An immune system based genetic algorithm using permutation-based dualism for dynamic traveling salesman problems

Copyright @ Springer-Verlag Berlin Heidelberg 2009.In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.This work was supported by the Key Program of National Natural Science Foundation (NNSF) of China under Grant No. 70431003 and Grant No. 70671020, the Science Fund for Creative Research Group of NNSF of China under GrantNo. 60521003, the National Science and Technology Support Plan of China under Grant No. 2006BAH02A09 and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant No. EP/E060722/1

An interacting replica approach applied to the traveling salesman problem

We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with multiple extrema. Our method involves (i) coupling otherwise independent simulations of a system ("replicas") via geometrical distances as well as (ii) probabilistic inference applied to the solutions found by individual replicas. The {\it ensemble} of replicas evolves as to maximize the inter-replica correlation while simultaneously minimize the local intra-replica cost function (e.g., the total path length in the Traveling Salesman Problem within each replica). We demonstrate how our method improves the performance of rudimentary local optimization schemes long applied to the NP hard Traveling Salesman Problem. In particular, we apply our method to the well-known "$k$-opt" algorithm and examine two particular cases- $k=2$ and $k=3$. With the aid of geometrical coupling alone, we are able to determine for the optimum tour length on systems up to $280$ cities (an order of magnitude larger than the largest systems typically solved by the bare $k=3$ opt). The probabilistic replica-based inference approach improves $k-opt$ even further and determines the optimal solution of a problem with $318$ cities and find tours whose total length is close to that of the optimal solutions for other systems with a larger number of cities.Comment: To appear in SAI 2016 conference proceedings 12 pages,17 figure

Solving Optimization Problems by the Public Goods Game

This document is the Accepted Manuscript version of the following article: Marco Alberto Javarone, ‘Solving optimization problems by the public goods game’, The European Physical Journal B, 90:17, September 2017. Under embargo. Embargo end date: 18 September 2018. The final, published version is available online at doi: https://doi.org/10.1140/epjb/e2017-80346-6. Published by Springer Berlin Heidelberg.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.Peer reviewedFinal Accepted Versio