Multi-objective optimization with fuzzy measures and its application to flow-shop scheduling

Most of the research in multi-objective scheduling optimization uses the classical weighted arithmetic mean operator to aggregate the various optimization criteria. However, there are scheduling problems where criteria are considered interact and thus a different operator should be adopted. This paper is devoted to the search of Pareto-optimal solutions in a tri-criterion flow-shop scheduling problem (FSSP) considering the interactions among the objectives. A new hybrid meta-heuristic is proposed to solve the problem which combines a genetic algorithm (GA) for solutions evolution and a reduced variable neighborhood search (RVNS) technique for fast solution improvement. To deal with the interactions among the three criteria the discrete Choquet integral method is adopted as a means to aggregate the criteria in the fitness function of each individual solution. Experimental comparisons (over public available FSSP test instances) with five existing multi-objective evolutionary algorithms (including the well known SPEA2 and NSGAII algorithms as well as the recently published L-NSGA algorithm) showed a superior performance for the developed approach in terms of diversity and domination of solutions.