Uniform Deployment of the p-Location Problem Solutions

The uniform deployment has emerged from the need to inspect the enormously large set of feasible solutions of an optimization problem and due to inability of the exact methods to terminate the computation in an acceptable time. The objective function values of the solutions of the uniformly deployed set enable to determine areas of great interest. The uniformly deployed set can also represent population with maximal diversity for evolutionary metaheuristics. The paper deals with a notion of uniformity based on minimal Hamming distance between each pair of solutions. The set of selected solutions is considered to be uniformly deployed if the minimal Hamming distance across the set of all pairs of selected solutions is greater than or equal to a given threshold and if there is no possibility to add any other solution to the set. The paper contains a way of suggesting an initial uniformly deployed set of solutions and an iterative approach to the set enlargement.