A Synthesizing Effect-Based Solution Method for Stochastic Rough Multi-objective Programming Problems

Multi-objective programming with uncertain information has been widely applied in modeling of industrial produce and logistic distribution problems. Usually the expectation value model and chance-constrained model as solution models are used to deal with such uncertain programming. In this paper, we consider the uncertain programming problem which contains random information and rough information and is hard to be solved. A new solution model, called stochastic rough multi-objective synthesis effect (MOSE) model, is developed to deal with a class of multiobjective programming problems with random rough coefficients. The MOSE model contains expectation value model and chance-constrained model by choosing different synthesis effect functions and can be considered as an extension of crisp multi-objective programming model. Combined with genetic algorithm, the optimal solution of the MOSE model can be obtained. It shows that the solutions of the MOSE model are better than that of other solution models. Finally, an illustrative example is provided to show the effectiveness of the proposed method.