AN INTERACTIVE PROCEDURE USING DOMINATION CONES FOR BICRITERION SHORTEST-PATH PROBLEMS

In this paper an interactive procedure is developed for the bicriterio n shortest path problem. It is assumed that the decision maker's inher ant utility function is quasi-concave and non-increasing, and that the network consists of non-negative, integer valued are lengths. The pro posed procedure uses the concept of domination cones, which it develop s from pairwise comparisons of alternatives. These domination cones ar e used to fathom a large number of Pareto-optimal solutions. Extensive computational testing was performed on large grid networks, simulatin g the decision maker's response using polynomial utility functions. Th e results indicate that our proposed procedure is able to converge to the optimal solution in a reasonably small number of pairwise comparis ons, even for those problems with a large number of Pareto-optimal sol utions.