Solving large immobile location–allocation by affinity propagation and simulated annealing. Application to select which sporting event to watch

Immobile Location-Allocation (ILA) is a combinatorial problem which consists in, given a set of facilities and a set of demand points, determining the optimal service each facility has to offer and allocating the demand to such facilities. The applicability of optimization methods is tied up to the dimensionality of the problem, but since the distance between data points is a key factor, clustering techniques to partition the data space can be applied, converting the large initial problem into several simpler ILA problems that can be solved separately. This paper presents a novel method that combines clustering and heuristic methods to solve an ILA problem, which reduces the elapsed time keeping the quality of the solution found compared with other heuristics methods.