Enumerating Knight\u27s Tours using an Ant Colony Algorithm

In this paper, we show how an ant colony optimisation algorithm may be used to enumerate knight\u27s tours for variously sized chessboards. We have used the algorithm to enumerate all tours on 5×5 and 6×6 boards, and, while the number of tours on an 8×8 board is too large for a full enumeration, our experiments suggest that the algorithm is able to uniformly sample tours at a constant, fast rate for as long as is desired

Parallel ant algorithms for the minimum tardy task problem

Ant Colony Optimization algorithms are intrinsically distributed algorithms where independent agents are in charge of building solutions. Stigmergy or indirect communication is the way in which each agent learns from the experience of the whole colony. However, explicit communication and parallel models of ACO can be implemented directly on different parallel platforms. We do so, and apply the resulting algorithms to the Minimum Tardy Task Problem (MTTP), a scheduling problem that has been faced with other metaheuristics, e.g., evolutionary algorithms and canonical ant algorithms. The aim of this article is twofold. First, it shows a new instance generator for MTTP to deal with the concept of “problem class”; second, it reports some preliminary results of the implementation of two type of parallel ACO algorithms for solving novel and larger instances of MTTP.Eje: V - Workshop de agentes y sistemas inteligentesRed de Universidades con Carreras en Informática (RedUNCI

Parallel ant algorithms for the minimum tardy task problem

Ant Colony Optimization algorithms are intrinsically distributed algorithms where independent agents are in charge of building solutions. Stigmergy or indirect communication is the way in which each agent learns from the experience of the whole colony. However, explicit communication and parallel models of ACO can be implemented directly on different parallel platforms. We do so, and apply the resulting algorithms to the Minimum Tardy Task Problem (MTTP), a scheduling problem that has been faced with other metaheuristics, e.g., evolutionary algorithms and canonical ant algorithms. The aim of this article is twofold. First, it shows a new instance generator for MTTP to deal with the concept of “problem class”; second, it reports some preliminary results of the implementation of two type of parallel ACO algorithms for solving novel and larger instances of MTTP.Eje: V - Workshop de agentes y sistemas inteligentesRed de Universidades con Carreras en Informática (RedUNCI

Ant Colony Optimization with External Memory of Each Ant

Ant Colony Optimization (ACO)はDorigoに提案されて以降，様々なアルゴリズムの拡張が行われている。従来のACOでは個々のアリが独自の情報を持つことは無く，グローバルな情報のみに従って探索を行っていた。本稿では個々のアリの記憶情報を探索に利用するACOを提案する。さらに，個々のアリの記憶が一定確率で忘れられるケースも考える。また 性能比較実験にはTSPライブラリーの標準テスト問題を使い，拡張アルゴリズムの有効性を示す。Since Ant Colony Optimization (ACO) algorithm was introduced by Dorigo in 1992, several researchers have enhanced it. Each ant in basic ACO algorithm has no long-term memory; it searches using only pheromone information. In this paper, we propose a variant of ACO algorithm that uses external memory of each ant to seek an optimum solution. Moreover, it incorporates not only the case in which each ant’s memory is permanent but also the case in which the memory is lost with a certain probability. The effectiveness of our proposed algorithm is demonstrated by testing with benchmark test problems from the TSP library (TSPLIB)

Reactive approach for automating exploration and exploitation in ant colony optimization

Ant colony optimization (ACO) algorithms can be used to solve nondeterministic polynomial hard problems. Exploration and exploitation are the main mechanisms in controlling search within the ACO. Reactive search is an alternative technique to maintain the dynamism of the mechanics. However, ACO-based reactive search technique has three (3) problems. First, the memory model to record previous search regions did not completely transfer the neighborhood structures to the next iteration which leads to arbitrary restart and premature local search. Secondly, the exploration indicator is not robust due to the difference of magnitudes in distance matrices for the current population. Thirdly, the parameter control techniques that utilize exploration indicators in their feedback process do not consider the problem of indicator robustness. A reactive ant colony optimization (RACO) algorithm has been proposed to overcome the limitations of the reactive search. RACO consists of three main components. The first component is a reactive max-min ant system algorithm for recording the neighborhood structures. The second component is a statistical machine learning mechanism named ACOustic to produce a robust exploration indicator. The third component is the ACO-based adaptive parameter selection algorithm to solve the parameterization problem which relies on quality, exploration and unified criteria in assigning rewards to promising parameters. The performance of RACO is evaluated on traveling salesman and quadratic assignment problems and compared with eight metaheuristics techniques in terms of success rate, Wilcoxon signed-rank, Chi-square and relative percentage deviation. Experimental results showed that the performance of RACO is superior than the eight (8) metaheuristics techniques which confirmed that RACO can be used as a new direction for solving optimization problems. RACO can be used in providing a dynamic exploration and exploitation mechanism, setting a parameter value which allows an efficient search, describing the amount of exploration an ACO algorithm performs and detecting stagnation situations

Parallélisation d'un algorithme d'optimisation par colonies de fourmis pour la résolution d'un problème d'ordonnancement industriel

Les problèmes d'optimisation combinatoire peuvent être retrouvés, sous différentes formes, dans un grand nombre de sphères d'activité économique au sein de notre société. Ces problèmes complexes représentent encore un défi de taille pour bon nombre de chercheurs issus de domaines scientifiques variés tels les mathématiques, l'informatique et la recherche opérationnelle, pour ne citer que quelques exemples. La nécessité de résoudre ces problèmes de façon efficace et rapide a entraîné le prolifération de méthodes de résolution de toutes sortes, certaines étant plus spécifiques à un problème et d'autres étant plus génériques. Ce mémoire réunit différentes notions du parallélisme et des métaheuristiques afin d'apporter une méthode de résolution performante à un problème d'optimisation combinatoire réel. Il démontre que l'introduction de stratégies de parallélisation à un algorithme d'Optimisation par Colonies de Fourmis permet à ce dernier d'améliorer considérablement ses facultés de recherche de solutions. Le succès de cette approche dans la résolution d'un problème d'ordonnancement industriel rencontré dans une entreprise de fabrication d'aluminium montre l'intérêt pratique de ces méthodes et leurs retombées économiques potentielles. Ce travail de recherche, loin d'être une fin en soi, représente plutôt une première exploration des possibilités offertes par deux domaines fort prometteurs de l'informatique et de la recherche opérationnelle. L'union de méthodes d'apprentissage intelligentes et d'une puissance de calcul imposante pourrait fort bien se révéler un outil performant pour la résolution de problèmes d'une telle envergure

Estudio e implementación de metaheurísticas para solucionar el problema de la selección deseada

Evolutionary algorithms are among the most successful approaches for solving a number of problems where systematic search in huge domains must be performed. One problem of practical interest that falls into this category is known as The Root Identification Problem in Geometric Constraint Solving, where one solution to the geometric problem must be selected among a number of possible solutions bounded by an exponential number. In this work we analize habilities and drawbacks of a series of metaheuristics in relation with the Root identification problem.Postprint (published version

Cooperative Models of Particle Swarm Optimizers

Particle Swarm Optimization (PSO) is one of the most effFective optimization tools, which emerged in the last decade. Although, the original aim was to simulate the behavior of a group of birds or a school of fish looking for food, it was quickly realized that it could be applied in optimization problems. Different directions have been taken to analyze the PSO behavior as well as improving its performance. One approach is the introduction of the concept of cooperation. This thesis focuses on studying this concept in PSO by investigating the different design decisions that influence the cooperative PSO models' performance and introducing new approaches for information exchange. Firstly, a comprehensive survey of all the cooperative PSO models proposed in the literature is compiled and a definition of what is meant by a cooperative PSO model is introduced. A taxonomy for classifying the different surveyed cooperative PSO models is given. This taxonomy classifies the cooperative models based on two different aspects: the approach the model uses for decomposing the problem search space and the method used for placing the particles into the different cooperating swarms. The taxonomy helps in gathering all the proposed models under one roof and understanding the similarities and differences between these models. Secondly, a number of parameters that control the performance of cooperative PSO models are identified. These parameters give answers to the four questions: Which information to share? When to share it? Whom to share it with? and What to do with it? A complete empirical study is conducted on one of the cooperative PSO models in order to understand how the performance changes under the influence of these parameters. Thirdly, a new heterogeneous cooperative PSO model is proposed, which is based on the exchange of probability models rather than the classical migration of particles. The model uses two swarms that combine the ideas of PSO and Estimation of Distribution Algorithms (EDAs) and is considered heterogeneous since the cooperating swarms use different approaches to sample the search space. The model is tested using different PSO models to ensure that the performance is robust against changing the underlying population topology. The experiments show that the model is able to produce better results than its components in many cases. The model also proves to be highly competitive when compared to a number of state-of-the-art cooperative PSO algorithms. Finally, two different versions of the PSO algorithm are applied in the FPGA placement problem. One version is applied entirely in the discrete domain, which is the first attempt to solve this problem in this domain using a discrete PSO (DPSO). Another version is implemented in the continuous domain. The PSO algorithms are applied to several well-known FPGA benchmark problems with increasing dimensionality. The results are compared to those obtained by the academic Versatile Place and Route (VPR) placement tool, which is based on Simulated Annealing (SA). The results show that these methods are competitive for small and medium-sized problems. For higher-sized problems, the methods provide very close results. The work also proposes the use of different cooperative PSO approaches using the two versions and their performances are compared to the single swarm performance