Optimal Strategy for Resource Allocation of Two-Dimensional Potts Model Using Genetic Algorithm

Abstract

The problem of optimal strategies of resource allocation for companies competing in the shopping malls in a metropolis is investigated in the context of two-dimensional three state Potts model in statistical physics. The aim of each company is to find the best strategy of initial distribution of resource to achieve market dominance in the shortest time. Evolutionary Algorithm is used to encode the ensemble of initial patterns of three states Potts model and the fitness of the configuration is measured by the market share of a chosen company after a fixed number of Monte Carlo steps of evolution. Numerical simulation indicates that initial patterns with certain topological properties do evolve faster to market dominance. The description of these topological properties is measured by the degree distribution of each company. Insight on the initial patterns that entail fast dominance is discussed.