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A Multi-criteria fuzzy random crop planning problem using evolutionary optimization

Hoang Dao Minh, Xuan Tran Van, Thang Tran Ngoc

Annals of Computer Science and Information Systems

2021

Vol. 27

49--52

In this paper, we deal with fuzzy random objectives in a multi-criteria crop planning problem considered as a multi-objective linear programming problem. These fuzzy random factors are related to decision making processes in practice, especially the uncertainty and synthesized objectives of experts. The problem is transformed into a multi-objective nonlinear programming problem by a step of evaluating expectation value. Instead of using classical methods, we use a multi-objective evolutionary algorithms called NSGA-II to solve the equivalent problem. This helps finding many approximate solutions concurrently with a low time consumption. In computational experiments, we create a specific fuzzy random crop planning problem with the data synthesized from government's reports and show convergence of the algorithm for proposed model.

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

Arora R., Gupta K.

Archives of Control Sciences

2020

Vol. 30, No. 4

683--699

Bilevel programming problem is a non-convex two stage decision making process in which the constraint region of upper level is determined by the lower level problem. In this paper, a multi-objective indefinite quadratic bilevel programming problem (MOIQBP) is presented. The defined problem (MOIQBP) has multi-objective functions at both the levels. The followers are independent at the lower level. A fuzzy goal programming methodology is employed which minimizes the sum of the negative deviational variables of both the levels to obtain highest membership value of each of the fuzzy goal. The membership function for the objective functions at each level is defined. As these membership functions are quadratic they are linearized by Taylor series approximation. The membership function for the decision variables at both levels is also determined. The individual optimal solution of objective functions at each level is used for formulating an integrated pay-off matrix. The aspiration levels for the decision makers are ascertained from this matrix. An algorithm is developed to obtain a compromise optimal solution for (MOIQBP). A numerical example is exhibited to evince the algorithm. The computing software LINGO 17.0 has been used for solving this problem.