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Ant Colony System: A cooperative learning approach to the traveling salesman problem
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1997
"... This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a pher ..."
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Cited by 1029 (53 self)
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This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a pheromone they deposit on the edges of the TSP graph while building solutions. We study the ACS by running experiments to understand its operation. The results show that the ACS outperforms other natureinspired algorithms such as simulated annealing and evolutionary computation, and we conclude comparing ACS3opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSP’s.
Ant algorithms for discrete optimization
 ARTIFICIAL LIFE
, 1999
"... 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 ..."
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Cited by 489 (42 self)
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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.
The ant colony optimization metaheuristic
 in New Ideas in Optimization
, 1999
"... Ant algorithms are multiagent systems in which the behavior of each single agent, called artificial ant or ant for short in the following, is inspired by the behavior of real ants. Ant algorithms are one of the most successful examples of swarm intelligent systems [3], and have been applied to many ..."
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Cited by 389 (23 self)
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Ant algorithms are multiagent systems in which the behavior of each single agent, called artificial ant or ant for short in the following, is inspired by the behavior of real ants. Ant algorithms are one of the most successful examples of swarm intelligent systems [3], and have been applied to many types of problems, ranging from the classical traveling salesman
Ant colonies for the travelling salesman problem
, 1997
"... We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer si ..."
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Cited by 286 (5 self)
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We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to both symmetric and asymmetric instances of the TSP. The method is an example, like simulated annealing, neural networks and evolutionary computation, of the successful use of a natural metaphor to design an optimization algorithm.
MAXMIN Ant System and Local Search for the Traveling Salesman Problem
 IEEE INTERNATIONAL CONFERENCE ON EVOLUTIONARY COMPUTATION (ICEC'97)
, 1997
"... Ant System is a general purpose algorithm inspired by the study of the behavior of Ant Colonies. It is based on a cooperative search paradigm that is applicable to the solution of combinatorial optimization problems. In this paper we introduce MAX MIN Ant System, an improved version of basic Ant S ..."
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Cited by 138 (15 self)
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Ant System is a general purpose algorithm inspired by the study of the behavior of Ant Colonies. It is based on a cooperative search paradigm that is applicable to the solution of combinatorial optimization problems. In this paper we introduce MAX MIN Ant System, an improved version of basic Ant System, and report our results for its application to symmetric and asymmetric instances of the well known Traveling Salesman Problem. We show how MAX MIN Ant System can be significantly improved extending it with local search heuristics. Our results clearly show that MAX MIN Ant System has the property of effectively guiding the local search heuristics towards promising regions of the search space by generating good initial tours. I. Introduction The Ant System algorithm, originally introduced in [3], [4], is a new cooperative search algorithm inspired by the behavior of real ants. Ants are able to find good solutions to shortest path problems between a food source and their home colony...
MAXMIN Ant System
, 1999
"... Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Sa ..."
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Cited by 128 (3 self)
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Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this ares has mainly focused on the development of algorithmic variants which achieve better performance than AS. In this article, we present¨�©� � –¨��� � Ant System, an Ant Colony Optimization algorithm derived from Ant System.¨�©� � –¨��� � Ant System differs from Ant System in several important aspects, whose usefulness we demonstrate by means of an experimental study. Additionally, we relate one of the characteristics specific to¨� ¨ AS — that of using a greedier search than Ant System — to results from the search space analysis of the combinatorial optimization problems attacked in this paper. Our computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that ¨�©� � –¨��� � Ant System is currently among the best performing algorithms for these problems.
The ant colony optimization metaheuristic: Algorithms, applications, and advances
 Handbook of Metaheuristics
, 2002
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Solving Symmetric and Asymmetric TSPs by Ant Colonies
, 1996
"... In this paper we present ACS, a distributed algorithm for the solution of combinatorial optimization problems which was inspired by the observation of real colonies of ants. We apply ACS to both symmetric and asymmetric traveling salesman problems. Results show that ACS is able to find good sol ..."
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Cited by 102 (21 self)
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In this paper we present ACS, a distributed algorithm for the solution of combinatorial optimization problems which was inspired by the observation of real colonies of ants. We apply ACS to both symmetric and asymmetric traveling salesman problems. Results show that ACS is able to find good solutions to these problems. I. Introduction In this paper we present Ant Colony System (ACS), a novel distributed approach to combinatorial optimization based on the observation of real ant colonies behavior. ACS finds its ground in one of the authors previous work on the socalled Ant System (AS) [1],[2],[5],[7] and in AntQ [8] an extension of AS with Qlearning [12], a reinforcement learning technique. In particular, ACS is a revisited version of AntQ where a different way to update the experience accumulated by the artificial ants has been introduced [6]. All the mentioned systems belong to the Artificial Ant Colonies (AAC) family of algorithms that has been applied to various combinat...
A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems
 In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation
, 1996
"... The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and ..."
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Cited by 87 (12 self)
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The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and genetic algorithms are used to search the space of local optima in order to find the global optimum. New genetic operators for realizing the proposed approach are described, and the quality and efficiency of the solutions obtained for a set of symmetric and asymmetric TSP instances are discussed. The results indicate that it is possible to arrive at high quality solutions in reasonable time. I. Introduction In the Traveling Salesman Problem (TSP) [18], [27], a number of cities with distances between them is given and the task is to find the minimumlength closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...
Genetic Local Search for the TSP: New Results
 In Proceedings of the 1997 IEEE International Conference on Evolutionary Computation
, 1997
"... The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding nearoptimum solutions to the traveling salesman problem. In this paper, previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman pr ..."
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Cited by 85 (13 self)
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The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding nearoptimum 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...