Public Service System Design With Conflicting Criteria

Multi-criteria optimization problems represent a crucial task for any designer of a public service system due to conflicting criteria, which have to be faced. Possible solution of this almost unsolvable situation can be seen in obtaining a series of solutions, where it is impossible to improve one of the criteria without worsening some of the others. Full set of such non-dominated solutions is called Pareto front. The multi-criteria optimization problem can be solved by submitting the Pareto front or its approximation on contracting authority’s board for possible negotiation with representative of public. This paper deals with methods, which are able to produce a series of non-dominated solutions of bi-criteria public service system design problem. The first criterion considered is average response time and the second one corresponds to the number of users located behind a given limit of response time. We suggest two approaches to the problem. The first of them is an exact approach, which produces Pareto front of the bi-criteria problem. The second approach makes use of an evolutionary hybridized algorithm, which uses so called elite set, to save temporary non-dominated solutions. In the computational study, we try to verify the hypothesis that it is possible to approximate the Pareto front by utilizing the evolutionary algorithm. We also suggest a way of hybridization and tuning the algorithm to obtain a good approximation in acceptable computational time.