An efficient procedure for optimization of linear objective function subject to fuzzy relation equations with max-product composition

摘要

An optimization model with a linear objective function subject to a system of fuzzy relation equations (FRE) is considered. Since, feasible domain is non-convex; the traditional methods for solving this linear programming problem (l.p.p.) can not be applied. The problem is transformed into 0-1 integer programming problem. Based on the upper bound and rearranging the structure of the problem, We present a backward jump-tracking branch-and-bound technique for solving this optimization problem. It is remarked that taking the advantage of special structure of feasible domain, the problem size can be reduced so that the effort to solve the problem is minimized. A numerical example is provided-to illustrate our scheme.