Adapted Path-relinking Based Search for Non-dominated Set of Emergency Medical System Designs

The path-relinking method has proved to be a very powerful tool, when searching for a good solution in the set of feasible solutions of a zero-one programming problem with one min-sum objective function. Nevertheless, designing of an emergency medical system includes making decisions on a balance between conflicting criteria, which reflect requirements of efficiency on one hand and requirements of fair access to minorities on the other hand. This decision-making process needs a series of non-dominated solutions, which enables to reduce the range of solutions for final implementation. This paper is focused on the path-relinking method exploitation to find a good approximation of the Pareto front of the emergency medical system designs. As the path-relinking method itself is able to inspect only one short path in the surface of a unit hypercube, the method must be embedded into a more sophisticated searching process. We present here a learning algorithm, which adaptively choices pair of input solutions for a single path-relinking method run. The learning algorithm also sets weights of the conflicting criteria to define composed objective function used in the control process of the path-relinking method. The complete searching process was tested on several real-sized benchmarks and the resulting sets of non-dominated solutions are compared to the exact Pareto fronts. The obtained results are reported in details in a computational study at the end of the paper.