Multiobjective combinatorial optimization for performance evaluation by a meta-heuristic satisficing tradeoff method

In this paper an effective meta-heuristic approach is proposed to realize a satisficing tradeoff method for solving multiobjective combinatorial optimization problems of performance evaluation. Firstly, Pareto optimal solutions (individuals) are generated by using a genetic algorithm with family elitist concept for a multiobjective combinatorial optimization problem. Then, we try to find a preferred solution of the decision maker based on the satisficing tradeoff method. Usually, a conventional satisficing tradeoff method needs to solve a complex min-max problem in each iteration of the algorithm for a given aspiration level of each objective function. The min-max problem is to minimize maximum value of a regularized regret function. In this paper a new meta-heuristic satisficing tradeoff method is proposed in which we do not need to solve a complex min-max problem in each iteration, but we try to find a min-max solution in the Pareto optimal solutions (individuals) generated by the genetic algorithm. We further revise the min-max solution by using a local search approach such as a simulated annealing method. As a numerical example a flowshop scheduling problem is included to verify the effectiveness of the method proposed in this paper.