The Experts below are selected from a list of 18135 Experts worldwide ranked by ideXlab platform
Seiichi Koakutsu - One of the best experts on this subject based on the ideXlab platform.
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visualization of Pareto Optimal Solution sets using the growing hierarchical self organizing maps
Electronics and Communications in Japan, 2017Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the multiobjective optimization. The Pareto Optimal Solution visualization method using the self-organizing maps is one of promising visualization methods. This method has two shortcomings. One is that the map size has to be determined in advance. The other is that infeasible Solutions can appear in the learnt maps. This paper proposes a new visualization technique using the growing hierarchical SOM GHSOM, which is expected to solve foregoing shortcomings. This paper also proposes to introduce a symmetric transformation of maps into the learning algorithm in order to obtain easily viewable unified map. The effectiveness of the proposed method is confirmed through several numerical experiments.
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a Pareto Optimal Solution visualization method using som ng with learning parameter optimization
Systems Man and Cybernetics, 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
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A Pareto Optimal Solution Visualization Method Using an Improved Growing Hierarchical Self-Organizing Maps Based on the Batch Learning
Journal of Advanced Computational Intelligence and Intelligent Informatics, 2016Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable Solutions called Pareto Optimal Solutions is an important issue. This paper focuses on the Pareto Optimal Solution visualization method using the growing hierarchical self-organizing maps (GHSOM) which is one of promising visualization methods. This method has a superior Pareto Optimal Solution representation capability, compared to the visualization method using the self-organizing maps. However, this method has some shortcomings. This paper proposes a new Pareto Optimal Solution visualization method using an improved GHSOM based on the batch learning. In the proposed method, the batch learning algorithm is introduced to the GHSOM to obtain a consistent visualization maps for a Pareto Optimal Solution set. Then, the symmetric transformation of maps is introduced in the growing process in the batch learning GHSOM algorithm to improve readability of the maps. Furthermore, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed through numerical experiments with comparing the proposed method to the conventional methods on the Pareto Optimal Solution representation capability and the readability of the visualization maps.
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SMC - A Pareto Optimal Solution visualization method using SOM-NG with learning parameter optimization
2016 IEEE International Conference on Systems Man and Cybernetics (SMC), 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
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CEC - Visualization of Pareto Optimal Solutions using MIGSOM
2015 IEEE Congress on Evolutionary Computation (CEC), 2015Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable Solutions called Pareto Optimal Solutions is important issue. This study focuses on the Pareto Optimal Solution visualization method using the self-organizing maps which is one of promising visualization methods. The method has advantages in grasping the overall structure of the Solutions and comparing the objective functions simultaneously. However, this method has shortcomings in its Solution representation capability. This study proposes a new Pareto Optimal Solution visualization method using MIGSOM. The MIGSOM is one of the self-organizing algorithms inspired by the neuronal migration. In the MIGSOM algorithm, all input data directly migrate in the projection map space so as to form a suitable map. This direct migration is expected to contribute to the improvements of the Solution representation capability. Three improvements are introduced for the application of MIGSOM to the visualization. The effectiveness of the proposed method is confirmed through comparisons to the visualization method using conventional MIGSOM.
Takashi Okamoto - One of the best experts on this subject based on the ideXlab platform.
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visualization of Pareto Optimal Solution sets using the growing hierarchical self organizing maps
Electronics and Communications in Japan, 2017Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the multiobjective optimization. The Pareto Optimal Solution visualization method using the self-organizing maps is one of promising visualization methods. This method has two shortcomings. One is that the map size has to be determined in advance. The other is that infeasible Solutions can appear in the learnt maps. This paper proposes a new visualization technique using the growing hierarchical SOM GHSOM, which is expected to solve foregoing shortcomings. This paper also proposes to introduce a symmetric transformation of maps into the learning algorithm in order to obtain easily viewable unified map. The effectiveness of the proposed method is confirmed through several numerical experiments.
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a Pareto Optimal Solution visualization method using som ng with learning parameter optimization
Systems Man and Cybernetics, 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
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A Pareto Optimal Solution Visualization Method Using an Improved Growing Hierarchical Self-Organizing Maps Based on the Batch Learning
Journal of Advanced Computational Intelligence and Intelligent Informatics, 2016Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable Solutions called Pareto Optimal Solutions is an important issue. This paper focuses on the Pareto Optimal Solution visualization method using the growing hierarchical self-organizing maps (GHSOM) which is one of promising visualization methods. This method has a superior Pareto Optimal Solution representation capability, compared to the visualization method using the self-organizing maps. However, this method has some shortcomings. This paper proposes a new Pareto Optimal Solution visualization method using an improved GHSOM based on the batch learning. In the proposed method, the batch learning algorithm is introduced to the GHSOM to obtain a consistent visualization maps for a Pareto Optimal Solution set. Then, the symmetric transformation of maps is introduced in the growing process in the batch learning GHSOM algorithm to improve readability of the maps. Furthermore, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed through numerical experiments with comparing the proposed method to the conventional methods on the Pareto Optimal Solution representation capability and the readability of the visualization maps.
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SMC - A Pareto Optimal Solution visualization method using SOM-NG with learning parameter optimization
2016 IEEE International Conference on Systems Man and Cybernetics (SMC), 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
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CEC - Visualization of Pareto Optimal Solutions using MIGSOM
2015 IEEE Congress on Evolutionary Computation (CEC), 2015Co-Authors: Naoto Suzuki, Takashi Okamoto, Seiichi KoakutsuAbstract:In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable Solutions called Pareto Optimal Solutions is important issue. This study focuses on the Pareto Optimal Solution visualization method using the self-organizing maps which is one of promising visualization methods. The method has advantages in grasping the overall structure of the Solutions and comparing the objective functions simultaneously. However, this method has shortcomings in its Solution representation capability. This study proposes a new Pareto Optimal Solution visualization method using MIGSOM. The MIGSOM is one of the self-organizing algorithms inspired by the neuronal migration. In the MIGSOM algorithm, all input data directly migrate in the projection map space so as to form a suitable map. This direct migration is expected to contribute to the improvements of the Solution representation capability. Three improvements are introduced for the application of MIGSOM to the visualization. The effectiveness of the proposed method is confirmed through comparisons to the visualization method using conventional MIGSOM.
Yusuke Kobayashi - One of the best experts on this subject based on the ideXlab platform.
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a Pareto Optimal Solution visualization method using som ng with learning parameter optimization
Systems Man and Cybernetics, 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
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SMC - A Pareto Optimal Solution visualization method using SOM-NG with learning parameter optimization
2016 IEEE International Conference on Systems Man and Cybernetics (SMC), 2016Co-Authors: Yusuke Kobayashi, Takashi Okamoto, Seiichi KoakutsuAbstract:The visualization of the Pareto Optimal Solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto Optimal Solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto Optimal Solution representation capability. One is that the maps have incorrect points that represent non-Pareto Optimal Solutions. The other is that the coverage of the maps for the edge region of the Pareto Optimal Solution set is not good. This study proposes a Pareto Optimal Solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.
Faouzi Masmoudi - One of the best experts on this subject based on the ideXlab platform.
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analytic hierarchy process based approach for selecting a Pareto Optimal Solution of a multi objective multi site supply chain planning problem
Engineering Optimization, 2017Co-Authors: Omar Ayadi, Houssem Felfel, Faouzi MasmoudiAbstract:ABSTRACTThe current manufacturing environment has changed from traditional single-plant to multi-site supply chain where multiple plants are serving customer demands. In this article, a tactical multi-objective, multi-period, multi-product, multi-site supply-chain planning problem is proposed. A corresponding optimization model aiming to simultaneously minimize the total cost, maximize product quality and maximize the customer satisfaction demand level is developed. The proposed Solution approach yields to a front of Pareto-Optimal Solutions that represents the trade-offs among the different objectives. Subsequently, the analytic hierarchy process method is applied to select the best Pareto-Optimal Solution according to the preferences of the decision maker. The robustness of the Solutions and the proposed approach are discussed based on a sensitivity analysis and an application to a real case from the textile and apparel industry.
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integrated ahp topsis approach for Pareto Optimal Solution selection in multi site supply chain planning
International Conference Design and Modeling of Mechanical Systems, 2017Co-Authors: Houssem Felfel, Faouzi MasmoudiAbstract:In this paper, a multi-objective, multi-period, multi-product stochastic model for a multi-site supply chain planning problem under demand uncertainty is proposed. The decisions to be made include the amounts of product to be produced, the amounts of products to be transported between the different sites and customers as well as the amounts of inventory of finished or semi-finished products. The developed model aims simultaneously to minimize the expected total cost, to maximize the customer demand satisfaction level and to minimize the downside risk. The e-constraint method is applied to solve the considered model and to generate the set of Pareto Optimal Solutions. This set of Pareto represents the trade-off between the different objective functions. Then, an integrated approach of the Analytic Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods is applied in order to select the best compromise Pareto Solution. A numerical example is presented to illustrate the proposed approach.
Isao Ono - One of the best experts on this subject based on the ideXlab platform.
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uniform sampling of local Pareto Optimal Solution curves by Pareto path following and its applications in multi objective ga
Genetic and Evolutionary Computation Conference, 2007Co-Authors: Ken Harada, Jun Sakuma, Shigenobu Kobayashi, Isao OnoAbstract:Although multi-objective GA (MOGA) is an efficient multi-objective optimization (MOO) method, it has some limitations that need to be tackled, which include unguaranteed uniformity of Solutions and uncertain finding of periphery of Pareto-Optimal Solutions. It has been shown that, on bi-objective problems, which are the subject of this paper, local Pareto-Optimal Solutions form curves. In this case, some of the limitations of MOGA can be resolved by sampling the curves uniformly in the variable space and in the objective space. This paper proposes Pareto Path Following (PPF) which does the sampling by extending the framework of Numerical Path Following, verifies that PPF exhibits the desired behaviors, and addresses the extension of PPF for problems with more than two objective functions.Application of PPF is not limited to refinement of Solutions obtained with MOGA. PPF makes it natural to have a local Pareto-Optimal Solution curve as the unit of search, which leads to curve-based MOGA. PPF also enables examination of which Pareto-Optimal Solution curves are found by MOO methods, and performance metrics based on it can be defined. This paper proposes these applications of PPF in MOGA and compares standard MOGA and curve-based MOGA using the metrics to reveal their characteristics.
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GECCO - Uniform sampling of local Pareto-Optimal Solution curves by Pareto path following and its applications in multi-objective GA
Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07, 2007Co-Authors: Ken Harada, Jun Sakuma, Shigenobu Kobayashi, Isao OnoAbstract:Although multi-objective GA (MOGA) is an efficient multi-objective optimization (MOO) method, it has some limitations that need to be tackled, which include unguaranteed uniformity of Solutions and uncertain finding of periphery of Pareto-Optimal Solutions. It has been shown that, on bi-objective problems, which are the subject of this paper, local Pareto-Optimal Solutions form curves. In this case, some of the limitations of MOGA can be resolved by sampling the curves uniformly in the variable space and in the objective space. This paper proposes Pareto Path Following (PPF) which does the sampling by extending the framework of Numerical Path Following, verifies that PPF exhibits the desired behaviors, and addresses the extension of PPF for problems with more than two objective functions.Application of PPF is not limited to refinement of Solutions obtained with MOGA. PPF makes it natural to have a local Pareto-Optimal Solution curve as the unit of search, which leads to curve-based MOGA. PPF also enables examination of which Pareto-Optimal Solution curves are found by MOO methods, and performance metrics based on it can be defined. This paper proposes these applications of PPF in MOGA and compares standard MOGA and curve-based MOGA using the metrics to reveal their characteristics.