Algorithm for Approximate Solution of the Generalized Weber Problem with an Arbitrary Metric

The multi-facility Weber location problem is transformed into a pseudo-Boolean optimization problem and solved with use of a heuristic random search anytime-algorithm. Fermat-Weber problem in its simplest form (unconstrained, single facility, Euclidean metric) is well investigated. A lot of algorithms are developed for more complex cases. However, the generalized multi-facility problem with barriers, restricted zones and arbitrary metric has no well-known algorithm for its solving. In this report, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method and prove its efficiency for approximate solving this problem by replacing the continuous coordinate values by discrete ones. Version of the algorithm for multiprocessor systems is proposed. An example of a problem solution is given.