  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.
