An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems

TL;DR

This paper introduces a novel evolutionary strategy for solving combinatorial optimization problems like the TSP, using a partial imitation mechanism that guides a population towards optimal or suboptimal solutions efficiently.

Contribution

The paper presents a new partial imitation approach within an evolutionary framework, enabling effective search in discrete, NP-hard problem spaces like the TSP.

Findings

The method can find optimal solutions within finite time.

Partial imitation promotes solution diversity and convergence.

The approach is effective for large, complex search spaces.

Abstract

In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem whose search space grows exponentially, increasing the number of cities, up to becoming NP-hard. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by 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 an imitative mechanism, we define `partial imitation'. In particular, agents receive a random solution and then, interacting among themselves, may imitate the solutions of agents with a higher fitness. Since the imitation mechanism is only partial, agents copy only one entry (randomly chosen) of another array (i.e. solution). 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 solutions over time, before reaching the final equilibrium. Results of numerical simulations show that our method is able to find, in a finite time, both optimal and suboptimal solutions, depending on the size of the considered search space.