Niching particle swarm optimization based euclidean distance and hierarchical clustering for multimodal optimization

Abstract : Multimodal optimization is still one of the most challenging tasks in the evolutionary computation field, when multiple global and local optima need to be effectively and efficiently located. In this paper, a niching Particle Swarm Optimization (PSO) based Euclidean Distance and Hierarchical Clustering (EDHC) for multimodal optimization is proposed. This technique first uses the Euclidean distance based PSO algorithm to perform preliminarily search. In this phase, the particles are rapidly clustered around peaks. Secondly, hierarchical clustering is applied to identify and concentrate the particles distributed around each peak to finely search as a whole. Finally, a small world network topology is adopted in each niche to improve the exploitation ability of the algorithm. At the end of this paper, the proposed EDHC-PSO algorithm is applied to the Traveling Salesman Problems (TSP) after being discretized. The experiments demonstrate that the proposed method outperforms existing niching techniques on benchmark problems, and is effective for TSP

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

An Approximate Algorithm Combining P Systems and Ant Colony Optimization for Traveling Salesman Problems

This paper proposes an approximate optimization algorithm combining P systems with ant colony optimization, called ACOPS, to solve traveling salesman prob- lems, which are well-known and extensively studied NP-complete combinatorial optimization problems. ACOPS uses the pheromone model and pheromone update rules defined by ant colony optimization algorithms, and the hierarchical membrane structure and transformation/communication rules of P systems. First, the parameter setting of the ACOPS is discussed. Second, extensive experiments and statistical analysis are investigated. It is shown that the ACOPS is superior to Nishida's algorithms and its counterpart ant colony optimization algorithms, in terms of the quality of solutions and the number of function evaluations

Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log^2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Groebner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp. 619-628. For source code and experimental results, see http://www.ics.uci.edu/~eppstein/projects/pairs