input. That is, the coupling coefficient is adjusted to have an appropriate value. This model data is usually called “teacher data”.

For supervised learning of a hierarchical neural network, an error back pr
Opposition method (BP method)
There is a highly versatile learning method.

In the unsupervised learning, data is successively given to the input side of the neural network to form a network that selectively responds to the case data, and no example is given. This function is also called self-organization.

The error backpropagation method prepares a large number of sets of modeled data, and sets a maximum value such that, when given input data to the neural network, the square error between the output value of the neural network and the teacher data is reduced. "Correcting Coupling Coefficient by Descent Method" is repeated many times to determine an optimal set of coupling coefficients.

The general learning procedure of the BP method is as follows.

Initialization: (Step 0) Initial values are given to all the coupling coefficients (normally, they are randomly set using random numbers).

Repetition: (Step 1) One piece of data is taken out and inputted to the neural network, and the output from the neural network is obtained. (Step 2) The output value is compared with the teacher data to determine an error. (Step 3) Correct the value of the coupling coefficient so as to reduce the error (correction is performed sequentially from the side closer to the output layer toward the input layer, and the correction amount is obtained by the steepest descent method). (Steps 1 to 3 are repeated for all data) (Step 4) End determination: When the sum of errors over all data becomes equal to or less than a preset value, the iteration is terminated. Alternatively, if the number of repetitions reaches a preset value, the repetition is terminated. (If the end determination is not satisfied, return to step 1 and perform steps 1 to 3)

In order to execute the above algorithm, it is necessary to know how the output value is determined from the value entered in the input layer, and how the change in the input value or the coupling coefficient causes the output value to change. is there. When these are known, it is known how much the coupling coefficient should be changed to compensate for the difference between the output value and the teacher data, and the amount to be corrected can be determined.

Next, a case where a neural network is used to approximate a nonlinear preference function indicating a preference solution of the multi-objective optimization will be described with reference to FIG.

FIG. 1 shows the configuration of the neural network of the present embodiment. In the present embodiment, the multi-purpose (3
(Purpose) Approximate a nonlinear preference function in optimization. 3
The input layer is a three-layer neural network consisting of three neurons, three hidden neurons and one output layer neuron according to the number of objectives. The number of neurons in the input and output layers is almost inevitably determined from a given problem. How many neurons in the hidden layer are needed generally cannot be determined without careful consideration.

First, in the neural network of FIG. 1, initial values of coupling coefficients are given. X1, x2, and x3 are input to the three neurons in the input layer, respectively. Also, the value of Z output from the neural network is given as teacher data.

X1 is an evaluation value (object evaluation value) in the first objective function. x2 is an evaluation value in the second objective function. x3 is an evaluation value in the third objective function.

Alternatively, each of x1, x2, and x3 can be a Pareto solution selected from a Pareto solution set in the three-objective optimization. In this case, when selecting Pareto solutions x1, x2, and x3 from the Pareto solution set, x1, x2, and x3 can be selected based on the result of performing Pareto solution analysis on the Pareto solution set. .

Here, x1, x2, and x3 input to the neural network are shown to the decision maker as sample data. The value of Z reflecting the preference of the decision maker for these x1, x2, and x3 is given as teacher data. By giving the teacher data Z, the value of each coupling coefficient of the neural network is adjusted, and the error between the value of Z actually output from the neural network and the value of the teacher data Z reflecting the preference of the decision maker is given. Reduce.

As described above, "sample data x1, x
2, and Z that reflects the preference of the decision maker when x3 is input is given as teacher data. ”Is performed by using a plurality of combinations of other sample data and teacher data (x1a,
x2a, x3a, za), (x1b, x2b, x3b,
zb), (x1c, x2c, x3c, zc),... are repeated in the same manner as described above.

By correcting the coupling coefficient by performing learning a plurality of times in this manner, any given input data x1m, x1m
When 2m and x3m are input, the error between Z that reflects the preference of the decision maker and Z that is actually output is reduced. Thereby, the neural network can express the preference criterion of the decision maker with higher accuracy.

As described above, by using the neural network which is an approximation method of the nonlinear function, it is possible to realize the nonlinear preference function in the multi-objective optimization. In the present embodiment, one of the points is that a neural network, which is a nonlinear function approximation method, is applied when realizing a nonlinear preference function in multi-objective optimization.

Here, what is applied can be an RBF network that is part of a neural network. The RBF network and the neural network are basically used in the same manner. However, the RBF network learns faster than the neural network. Further, the RBF network has a simple structure and is suitable for hardware implementation.

The function approximation in the selection process of the multi-objective optimization is RB
If you use F network or neural network,
By performing relearning or additional learning, for example, the following effects (1) to (4) can be obtained.

(1) Even when the selection tendency of the decision maker (preference criteria) has changed, the preferred solution which reflects the decision maker's preference at that time in the best way by re-learning or additional learning. Obtainable. (2) It is possible to cope with a sudden event being added in the course of learning, an increase in the number of objective functions in the middle, a change in the purpose itself, a change in constraint conditions, and the like. A sudden event is, for example,
It is conceivable that a secondary disaster occurs afterwards in the route problem due to a collection request during delivery or in a facility arrangement problem in the event of a disaster. (3) A preference function can be generated in real time even under these constantly changing situations. (4) It can respond to changes on the time axis. Even if the constraint condition changes with time, the preference function changes in real time so as to follow the change.

The learning of the neural network will be described. As for the learning method itself, conventional methods can be widely applied. In addition to the BP method (iterative learning), a method of allocating a coupling coefficient to a gene and directly determining an optimal set of coupling coefficients by GA is also applicable. Unsupervised learning (for example, reinforcement learning) is also applicable.

However, the BP method is not suitable for those whose structure is not well understood, such as preference. This is because the BP method easily falls into local minimum depending on the initial value of the weight. In that sense, it is more appropriate to learn using a GA that allows a wider search. GA is suitable for re-learning and for environmental changes. In particular, good results have been obtained with the combination of the RBF network and the GA.

With respect to unsupervised learning, a preference structure can be created by outputting a positive reinforcement signal when evaluated as good and outputting a negative reinforcement signal when evaluated as bad.

Next, with reference to FIG. 3 and FIG. 4, a travel basic planning will be described as an application example of the present embodiment.

For example, even if it is decided to go to the United States, there are various ways to go to a specific tourist destination in the United States (destination). For example, the preferences of the people who go on a trip vary from person to person, and the taste (selection) of the destination changes depending on the time and season.
In addition, destinations will change depending on the trend of the year (for example, this year the countryside is popular, so a plan to go around the suburbs slowly is preferred).

In this application example, even when there are many conditions to be considered when determining a travel plan, it is possible to provide a travel plan as a preferred solution in which the preferences of the decision maker are reflected by balancing these multipurposes. Is what you do.

As shown in FIG. 3, in this application example, first,
The destination is selected by a genetic algorithm (GA). The GA determines which sightseeing spot (single or plural) is the destination among the sightseeing spots 1 to N (see reference numeral 11).

Here, it is assumed that three tourist destinations of New York, Las Vegas, and Los Angeles have been determined as destinations of the US tour plan. The United States tour plan consisting of these three tourist destinations is output as reference numeral 11.

Next, based on the United States tour plan (target value) output as the reference numeral 11, the evaluation index data 12 included in the United States tour plan can be obtained mechanically and without the intention of the decision maker. Automatically extracted.

The evaluation index data 12 is a value that is determined objectively based on the output value (S1) from the GA. The evaluation index data 12 includes data such as the number of days, the stay rate, the amount of movement, and the attractiveness.

In the above description, the number of days is the number of days required for sightseeing at three sightseeing spots determined as the destination. The stay rate is a ratio of days that can be stayed at the remaining one sightseeing spot in relation to the number of days required for the other two sightseeing spots in the entire itinerary plan of the United States. The moving amount and the moving time are the moving amount and the moving time when moving between the three sightseeing spots. Attraction is reflected in the previous year's trip questionnaire to the same area for each of the three tourist destinations.

Next, the destination 11 is evaluated based on the evaluation index data 12 extracted from the target value 11 output from the GA. The weighting of each evaluation index data 12 used at the time of this evaluation is changed by, for example, a consideration condition 13 such as a target age and a travel time.

For example, if the target age (13) of the US tour plan for the destination 11 is an elderly person, a plan with a high stay rate and a small amount of travel is preferred, so that the preference is reflected. Change the weight of the stay rate and the amount of movement.

The destination 11 output from the GA is evaluated based on the evaluation index data 12 and the weighting of the evaluation index data 12, reflecting the consideration conditions 13 such as the target age and travel time (reference numeral). 14).

Evaluation 1 for destination 11 described above
4 is performed in the RBF network 10 shown in FIG. The input layer of the RBF network 10 has a destination 11
(X1, x
2, x3) and consideration conditions 13 for the destination 11
(Y1, y2, y3) are input. The evaluation 14 for the destination 11 is the RBF network 1
Output from 0 to Z.

For example, the input data to the RBF network 10 is as follows. x1 is the destination 11
Is the number of days. x2 is the stay rate for the destination 11. x3 is the movement amount of the destination 11. y1 is the target age for the destination 11. y2 is a travel time for the destination 11.

Here, x1, x2, x3, y1, y2, and y3 input to the RBF network 10 are shown to the decision maker as sample data. These x1, x2,
A value of Z reflecting the decision maker's preference for x3, y1, y2, and y3 is provided to the RBF network 10 as teacher data. By giving the teacher data Z, the RBF
The value of each coupling coefficient of the network 10 is adjusted to reduce the error between the value of Z actually output from the RBF network 10 and the value of the teacher data Z reflecting the preference of the decision maker.

As described above, "sample data x1, x
2, Z3, y1, y2, and y3 are input as teacher data, reflecting the preference of the decision maker. "For the other destinations 11, the same operation is repeated. By correcting the coupling coefficient by performing learning a plurality of times in this manner, data x1m, x2m, x3m, y1m, y2m, y for a given destination 11 can be obtained.
When 3m is input, the error between Z that reflects the decision maker's preference and Z that is actually output is reduced. Thereby, the accuracy of the RBF network 10 increases.

That is, for each of the plurality of destinations 11 output from the GA, based on the evaluation index data 12 and the consideration condition 13 of each of the destinations 11, an evaluation 14 of the destination 11 is determined by the decision maker. Do. The input (the evaluation index data 12 and the consideration condition 13) and the output (the result of the evaluation 14) are learned by the RBF network 10 as teacher data. Thus, it is possible to form the RBF network 10 that approximates a non-linear preference function reflecting the decision maker's preference.

As described above, in the RBF network 10, the trend (charm) (12) of the year and the target age (1)
A non-linear preference function according to 3) can be approximated. For example, if the target age (y1) is young, the movement amount (x
Destination 11 having large attractiveness (x4) even if 3) is large
A preference function is generated such that the evaluation 14 (Z) of is higher.

Since the preference solution Z output from the RBF network 10 is an evaluation 14 reflecting the preference of the decision maker, the destination 11 having a high evaluation value 14 is an individual having a high fitness in GA. Is done. In GA
In the next generation (replanning in FIG. 10), the proportion of individuals (destination 11) with higher fitness is higher than in the current generation. When such an operation is repeated for each generation, an individual population having high fitness is formed. This is the evolution in GA and the approach to the optimal solution (preferred solution in multi-objective optimization).

In this application example, the fitness of the destination 11 as each individual in the GA is obtained as the evaluation 14 reflecting the preference of the decision maker. For this reason, GA is a destination 1 that is more suitable for the decision criterion's preference criteria.
1 is selected as the final destination (optimal solution).

The above application example discloses the following technology.

The RBF network 10 approximates a preference function in a multi-objective optimization problem. As shown in FIG. 3, the sightseeing spots 1 to N to the destination 11 are individuals each having fitness for the multi-objective optimal problem.

In the GA, a solution search is performed using a genetic algorithm that performs an operation of performing natural selection for a plurality of generations so that the individual having a higher fitness level has a higher selection probability from the individual group.

The GA outputs the destination 11 which is the result when the operation of a single generation of the plurality of generations is performed. The evaluation index data 12 and the consideration condition 13 relating to the destination 11 are input to the RBF network 10.

The destination 11 is the RBF network 10
Then, the destination 11 (individual) having a high evaluation 14 output from the RBF network 10 is set as the individual having the high fitness, and the next-generation operation of the GA is performed.

Next, a second embodiment will be described with reference to FIG.

Consider a case where some teacher data are selected from a plurality of sampling data when using the RBF network to obtain a preference function.

The selected teacher data is used to adjust the coupling coefficient of the RBF network. Therefore, the teacher data given to the RBF network must represent the characteristics of the preference function to be obtained. What should be selected from a plurality of sample data as teacher data to be given to the RBF network is a problem. In the second embodiment, in order to solve the above problem, a pre-processing unit is provided at a stage preceding the RBF network.

All that is needed to adjust the parameters of the RBF network is the teacher data. There are the following two points regarding teacher data. Adjustment of RBF parameters becomes more difficult as the amount of teacher data increases. If the amount of teacher data is small, it is difficult to determine whether the teacher data is data representing characteristics of a desired preference function.

Therefore, as much data as possible is collected as the sample data, and as a result of giving the data from the many sample data,
It is desirable to select, as the teacher data, data in which the parameters of the RBF network better express the desired preference function.

In the second embodiment, the following operation is performed. Here, it is assumed that there are 40 sample data. As teacher data, 10 points of data are randomly selected from 40 points of sample data. The parameters of the RBF network are adjusted by giving the ten points of teacher data. An error between the evaluation value of the sample data of 40 points and the output value of the RBF function obtained as an adjustment result is obtained.
As the error is smaller, a higher value is given to the evaluation of the selected data as teacher data. Do again from Are repeated to select several sets (several patterns) of highly evaluated data as teacher data. An optimum RBF function is selected from the evaluation value change when one element is changed. One of the criteria for selecting a teacher data set is “a small error from all sample data”. However, since it is difficult to obtain a correct evaluation by only this, the second criterion is provided. Usually, it is difficult to have a clear evaluation criterion when the number of elements is changed, but the evaluation criterion when other elements are fixed and only one point is changed is often clear. For example, when the elements such as the number of days and the amount of movement are the same, the higher the “attractive” element is, the better.

As described above, in the present embodiment, when teacher data to be given to the RBF network is selected from a plurality of sample data, a method of gradually converging through trial and error is used.

Here, in the above case, when the selection is repeated, if a GA or a search method is used, data with a high evaluation as teacher data can be collected more effectively.

According to the second embodiment, a preference function desired by the user can be created by using more characteristic data as teacher data.

Although the decision maker himself knows which is better as the teacher data by comparing the two sample data, the data which is selected as the teacher data by repeating the comparison of each two is finally determined. It is not known whether or not the sample data indicates a characteristic of preference in the plurality of sample data. This is the difficulty in simplifying the selection process.

In the present embodiment, the generation of a plurality of sample data itself is performed by a person, and the selection and narrowing down of characteristic data from the sample data is performed by the preprocessing unit. The above operation in which the preprocessing unit selects data suitable as teacher data from a plurality of sampling data can be automated.

Conventionally, there is no clear theory about how to select characteristic data from sample data, and it has been performed based on experience and intuition. Also, a method called clustering is known. This is a method in which a plurality of sample data is classified into classes on a statistical basis, teacher data is selected for each class, a neural network is created for each class, and applied to each space region.
Using this clustering, for a local population,
The technique of creating a neural network is known in pattern recognition. However, the preference of people is
It cannot be represented by clustering or statistics. Therefore, the second
Using the preprocessing unit of the embodiment, more appropriate teacher data is selected.

[0106]

According to the multi-objective optimization method of the present invention, multi-objective optimization can be performed particularly under a nonlinear preference function.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a neural network used in a first embodiment of a plan drafting device of the present invention.

FIG. 2 is a diagram illustrating a configuration of a neural network used for approximation of a multivariable function.

FIG. 3 is a diagram for explaining an application example of the first embodiment of the plan drafting apparatus of the present invention.

FIG. 4 is a diagram showing a configuration of a neural network used in an application example of the first embodiment of the plan drafting apparatus of the present invention.

FIG. 5 is a diagram showing a configuration of a neural network used in a second embodiment of the plan drafting apparatus of the present invention.

[Explanation of symbols]

 Reference Signs List 10 RBF network 11 Destination 12 Evaluation index data 13 Consideration condition 14 Evaluation 20 Neural network x1 Input data x2 Input data x3 Input data y1 Input data y2 Input data y3 Input data z Output (teacher data)

 ────────────────────────────────────────────────── ─── Continuing on the front page (72) Inventor Masanobu Mizoguchi 1 Industrial Highway, Iwatsuka-cho, Nakamura-ku, Nagoya-shi, Aichi, Japan

Claims (17)

[Claims] (A) providing a neural network; (b) providing the neural network with a plurality of input data relating to a multi-objective optimization problem; (c) providing the neural network as a result of (b). The network learning step; (d)
Obtaining the neural network approximating a preference function in the multi-objective optimization problem as a result of (c). 2. The multi-objective optimization method according to claim 1, wherein in (b), each of the plurality of input data provided to the neural network is a respective objective evaluation value in the multi-objective optimization problem. Optimization method. 3. The multi-objective optimization method according to claim 1, wherein in (b), each of the plurality of input data provided to the neural network is selected from a Pareto solution set in the multi-objective optimization problem. A multi-objective optimization method that is a Pareto solution. 4. The multi-objective optimization method according to claim 3, wherein the Pareto solution is selected based on a result of performing a Pareto solution analysis on the Pareto solution set. 5. The multi-objective optimization method according to claim 1, wherein the learning of (c) is supervised learning, and the (b) is a learning of the plurality of input data. Multi-objective optimization method including the step of providing teacher data corresponding to the above to the neural network. 6. The multi-objective optimization method according to claim 5, wherein the teacher data is a preferred solution to the plurality of input data by a decision maker of the multi-objective optimization problem. 7. The multi-objective optimization method according to claim 1, wherein (c) is performed again when a preference criterion of the multi-objective optimization problem changes. Method. 8. The multi-objective optimization method according to claim 1, wherein (c) is performed again when the multi-objective optimization problem changes. 9. A step of providing a neural network, (b) providing the neural network with a plurality of input data relating to a multi-objective optimization problem, and (c) the neural network as a result of the step (b). The network learning step; (d)
Obtaining the neural network approximating a preference function in the multi-objective optimization problem as a result of (c), wherein the plurality of input data includes first input data and second input data The first input data is an evaluation index of the multi-objective optimization problem; and the second input data is data for adjusting the weight of the first input data as the evaluation index. Optimization method. (A) providing a neural network; (b) providing said neural network with a plurality of input data relating to a multi-objective optimization problem; and (c) providing said neural network as a result of said (b). The network learning step; (d)
(C) obtaining the neural network approximating a preference function in the multi-objective optimization problem as a result of (c); and (e) providing a group of individuals each having fitness for the multi-objective optimization problem. (F) performing a solution search using a genetic algorithm that performs an operation of performing natural selection for a plurality of generations so that the individual with the higher fitness from the individual group has a higher selection probability; (f) inputting a result when the operation of a single generation of the plurality of generations is performed to the neural network obtained as a result of (d); and (h) inputting the result of (g). )
Executing the above (f) with the individual having a high evaluation outputted from the neural network as the individual having a high fitness. (I) providing a plurality of sample data; (j) providing a neural network; and (k) providing the neural network with a multi-objective optimization problem selected from the plurality of sample data. Providing a plurality of input data and teacher data corresponding to the plurality of input data;
(L) the neural network performing supervised learning as a result of (k); and (m) evaluating values output from the neural network as a result of (l) and evaluating the plurality of sample data. Calculating an error from the value; (n) performing the above (k) to (m) a plurality of times; and (o) as a result of the above (n), the plurality of values used when the error is small. Training the neural network using input data and the teacher data corresponding to the plurality of input data; (p) approximating a preference function in the multi-objective optimization problem as a result of the (o); Obtaining the above neural network. 12. The multi-objective optimization method according to claim 11, wherein in performing (n), a solution search using a genetic algorithm is performed. 13. The multi-objective optimization method according to claim 1, wherein the neural network that approximates the preference function approximates the nonlinear preference function. 14. The multi-objective optimization method according to claim 1, wherein the neural network is an RBF network. 15. A program for causing a computer to execute each step of the multi-objective optimization method according to claim 1. Description: 16. A plan drafting apparatus for drafting a plan defined by a multi-objective optimization problem, comprising a neural network, wherein the neural network is provided with a plurality of input data on the multi-objective optimization problem of the plan. And
As a result, the neural network learns,
A plan planning device that approximates a preference function in the multi-objective optimization problem by the learned neural network, and outputs the plan based on the approximated preference function. 17. The plan drafting apparatus according to claim 16, wherein the plan includes a travel plan, a facility deployment plan,
A plan drafting device that includes one of a facility allocation plan, a logistics plan, and a design plan.