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Solving Optimization Problems by the Public Goods Game
Aug 29, 2017
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.
An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems
Aug 04, 2016
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.
* 18 pages, 6 figures