Re-Labeling Differential Evolution for Combinatorial Optimization and Interactive Evolutionary Computation

Transcription

1 SICE Journal of Control, Measurement, and System Integration, Vol. 9, No. 1, pp , January 2016 Re-Labeling Differential Evolution for Combinatorial Optimization and Interactive Evolutionary Computation Ryohei FUNAKI, Hirotaka TAKANO, and Junichi MURATA Abstract : The authors proposed a new differential evolution technique, Re-Labeling Differential Evolution (RLDE), which, in this paper, is refined and evaluated in the context of interactive solution of combinatorial optimization problems. Many of the practical design problems such as web page layout design and room lighting design are combinatorial optimization problems where the numerical evaluations are not available. The evaluation should be made by humans. There are two essential properties necessary for the solution methods to the above problems: (1) interaction between the methods and the users to extract human evaluations accurately without imposing too much burden on the users, and (2) abilities to solve combinatorial optimization problems. Interactive differential evolution (IDE) techniques possess the first property because they utilize pairwise comparisons but lack the second property, while interactive genetic algorithms have the second property but not the first one. RLDE is an extended algorithm of IDE so that it can solve combinatorial optimization problems. In differential evolution (DE), solution candidates are represented by numerical values. In combinatorial optimization problems, however, the numerical values are only labels to distinguish the components to be combined, and there are no structural relationships such as large/small and far/near among them which the DE relies on. RLDE collects information on the problem while it searches for the solution, and, based on the obtained information, re-labels the components so that the DE algorithm works more efficiently. RLDE was originally proposed as a technique for simple combinatorial optimization. In this paper, the authors extend RLDE to permutation-based combinatorial optimization. The performance of RLDE in terms of the burden on the users and the quality of the obtained solutions is evaluated and compared with the other techniques in numerical experiments. Key Words : differential evolution, interactive evolutionary computation, combinatorial optimization, permutation-based combinatorial optimization. 1. Introduction Evolutionary Computation (EC) can solve optimization problems using only evaluation values (called fitness values in EC) of candidates of solutions (called individuals in EC) calculated from an objective function but no additional information on the objective function such as derivatives. EC can solve problems which need preference or sensitivity of humans for evaluation, and EC for such problems is especially called Interactive Evolutionary Computation (IEC). IEC is applied to various fields such as medicine and art, more specifically to GUI layout design systems [1], lighting design support systems with 3-dimensional computer graphics [2] and cochlear implant parameter turning systems [3]. User s fatigue remains a problem for practical IEC applications because repetitious evaluations by the user are required to optimize the target system and user s fatigue affects search performance. Therefore, the requirements for IEC is to work well with smaller population size and fewer search generations [4]. Interactive Genetic Algorithm (IGA) is a well-known technique that is extended from Genetic Algorithm (GA) [5] for IEC. IGA solves problems using evaluation by a user instead of Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan r.funaki620802@kyudai.jp, takano@ees.kyushuu.ac.jp, murata@ees.kyushu-u.ac.jp (Received April 6, 2015) (Revised August 11, 2015) fitness values calculated from an objective function. The user needs to give every individual a score comparing all the individuals. In the case of optimization problems whose individuals can be evaluated in a short time such as optimization of images, it is easy for the user to evaluate individuals again which have been already evaluated. On the other hand, in the case of optimization problems whose individuals need a long time for evaluation such as optimization of movies and pieces of music, the user must evaluate individuals one by one and give them scores memorizing the evaluations made so far. The evaluation which heavily relies on user s memory accumulates user s fatigue and increases the risk of mistakes in evaluations [4]. Consequently, search performance of IGA may decrease. Therefore, several approaches have been proposed to reduce user s fatigue. These include improving IEC interfaces, devising new EC algorithms, accelerating EC searches, and others [4]. Tournament GA (TGA) [6] adopts pairwise comparison evaluation, and Tournament IGA (TIGA) is one example of approaches to reduce user s fatigue. In pairwise comparison evaluation, the better individual is chosen between two individuals by the user. In TIGA evaluation, fitness is the rank among individuals obtained from tournaments. First, pairs of individuals are made from all the individuals, and from each pair the better one is chosen by the user. Next new pairs are made from the winners, and the user chooses the better one from each new pair. The operation is repeated until the best individual is identified, and each individual is given the score which is equal to the number of wins. It is not necessary to memorize evalua- JCMSI 0001/16/ c 2015 SICE

2 SICE JCMSI, Vol. 9, No. 1, January tions of many individuals, therefore TIGA reduces user s fatigue especially in optimization problems which does not allow easy comparison of all the individuals. Consequently it can reduce the risk of wrong evaluations by the user. However, the tournament-based evaluation cannot provide an accurate fitness value or order of them for GA to perform satisfactorily. For example, if the second best individual opposes the best individual in the early stage of tournament, it is given a low score in spite of its superiority. As a result, search performance worsens [7]. Interactive Differential Evolution (IDE) [7] can also adopt pairwise comparison evaluation and reduce user s fatigue. IDE exhibits high search performance due to the effective search withdifference vectors between two individuals. Unlike TIGA, the pairwise comparison in IDE does not cause undesirable effects on the basic DE operations. Consequently, it can reduce user s fatigue while keeping high performance. Neither Differential Evolution (DE) [8],[9] nor IDE can, as it is, solve combinatorial optimization problems because it is a technique for continuous-valued optimization problems. On the other hand, there are a lot of combinatorial optimization problems which need user s subjective evaluation such as optimization of web page layouts, arrangement of illuminations, and so on. The combinatorial optimization problems can be solved with less user s fatigue by the pairwise comparison and effective search by difference vectors if DE is extended for combinatorial optimization problems. Relative Position Indexing [10] is one of the DE methods which are extended for permutation-based combinatorial optimization problems. However, the conventional methods are not necessarily effective for IEC where the population size and the search generations are restricted due to user s fatigue. The authors proposed an extended DE technique named Relabeling Differential Evolution (RLDE) [11] for combinatorial optimization where solutions are expressed by arrays of integers. These integers are not used as numerical values but indices to identify alleles (elements of arrays). At this time, assignment of indices to alleles has a serious influence on the performance of search because DE uses the addition, subtraction, multiplication operations for the individuals. RLDE can solve combinatorial optimization problems efficiently by sorting index numbers of alleles. RLDE was originally proposed as a technique for simple combinatorial optimization. In this paper, the authors extend RLDE to permutation-based combinatorial optimization which is one of the more difficult combinatorial optimization problems, evaluate effectiveness of RLDE in simulations in the context of IEC requirements which are smaller population size and fewer search generations, and discuss features of RLDE. 2. Differential Evolution and Interactive Differential Evolution Recently, research has been getting more active on DE which is an optimization technique in continuous search space. DE implements effective search using difference vectors between two individuals. In the early stages of search, individuals are widely spread and a global search is operated with larger difference vectors. As individuals converge towards the global optimum, a local search is operated because the difference vectors become smaller. In this way, the DE algorithm automatically controls the global search and the local search. Therefore it can solve problems efficiently in continuous search space. IDE attracts much attention as IEC method for continuousvalued optimization problems. Most of IDE adopts pairwise comparison evaluation. It reduces user s fatigue because the user does not need to memorize evaluations of all individuals. This advantage is especially useful in the case of optimization problems which does not allow easy comparison of all the individuals. Unlike the TIGA, pairwise comparison in IDE does not cause undesirable effects on the basic DE operations. As a result, IDE as well as original DE shows high search performance. Figures 1 and 2 show human interfaces for comparing and scoring all the candidate images and a pair of images only, respectively. When all the images are compared, the displayed images are small, and the user may need enlargement manipulation or a larger monitor. Inputting scores or ranks to all the images on the interface is tedious. On the other hand, when a pair of images is to be compared, i.e. in the case of pairwise comparison, all the user has to do is to select the better image and maybe just click on it. In this way, the pairwise comparison is better than comparison of all individuals from the viewpoint of fatigue by inputting evaluations. Fig. 1 Fig. 2 An interface of comparison of all individuals. An interface of pairwise comparison. 3. Re-Labeling Differential Evolution 3.1 Issues with DE for Combinatorial Optimization and Their Resolution Combinatorial optimization problems can be solved with less user s fatigue by the pairwise comparison and the effective

3 20 SICE JCMSI, Vol. 9, No. 1, January 2016 search using difference vectors if DE is extended for combinatorial optimization problems. However, neither DE nor IDE can, as it is, solve combinatorial optimization problems. EC techniques for continuous-valued optimization problems which includes DE and Particle Swarm Optimization (PSO) presuppose that fitness values of solutions are close to each other if those solutions are near in the search pace. In combinatorial optimization problems, the solutions are expressed by arrays of integers used as indices to identify alleles (elements of arrays). These integers are irrelevant to the features such as order (larger or smaller) and distance (far or near). Accordingly, it is possible that the fitness values of solutions are greatly different even if those solutions are close to each other in the search space. In other words, good solutions are widely distributed in the search space. If DE is applied to combinatorial optimization problems without any changes, the difference vectors between good solutions can be large because the good solutions widely distribute in the search space. Furthermore better solutions are not necessarily located around good individuals, therefore local search cannot be performed by small difference vectors. For this reason, DE operates inefficient local search in final stages of the search in the combinatorial optimization problems. RLDE [11] is a technique to solve combinatorial optimization problems efficiently by sorting index numbers of alleles. RLDE focuses on the alleles which are contributing factors of the good fitness values and re-labels indices so that difference vectors between the good alleles are small. Owing to this, difference vectors between individuals whose fitness values are close to each other become small and better individuals are located around good one. Namely, efficient local search can be performed. This technique can be applied to other EC methods for continuous space such as PSO [12] although it is introduced as DE extension in this paper. 3.2 Algorithms Algorithms of the ordinary re-labeling differential evolution First, RLDE identifies alleles which are contributing factors of good fitness values. However, in IDE the user does not give individuals scores but selects the better individual between a parent and an offspring. Evaluations by the user cannot be used for identification of good alleles because the order of fitness values among all the individuals is unknown. The authors proposed the technique to identify alleles which are contributing factors of good fitness value. In the case of combinatorial optimization by DE, individuals are distributed widely and randomly in the search space in the first stages of the search (Fig. 3). As the search proceeds, individuals which have bad fitness values are discarded, and good individuals dominate the population (Fig. 4). The alleles which appear in many individuals are presumed to be the contributing factors of good fitness value. Therefore, the alleles are given scores called the allele appearance frequency and those which appear frequently in the individuals get high scores. Next, the alleles are sorted by the allele appearance frequency. The allele which obtains the highest allele appearance frequency gets the new index 1, and the allele which obtains the second best allele appearance frequency gets new index 2, and so on (Fig. 5). If some alleles have the same allele appearance frequency, the order among them are kept the same as in the previous generation. These operations are carried out in every element of solution arrays independently. Fig. 3 Fig. 4 Fig. 5 The early stages of optimization. X is an element of a solution array. The last stages of optimization. X is an element of a solution array. New indices by Re-labeling DE. X is an element of a solution array Additional algorithms for permutation-based combinatorial optimization RLDE was originally proposed as a technique for simple combinatorial optimization. In this paper, the authors extend RLDE to permutation-based combinatorial optimization. In the permutation-based optimization problems, the solutions are arrays of integers and express the order of some objects. Every integer must appear once and only once in a solution. However, it is possible that DE generates solutions which include same integers. The authors propose the technique to modify solutions which include the same integers. First, trace the permutation of a target solution. If the integer appears twice in a solution, the latter one is overwritten by another integer which is the closest integer which has not appeared in the tracing permutation yet. This overwriting operation destroys characteristics of parents individuals. However, alleles whose values are close to each other have similar features owing to the re-labeling operation. Therefore, replacing a duplicate integer with a closest integer provides the minimum destruction of chromosomes of parents. The RLDE algorithm is described below. 1. Initialize individuals. 2. Choose a target vector. 3. Choose three individuals X R1, X R2,andX R3 randomly from the population aside from the target vector.

4 SICE JCMSI, Vol. 9, No. 1, January Generate a mutant vector M according to the following equation. M = X R1 + F (X R2 X R3 ) (1) F is a positive constant and scales the differential vector length between individuals X R2 and X R3. 5. Generate a trial vector by crossing the target vector and the mutant vector. 6. Compare the target vector and the trial vector and replace the target vector with the vector which has the better evaluation. 7. Repeat 2 6 for all individuals and this cycle is called a generation. 8. Count the number of appearance of each allele in all individuals, and set the number of appearance as the allele appearance frequency. 9. Sort the alleles in the descending order of the allele appearance frequency. 10. Repeat generations until a solution which satisfies the user is obtained. 4. Experimental Condition 4.1 Test Problems In this paper, RLDE is evaluated with traveling salesman problems (TSPs). They are well-known permutation-based combinatorial optimization problems to find the tour which minimizes the total distance. The solutions are arrays of integers and express the order of cities to travel. TSPs are not problems for IEC, however, they have the same property as other permutation-based combinatorial optimization problems including those for IEC. The property is that two permutations which are quite different get quite different fitness values, and those which are close to each other get close fitness values. The authors consider that TSPs can be used as test problems for IEC, and adopt them in this paper. Note that TSP is adopted as a representative of the permutation-based combinatorial optimization problems. Therefore, the techniques for only TSPs are not compared with RLDE in this paper. For example, DE techniques in [13] and [14] use distances between cities for the local search. RLDE is evaluated using three TSPs, F1, F2 andf3 which are Groetschel 17-, Groetschel 21- and Groetschel 24-city problems, respectively [15]. The length of array of solutions and the number of alleles are equal to the number of cities. 4.2 Parameter Setting In the numerical experiments, RLDE, GA, TGA, Relative Position Indexing DE (RPIDE) [10] and basic DE are evaluated whose alleles are set randomly in the initialization and the population size N p is 8. This condition assumes IEC where a good solution should be discovered in as a small number of evaluations as possible. The fitness value of individuals are not recorded or reused in other generations because it is difficult for the user to memorize evaluations of many individuals in IEC. In addition, to discuss features of RLDE, the authors evaluate the methods whose population size is 16 and 24. Adjacent representation [16] is used as a genotype of individuals in RLDE and basic DE, and binominal crossover is performed in RLDE, RPIDE and basic DE. In adjacent representation, array numbers represent starting cities, and elements represent next cities, and tours are represented by each element of arrays independently. Therefore, binominal crossover is adopted. In GA, the user gives individuals scores from one to five as the fitness value [17], path representation [16] is used as a genotype of individuals and edge recombination crossover [18] is performed. Table 1 shows parameter settings of RLDE, RPIDE and basic DE, and Table 2 shows parameter settings of GA and TGA. The parameters F and the crossover rate in RLDE can be set in the same way as original DE. Individuals greatly mutate if the parameters are large values, and mutate a little if the parameters are small values. In RLDE and RPIDE, the values of F are set in small values in order to enhance convergence speeds in the early stages of search [12]. First, a value of F is set in 0.3 temporarily, and the crossover rate is adjusted between 0.1 and 1.0 at 0.1 intervals so as to get a better result in the 10th generations. Next, the crossover rate is set in the getting value, and F is adjusted between 0.1 and 1.0 at 0.1 intervals. DE uses the same parameter settings as RLDE because of control experiments. Table 1 The parameter settings of Re-labeling DE, Relative Position Indexing DE and basic DE. Crossover rate F F F F Table 2 The parameter settings of GA and Tournament GA. Crossover rate Mutation rate F F F Experimental Results and Discussions 5.1 Comparison under the IEC Requirements First, the techniques which adopt pairwise comparison evaluation, specifically TGA, RLDE, RPIDE and basic DE, are compared. Figures 6 8 show the changes of the best fitness values of each method where population size is 8 and the maximum number of evaluations is 200. The horizontal axes show the number of pairwise comparison evaluations, and the vertical axes of these graphs show the best fitness values averaged over 100 trials. The optimal fitness means the global optimal fitness value in the test problem. In an IEC-based cochlear implant parameter turning [3], the patient was able to evaluate hearing quality for 12 generations of 16 individuals without big problems. Therefore, the user can evaluate for about 24 generations in the case of 8 individuals. When images are targets of optimization, the evaluation will be easier and take a shorter time. In such a case, more number of generations would be acceptable. Here we will evaluate the performance of the methods by the 25th generation, namely 200th evaluation.

5 22 SICE JCMSI, Vol. 9, No. 1, January 2016 In the first stages of F1 and F3, the performance of RLDE is lower than other methods which adopt pairwise comparison evaluation. However, the performance of RLDE becomes higher as the search proceeds and better than other methods since the 13th generation in F1 and the 6th generation in F3, respectively. In the whole stage of F2, the performance of RLDE is better than other methods. the performance of RLDE is better than GA since the 12th generation in F2 and the 10th generation in F3. User s fatigue in a generation depends on the target problems, and GA cannot easily optimize movies, pieces of music and so on. As mentioned in section 2, in the case of optimization of movies and pieces of music, user s fatigue in GA increases and the pairwise comparison reduces user s fatigue. Accordingly, RLDE are suitable for those optimization problems especially. Fig. 6 The change of the best fitness value of F1 with 8 individuals. Fig. 9 The change of the best fitness value of GA, TGA and RLDE in F1 with 8 individuals. Fig. 7 The change of the best fitness value of F2 with 8 individuals. Fig. 10 The change of the best fitness value of GA, TGA and RLDE in F2 with 8 individuals. Fig. 8 The change of the best fitness value of F3 with 8 individuals. Next, RLDE is compared with GA-based techniques, namely basic GA and TGA. Figures 9 11 show the changes of the best fitness values in each generation, where population size is 8 and the maximum number of generations is 25. These techniques cannot be compared in the number of evaluations because GA does not adopt pairwise comparison, therefore the horizontal axes show the number of generations. The vertical axes of these graphs show the best fitness values averaged over 100 trials. GA shows higher performance than TGA. It shows that the accuracy of fitness value affects the performance of GA. In the first stages of all problems, the performance of RLDE is lower than GA. However, the performance of RLDE becomes higher as the search proceeds. In F1, the performance of RLDE is the same level as GA since the 15th generation. In F2 and F3, Fig. 11 The change of the best fitness value of GA, TGA and RLDE in F3 with 8 individuals. 5.2 Discussions about Features of RLDE The best fitness values with 8, 16 and 24 individuals in the 200th and the 50,000th pairwise comparison evaluations are shown in Figs GA does not adopt pairwise comparison evaluations, therefore the fitness values of GA in the same generations as TGA are described. The horizontal axes show population size (8, 16, 24), and the vertical axes show average fitness values of best individuals in 100 trials. In the 200th evaluation, the performance of RLDE is better than other methods with population size 8 in all test problems, however, the performance of RLDE decreases with 8 individ-

6 SICE JCMSI, Vol. 9, No. 1, January Fig. 12 The best fitness values in the 200th evaluation step of F1. Fig. 16 The best fitness values in the 200th evaluation step of F3. Fig. 13 The best fitness values in the 50,000th evaluation step of F1. Fig. 17 The best fitness values in the 50,000th evaluation step of F3. Fig. 14 The best fitness values in the 200th evaluation step of F2. Fig. 18 The variance of population of F1 of Re-labeling DE. Fig. 15 The best fitness values in the 50,000th evaluation step of F2. Fig. 19 The variance of population of F1 of basic DE. uals in the 50,000th evaluation especially in F1. It shows convergence of RLDE is fast in the case of small population size, however, the individuals fall into a local optimum because new indices by re-labeling operation does not work well. On the other hand, in the case of the 50,000th evaluation and 24 individuals, RLDE is better than other methods. Therefore the convergence of RLDE is fast in the case of small population size, and RLDE can discover a better solution at the expense of quickness of the convergence in the case of the large population size. It shows that RLDE is suited to both IEC which requires quickness of the convergence and EC which requires accuracy of solution. The performance of RPIDE in the 200th evaluation is not good, while it is good in the 50,000th evaluation with many individuals. RPIDE succeeds in extending to combinatorial optimization as EC methods. However it is not suitable for IEC because of the low performance of the convergence in the early stage. Figures 18 and 19 show changes of population variance in RLDE and DE in F1. The horizontal axes show the number of evaluations, and the vertical axes show the average of population variance in 100 trials. Population variance is the variance of individuals in a population. The variance is first calculated

7 24 SICE JCMSI, Vol. 9, No. 1, January 2016 for each array element and then averaged over all the elements. It is calculated as, V = 1 Np D D Np (x j,i x i ) 2 (2) i=1 j=1 where x j,i denotes the i-th element of the j-th individual and x i denotes the average of the values in the i-th elements of all individuals. In the 200th evaluation step, V values in RLDE with 8, 16 and 24 individuals are 18.1, 21.4 and 22.3 respectively, and those in basic DE are 19.1, 21.5 and 22.4, respectively. Individuals of RLDE converges more quickly than those of basic DE in the case of 8 individuals. In the 50,000th evaluation step, V values in RLDE with 8, 16 and 24 individuals are 1.1, 5.1 and 7.9 respectively, and those in basic DE are 10.5, 15.7 and 17.8, respectively. The difference between V values in RLDE and those in basic DE becomes larger. In RLDE, the individuals converge more quickly than those of basic DE in whole stages of the searches. Accordingly, RLDE can be regarded as a technique that promotes convergence on alleles which may be contributing factors of good fitness values. Consequently, RLDE is a suitable method for IEC which requires a good solution in the early stage. In Fig. 13, however, the performance of RLDE decreases in the 50,000th evaluation steps with population size 8 because individuals converge before good alleles are discovered. RLDE need to search with enough population sizeormorelargerf value if one needs a more accurate solution. Figure 20 shows the fitness values of GA, TGA, RLDE with three types of F values, 0.3, 0.8 and 1.2 in the 50,000th evaluate of F1. A high F value provides the global search and a good fitness value in the 50,000th evaluation even if the number of individuals is small. Fig. 20 The fitness values of GA, TGA and RLDE with three types of F, 0.3, 0.8 and 1.2 in the 50,000th evaluation of F1. 6. Conclusions In this paper, the authors extended Re-labeling Differential Evolution for simple combinatorial optimization to permutation-based combinatorial optimization and showed the effectiveness as an IEC method. RLDE is suited to Interactive Evolutionary Computation because individuals converge on the good solution with smaller population size in fewer search generations. Especially, RLDE can be applied to optimization of movies and pieces of music which can not be solved by IGA easily. Furthermore, RLDE is not restricted to IEC, but it is effective in EC which can use many individuals and large number of evaluations. References [1] T. Masui, Graphic object layout with interactive genetic algorithms, IEEE Workshop on Visual Language, pp , [2] K. Aoki and H. Takagi, 3-D CG lighting with an interactive GA, 1st International Conference on Conventional and Knowledge-based Intelligent Electronic Systems (KES 97), pp , [3] R. Funaki and H. Takagi, Paired comparison-based interactive differential evolution for cochlear implant fitting, 6th Japanese Society for Evolutionary Computation, pp , 2014 (in Japanese). [4] H. Takagi, T. Unemi, and T. Terano, Perspective on interactive evolutionary computing, The Journal of the Japanese Society for Artificial Intelligence, Vol. 13, No. 5, pp , [5] J.H. Holland, Adaptation In Natural and Artificial Systems, University of Michigan Press, [6] L. Panait and S. Luke, A comparison of two competitive fitness functions, Genetic and Evolutionary Computation Conference (GECCO2002), pp , [7] H. Takagi and D. Pallez, Paired comparison-based interactive differential evolution, The first World Congress on Nature and Biologically Inspired Computing (NaBIC2009), pp , [8] R. Storn and K. Price, Minimizing the real functions of the ICEC 96 contest by differential evolution, International Conference on Evolutionary Computation (ICEC1996), pp , [9] R. Storn and K. 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8 SICE JCMSI, Vol. 9, No. 1, January Ryohei FUNAKI He received a Masters degree of Design, Kyushu University and is a student in the doctoral program of the Graduate School of Information Science and Electrical Engineering, Kyushu University, Japan. His research interests include evolutionary algorithms and interactive evolutionary algorithms. Hirotaka TAKANO (Member) He received the M.S. and the Dr. Eng. degrees from University of Fukui, Japan, in 2003 and 2006, respectively. He then became an Assistant at Department of Electrical and Computer Engineering, Gifu National College of Technology. He is an Assistant Professor at Faculty of Information Science and Electrical Engineering, Kyushu University. His research interests are in advanced operation and planning of electric power systems and optimization applications. He is a member of IEEE, IEEJ and IEIEJ. Junichi MURATA (Member) He received the Master and the Doctor of Engineering degrees from Kyushu University, Japan, in 1983 and 1986, respectively. He then became a Research Associate and now is a Professor at the Faculty of Information Science and Electrical Engineering, Kyushu University. His current research interests are in learning systems, optimization techniques and their applications especially to energy management systems. He is a member of ISCIE, IEEJ and IEEE.