Reduction of the Pareto Set in Bicriteria Asymmetric Traveling Salesman Problem
This work addresses the problem of wide Pareto sets in multicriteria optimization for researchers and practitioners in operations research, but it is incremental as it builds on existing axiomatic methods.
The paper tackles the bicriteria asymmetric traveling salesman problem by applying an axiomatic approach to reduce the Pareto set, using a new multi-objective genetic algorithm for approximation, and experimentally shows the degree of reduction for various information quanta and instance structures.
We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of "quanta of information" that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper shows the degree of reduction of the Pareto set approximation for various "quanta of information" and various structures of the bi-ATSP instances generated randomly.