Mixed-discrete fuzzy multiobjective optimization of fuzzy systems

Although much attention has been focused on the development and applications of fuzzy optimization, multiobjective programming and mixed-discrete optimization methods separately, fuzzy multiobjective optimization problems in mixed-discrete design space were not addressed in the literature. It is mainly due to the lack of mature and robust theories of mixed-discrete and multiobjective optimization. In most practical applications, designers often encounter problems involving imprecise or fuzzy information, multiple objectives and mixed-discrete design variables. This paper presents a new method in which the fuzzy μ-formulation and game theory techniques are combined with a mixed-discrete hybrid genetic algorithm for solving mixed-dixcrete fuzzy multiobjective programming problems. Three example problems, dealing with the optimal designs of a two-bar truss, a conical convective spine and a twenty-five bar truss, demonstrate that the method can be flexibly and effectively applied to various kinds of engineering design problems to obtain more realistic and satisfactory results in an imprecise environment.