Solving Optimization Problems by the Public Goods Game

TL;DR

This paper presents a novel heuristic for solving the Traveling Salesman Problem by applying the Public Goods Game, demonstrating its ability to find exact and suboptimal solutions through agent interactions.

Contribution

It introduces a new optimization approach based on evolutionary game theory, specifically using the Public Goods Game for combinatorial problems.

Findings

The method can compute exact solutions for TSP instances.

It effectively finds suboptimal solutions in complex search spaces.

Numerical simulations validate the approach's potential.

Abstract

We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities. The proposed method considers a population whose agents are provided with a random solution to the given problem. In doing so, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. Notably, agents with better solutions provide higher contributions, while those with lower ones tend to imitate the solution of richer agents for increasing their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization problems, our work aims to highlight the potentiality of evolutionary game theory beyond its current horizons.