Construction and reduction of the Pareto set in asymmetric travelling salesman problem with two criteria
This work addresses the problem of wide Pareto sets in multicriteria optimization for operations research and logistics, but it is incremental as it applies an existing reduction approach to a specific problem variant.
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 shows experimental results on the degree of reduction for various information quanta and instance structures.
We consider the bicriteria asymmetric travelling 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. For the first time 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 or from TSPLIB problems.