Pareto-optimal solutions for multi-objective flexible linear programming
TL;DR: An optimistic-pessimistic approach is proposed to solve multi- objective flexible linear programming with interval uncertainty (MOFLPIU) using an interval-valued fuzzy set representation and the Hurwicz optimism-p pessimism criterion.
Abstract: The aim of this paper is twofold. Firstly, to define a solution concept of Pareto-optimality for a multi-objective flexible linear programming (MOFLP) problem (or multi-objective fuzzy linear programming problem) and design a method to extract a Pareto-optimal solution of MOFLP problem from the set of optimal solutions of equivalent optimization problem formulated by Dubey and Mehra (2013). Secondly, to extend this study to multi-objective linear programming problem involving hard and flexible constraints with interval uncertainty. A flexible constraint with interval uncertainty generalizes a flexible constraint by allowing preferences to be expressed in the form of intervals. An optimistic-pessimistic approach is proposed to solve multi- objective flexible linear programming with interval uncertainty (MOFLPIU) using an interval-valued fuzzy set representation and the Hurwicz optimism-pessimism criterion.
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01 Jul 2020
TL;DR: A regional multi-objective linear programming model for theInitial post-earthquake stage is designed according to the different degree of road loss, the different demand for materials and the number of the injured due to the difference of population base on each disaster point in the initial postearthqu quake period.
Abstract: The earthquake, as one of the most harmful natural disasters to humanity, has been concerned for a long time. Considering some areas with underdeveloped economic and medical standards, it is of great significance to study the regional post-earthquake rescue problem. In the paper, a regional multi-objective linear programming model (MLPM) for the initial post-earthquake stage is designed according to the different degree of road loss, the different demand for materials and the number of the injured due to the difference of population base on each disaster point in the initial postearthquake period, and the method of vehicle deployment. And the model is solved by three introduced meta-heuristic algorithms which are ant colony optimization algorithm (ACOA), particle swarm optimization algorithm (PSOA), and tabu search algorithm (TSA). Through numerical experiments, the feasibility of the three algorithms is verified, and the performances of the three algorithms about the solutions and running time of solving are compared and analyzed. In the paper, the three algorithms are feasible to optimize the model. The solution obtained by the ACOA is optimal, and the TSA has the shortest running time. Under the same number of ants and particles, the PSOA runs faster than the ACOA, but the solution obtained by the ACOA is superior to the PSOA.
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Cites methods from "Pareto-optimal solutions for multi-..."
...[11-16] designed an effective method to study the multi-objective programming model of transportation including total cost, and a multi-objective fuzzy LP was defined and extended it to the programming problem with hard and flexible constraints with interval uncertainty which is solved by an optimal-pessimistic method proposed by them....
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References
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"Pareto-optimal solutions for multi-..." refers background in this paper
...I-fuzzy set and IV-fuzzy set of a fuzzy set is different but they turned out to be mathematically equivalent; to convince one can refer to [3]....
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01 Jan 1973
TL;DR: The main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh.
Abstract: In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.
593 citations