This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies’ foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the ACO metaheuristic are defined. In the second part of the article a number of applications of ACO algorithms to combinatorial optimization and routing in communications networks are described. We conclude with a discussion of related work and of some of the most important aspects of the ACO metaheuristic.

A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. Keywords: Graph coloring, solution recombination, tabu search, combinatorial optimization. 1 Introduction A recent and very promising approach for combinatorial optimization is to embed local search into the framework of population based evolutionary algorithms, leading to hybrid evolutionary algorithms (HEA). Such an algorithm is essentially based on two key elements: an eff...

The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding near-optimum solutions to the traveling salesman problem. In this paper, previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman problem are revisited and potential improvements are identified. Since local search is the central component in which most of the computation time is spent, improving the efficiency of the local search operators is crucial for improving the overall performance of the algorithms. The modifications of the algorithms are described and the new results obtained are presented. The results indicate that the improved algorithms are able to arrive at better solutions in significantly less time. I. Introduction Consider a salesman who wants to start from his home city, visit each of a set of n cities exactly once, and then return home. Since the salesman is interested in finding the shortest possible r...

Introduction The notion of fitness landscapes has been introduced to describe the dynamics of evolutionary adaptation in nature [40] and has become a powerful concept in evolutionary theory. Fitness landscapes are equally well suited to describe the behavior of heuristic search methods in optimization, since the process of evolution can be thought of as searching a collection of genotypes in order to find the genotype of an organism with highest fitness and thus highest chance of survival. Thinking of a heuristic search method as a strategy to "navigate" in the fitness landscape of a given optimization problem may help in predicting the performance of a heuristic search algorithm if the structure of the landscape is known in advance. Furthermore, the analysis of fitness landscapes may help in designing highly effective search algorithms. In the following we show how the analysis of fitness landscapes of combinatorial optimization problems can aid in designing the components of

In this paper, a fitness landscape analysis for several instances of the quadratic assignment problem (QAP) is performed and the results are used to classify problem instances according to their hardness for local search heuristics and meta-heuristics based on local search. The local properties of the tness landscape are studied by performing an autocorrelation analysis, while the global structure is investigated by employing a fitness distance correlation analysis. It is shown that epistasis, as expressed by the dominance of the flow and distance matrices of a QAP instance, the landscape ruggedness in terms of the correlation length of a landscape, and the correlation between fitness and distance of local optima in the landscape together are useful for predicting the performance of memetic algorithms - evolutionary algorithms incorporating local search - to a certain extent. Thus, based on these properties a favorable choice of recombination and/or mutation operators can be found.

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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.

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Augmenting genetic algorithms with local search heuristics is a promising approach to the solution of combinatorial optimization problems. In this paper, a genetic local search approach to the quadratic assignment problem (QAP) is presented. New genetic operators for realizing the approach are described, and its performance is tested on various QAP instances containing between 30 and 256 facilities/locations. The results indicate that the proposed algorithm is able to arrive at high quality solutions in a relatively short time limit: for the largest publicly known problem instance, a new best solution could be found. 1 INTRODUCTION In the quadratic assignment problem (QAP), n facilities have to be assigned to n locations at minimum cost. Given a set \Pi(n) of all permutations of f1; 2; : : : ; ng and two n \Theta n matrices A = (a ij ) and B = (b ij ), the task is to minimize the quantity C(ß) = n X i=1 n X j=1 a ij b ß(i)ß(j) ; ß 2 \Pi(n): (1) Matrix A can be interpreted as a ...

. This paper presents a new genetic local search algorithm for the graph coloring problem. The algorithm combines an original crossover based on the notion of union of independent sets and a powerful local search operator (tabu search). This new hybrid algorithm allows us to improve on the best known results of some large instances of the famous Dimacs benchmarks. 1 Introduction The graph coloring problem is one of the most studied NP-hard problems and can be defined informally as follows. Given an undirected graph, one wishes to color with a minimal number of colors the nodes of the graph in such a way that two colors assigned to two adjacent nodes must be different. Graph coloring has many practical applications such as timetabling and resource assignment. Given the NP-completeness of the coloring problem, it becomes natural to design heuristic methods. Indeed many heuristic methods have been developed, constructive methods in the 60's and 70's [1, 12], local search meta-heuristics ...