An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems

In this work we introduce an evolutionary strategy to solve optimization tasks. In particular, we focus on the Travel Salesman Problem (TSP), i.e., a NP-hard problem with a discrete search space. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by a fitness computed according to a cost function (e.g., the length of a path). Our method is based on the evolution of an agent population by means of a `partial imitation' mechanism. In particular, agents receive a random solution and then, interacting among themselves, imitate the solutions of agents with a higher fitness. Moreover, as stated above, the imitation is only partial, i.e., agents copy only one, randomly chosen, entry of better (array) solutions. In doing so, the population converges towards a shared solution, behaving like a spin system undergoing a cooling process, i.e., driven towards an ordered phase. We highlight that the adopted `partial imitation' mechanism allows the population to generate new solutions over time, before reaching the final equilibrium. Remarkably, results of numerical simulations show that our method is able to find the optimal solution in all considered search spaces.