Abstract
In the Weber location problem which was proposed for optimal location of industrial enterprises, the aim is to find the location of a point such that the sum of weighted distance between this point and a finite number of existing points is minimized. This popular model is widely used for optimal location of equipment and in many sophisticated models of cluster analysis such as detecting homogeneous production batches made from a single production batch of raw materials. The well-known iterative Weiszfeld does not converge efficiently to the optimal solution when the solution either coincides or nearly coincides with one of the demands point which is not the optimum. We propose a modified Particle Swarm Optimization (PSO) algorithm. The velocity update of the PSO is modified to enlarge the search space and enhance the global search ability. The preliminary results of these algorithms are analyzed and compared.
Highlights
Facility location problems seek to optimize the placement of facilities such that the demands of customers can be met at the lowest cost and/or shortest distance
We propose a modified Particle Swarm Optimization (PSO) algorithm
Known Methods Weiszfeld procedure is a one-point iterative method that involves the calculation of gradient in each iteration, and it is widely used in solving single facility Weber problem with Euclidean distances and in multi-facility procedures as a step in the solution algorithm [13], it was observed that the method can reach a non-optimal point, the situation described as “getting stuck”, and starting points of method leading to this situation are called “bad” starting points [14]
Summary
Facility location problems seek to optimize the placement of facilities such that the demands of customers can be met at the lowest cost and/or shortest distance. Location optimization problems have numerous applications in the field of mathematics, economics, physics and engineering. Many kinds of the distance functions can be employed, distances in the Weber problems are often taken to be Euclidean distances [1,2]. Weber problem ( often called the Fermat Steiner Weber problem, median problem, minisum problem, or, in the special case of three existing facilities having equal weights, as the Fermat Torricelli problem):.
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