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Multiobjective two-level simple recourse programming problems with discrete random variables

OPTIMIZATION AND ENGINEERING 2021年第2期22卷 1181-1202页

作者： Yano, Hitoshi Nishizaki, Ichiro Nagoya City Univ Grad Sch Humanities & Social Sci Mizuho Ku 1 YamanohataMizuho Cho Nagoya Aichi 4678501 Japan Hiroshima Univ Grad Sch Engn 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan

In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, a concept of Pareto Stackelberg solutions based on the reference objective levels is introduced. Using the Kuhn-Tucker approach in two-level programming, we formulate as a mixed integer programming problem, and propose an interactive algorithm to obtain a satisfactory solution of the leader from among a Pareto Stackelberg solution set based on the reference objective levels. A numerical example illustrates the proposed algorithm for a multiobjective two-level stochastic programming problem with simple recourses under the hypothetical leader.

关键词： Two-level programming simple recourse programming Multiobjective programming Pareto Stackelberg solutions

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Multiobjective Two-Level simple recourse programming Problems with Discrete-Type Fuzzy Random Variables and Optimistic and Pessimistic Pareto Stackelberg Solutions 11

Multiobjective Two-Level Simple Recourse Programming Problem...

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Joint 11th International Conference on Soft Computing and Intelligent Systems and 21st International Symposium on Advanced Intelligent Systems (SCIS-ISIS)

作者： Yano, Hitoshi Nagoya City Univ Grad Sch Humanities & Social Sci Nagoya Aichi 4678501 Japan

ISBN: (纸本)9781728197326

In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce new solution concepts called an optimistic and pessimistic Pareto Stackelberg solutions for the leader. It is shown that such optimistic and pessimistic Pareto Stackelberg solutions can be obtained by solving weighting problems of the leader. We propose an interactive algorithm to obtain a satisfactory solution of the leader from among an optimistic or pessimistic Pareto Stackelberg solution set.

关键词： two-level programming simple recourse programming LR fuzzy random variables possibility measure optimistic Pareto Stackelberg solutions pessimistic Pareto Stackelberg solutions

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Multiobjective Two-level simple recourse programming Problems with Discrete-type LR Fuzzy Random Variables

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Procedia Computer Science 2020年 176卷 531-540页

作者： Hitoshi Yano Graduate School of Humanities and Social Sciences Nagoya City University Nagoya 467-8501 Japan

In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce a new solution concept called an estimated Pareto Stackelberg solution for the leader. To obtain a candidate of a satisfactory solution for the leader from among an estimated Pareto Stackelberg solution set, using the Kuhn-Tucker approach and the transformation technique for complementarity conditions, an original problem is transformed into a mixed integer programming problem. Then, we propose an interactive algorithm to obtain a satisfactory solution of the leader from among an estimated Pareto Stackelberg solution set. A numerical example illustrates the proposed algorithm for a multiobjective two-level fuzzy random simple recourse programming problem under the hypothetical leader.

关键词： two-level programming simple recourse programming multiobjective programming discrete-type LR fuzzy random variables possibility measure estimated Pareto Stackelberg solutions

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