A Swarm Intelligence Method Combined to Evolutionary Game Theory Applied to the Resources Allocation Problem

Abstract

This paper addresses an allocation problem and proposes a solution using a swarm intelligence method. The application of swarm intelligence has to be discrete. This allocation problem can be modelled as a multi-objective optimization problem where the authors minimize the time and the distance of the total travel in a logistic context. This study uses a hybrid Discrete Particle Swarm Optimization (DPSO) method combined to Evolutionary Game Theory (EGT). One of the main implementation issues of DPSO is the choice of inertial, individual, and social coefficients. In order to resolve this problem, those coefficients are optimised by using a dynamical approach based on EGT. The strategies are either to keep going with only inertia, only with individual, or only with social coefficients. Since the optimal strategy is usually a mixture of the three, the fitness of the swarm can be maximized when an optimal rate for each coefficient is obtained. Evolutionary game theory studies the behaviour of large populations of agents who repeatedly engage in strategic interactions. Changes in behaviour in these populations are driven by natural selection via differences in birth and death rates. To test this algorithm, the authors create a problem whose solution is already known. This study checks whether this adapted DPSO method succeeds in providing an optimal solution for general allocation problems.