Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: An algorithm with reoptimization

Abstract

This paper addresses multicriteria combinatorial optimization problems involving one cost and several bottleneck objective functions. An algorithm is developed which generates the minimal complete set of Pareto-optimal solutions. This algorithm runs in polynomial time as long as the single objective problem considering only the cost function can be solved polynomially. A reoptimization procedure is used to accelerate the convergence of the algorithm. Applications are given. Computational results on randomly generated instances and planar grid graphs concerning the minimum cost spanning tree and the shortest path problem are presented.