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This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal k-coloring of that fuzzy graph such that the degree of the sum of incompatible vertices and edges is minimized. TFGC is also converted into an equivalent binary programming problem and solved using a CPLEX solver. The performance of both methods is examined on randomly generated fuzzy graphs and computational results are reported. An application based on TFGC is also explored and solved using both proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a genetic algorithm for multi-objective optimization problems with max-product fuzzy relation equations as constraints is presented. Since the non-empty feasible domain of such problems is, in general, a non-convex set; the traditional optimization methods cannot be applied. Here, we are presenting a genetic algorithm (GA) to find “Pareto optimal solutions” for solving such problems observing the role of non-convexity of the feasible domain of decision problem. Solutions are kept within feasible region during the mutation as well as crossover operations. Test problems are developed to evaluate the performance of the proposed algorithm and to determine satisficing decisions. In case of two objectives, weighting method is also applied to find the locus of optimal solutions. [Copyright &y& Elsevier]