Adaptive Swap Algorithm for Pareto Front Approximation

Implementation of any public service system is matter of negotiation of the system founder and public representatives, who try to apply conflicting criteria to the final system design. Pareto front or its approximation can be a very useful tool for the negotiation, as the set of solutions represents the set of such designs, which cannot be improved in one of the criteria unless some of the others get worsened. Nevertheless, constitution of the exact Pareto front represents serious computational problem, with big expected consumption of computational time. This drawback evoked the idea to use a heuristic for constituting a good approximation of the Pareto front of the public service system designs. In this paper, a swap algorithm is used as the base searching method due to its excellent efficiency, when applied to p-location problems with one objective function. The algorithm was adjusted for bi-criteria p-location problems so that its local objective function was formulated as a convex combination of the conflicting criteria and, furthermore, a run of the algorithm was limited by a maximal permitted computational time. This parameterized algorithm was embedded into an adaptive process, which randomly sets the parameters and a starting solution to active values based on results of previous algorithm runs. The adaptive algorithm was tested on real-sized benchmarks derived from existing emergency medical systems and the obtained results were compared to the exact Pareto fronts.