Fuzzy set-based multiobjective allocation of resources: Solution algorithms and applications

Abstract

This paper presents results of research in the use of the Bellman–Zadeh approach to decision- making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The application of the approach permits one to realize an effective (from the computational standpoint) as well as rigorous (in view of obtaining solutions from the Pareto set) method of analyzing multiobjective models. The use of the Bellman–Zadeh approach has served as a basis for solving problems of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision making system (AIDMS). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a non-local search (modification of Gelfand's and Tsetlin's “long valley” method) as well as a genetic algorithm. The comparison of their computational performance is given on the basis of solving problems of multiobjective power shortage allocation in power systems.