Interactive fuzzy programming for two-level nonconvex programming problems through the revised GENOCOP III

This paper formulates two-level nonconvex programming problems and presents an interactive fuzzy programming method through coevolutionary genetic algorithms. In our interactive method, after determining the fuzzy goals of the decision-makers at both levels, by updating the satisfactory degree of the decision-maker at the upper level with considerations of overall satisfactory balance among both levels, an overall satisfactory solution is derived efficiently through coevolutionary genetic algorithms which are effective for nonconvex programming problems. An illustrative numerical example for two-level nonconvex programming problems is provided to demonstrate the feasibility and efficiency of the proposed method.