An interactive fuzzy satisficing method for multiobjective nonconvex programming problems through floating point genetic algorithms |
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| Institution: | 1. Nanomedicine Lab, Univ. Bourgogne Franche-Comté, UTBM, F-90010, Belfort, France;2. Nanomedicine Lab, Univ. Bourgogne Franche-Comté, F-25000, Besançon, France;1. Rheumatology Unit, Hôtel-Dieu, Nantes University Hospital, 1, Place Alexis, 44093 Nantes-Cedex 01, France;2. Radiology Unit, Hôtel-Dieu, Nantes University Hospital, Place Alexis Ricordeau, 44093 Nantes-Cedex 01, France;3. Department of Gynecology-Obstetrics and Reproductive Medecine, Pelvic Pain Center, 38, Boulevard Jean Monnet, 44000 Nantes, France;1. Indian Institute of Management Ahmedabad, India;2. Anant National University Ahmedabad, India;1. Chemical Engineering, Pohang University of Science and Technology (POSTECH), 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea;2. School of Chemical Engineering & Materials Science, Chung-Ang University (CAU), 84 Heukseok-ro, Dongjak-gu, Seoul 06974, Republic of Korea;3. Graduate Institute of Ferrous & Energy Materials Technology (GIFT), Pohang University of Science and Technology (POSTECH), 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea;1. Programa de Pós Graduação em Ecologia e Conservação da Biodiversidade, Universidade Estadual de Santa Cruz, Rodovia Jorge Amado, KM 16, Salobrinho, Ilhéus, BA, 45662-900, Brazil;2. Departament of Biological Sciences, Macquarie University, Sydney, NSW, 2109, Australia;3. Departamento de Ciências Agrárias em Ambientais, Universidade Estadual de Santa Cruz, Rodovia Jorge Amado, KM 16, Salobrinho, Ilhéus, BA, 45662-900, Brazil |
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| Abstract: | In this paper, we focus on multiobjective nonconvex nonlinear programming problems and present an interactive fuzzy satisficing method through floating point genetic algorithms. After determining the fuzzy goals of the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the augmented minimax problems for which the floating point genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, we propose the revised GENOCOP III by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented together with an illustrative numerical example. |
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