Customization of Uniformly Deployed Set Kit for Path-relinking Method

The weighted p-median problem solving techniques represent basic tools for designing large emergency service systems, which have to provide public of a serviced region with service from a given number of service centers. A specific form of the set of all feasible solutions of the p-median problem enables to employ efficient incrementing heuristics to obtain a near-to-optimal solution. The incrementing heuristics proved their efficiency in combination with preliminary inspection of the set of all feasible solutions performed by a uniformly deployed set of p-median problem solutions. As obtaining uniformly deployed set for a specific p-median problem is very time consuming, an idea of a universal kit of uniformly deployed set has arisen. The idea consists in building up a standard family of uniformly deployed sets for given ranges of the number p of located centers and the number m of possible service center locations. If an emergency system has to be designed and its sizes p and m do not correspond with any standard uniformly deployed set, then a suitable standard set of the kit is adjusted to the sizes of the solved problem. This approach works excellently if the neighborhood search incrementing heuristics are applied, but it fails in case of path-relinking method based incrementing algorithms. This defect is caused by the fact that the solutions contained in the adjusted uniformly deployed set do not cover all possible service center locations of the solved problem. In this paper, we suggest an extending adjusted method overcoming the above-mentioned drawback and we study the impact of this improvement on efficiency of incrementing approaches based on the path-relinking inspection.