Vibrational Genetic Algorithm (Vga) for Solving Continuous Covering Location Problems

Abstract

This paper deals with a continuous space problem in which demand centers are independently served from a given number of independent, uncapacitated supply centers. Installation costs are assumed not to depend on either the actual location or actual throughput of the supply centers. Transportation costs are considered to be proportional to the square Euclidean distance travelled and a mini-sum criteria is adopted. In order to solve this location problem, a new heuristic method, called Vibrational Genetic Algorithm (VGA), is applied. VGA assures efficient diversity in the population and consequently provides faster solution. We used VGA using vibrational mutation and for the mutational manner, a wave with random amplitude is introduced into population periodically, beginning with the initial step of the genetic process. This operation spreads out the population over the design space and increases exploration performance of the genetic process. This makes passing over local optimums for genetic algorithm easy. Since the problem is recognized as identical to certain cluster analysis and vector quantization problems, we also applied Kohonen maps which are Artificial Neural Networks (ANN) capable of extracting the main features of the input data through a self-organizing process based on local adaptation rules. The numerical results and comparison will be presented.