On the Possibility to Design Evolutionary Algorithms with Optimal Equilibrium Distribution. The Case of Simulated Annealing

In this paper a thermodynamic approach is presented to the problem of convergence of evolutionary algorithms. The case of the Simulated Annealing algorithm for optimisation is considered as a simple evolution strategy with a control parameter allowing balance between the probability of obtaining an optimal or near-optimal solution and the time that the algorithm will take to reach equilibrium. This capacity is analysed and a theoretical frame is presented, stating a general condition to be fulfilled by an evolutionary algorithm in order to ensure its convergence to a global maximum of the fitness function.