A study of ACO capabilities for solving the maximum clique problem

Abstract

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses "pheromone trails" as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph.We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures -the re-sampling and the dispersion ratio-for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.

Ant Colony Optimization for Multi-Objective Optimization Problems

“…The ACO metaheuristic, described e.g. in [7], is a generalization of these first ant based algorithms, and has been successfully applied to different hard combinatorial optimization problems such as quadratic assignment problems [20], vehicle routing problems [3,9], constraint satisfaction problems [18], or maximum clique problems [19].…”

Analysis of reactive search optimisation techniques for the maximum clique problem and applications

“…The theoretical grounds for the analysis of Stochastic Local Search (SLS) can be found in [38] and [10]. Among the evolutionary algorithms we cite [44], which proposes a combination of local search and Genetic Algorithms for escaping from local optima; and [58], which proposes and analyses four variants of an Ant Colony Optimisation algorithm for the MC.…”

A leader-based parallel cross entropy algorithm for MCP

“…Although quite a lot of algorithms have been proposed for the MCP , and most algorithms have been empirically evaluated on benchmark instances from the Second DIMACS Challenge [6], there is no single best algorithm based on the recent literature reports. Nevertheless, Reactive Local Search [7], QUALEX-MS [8], Deep Adaptive Greedy Search [9], the k-opt algorithm [10], Edge-AC+LS [11] and Dynamic Local earch [12] are state-of-the-art algorithms.…”