Convergence results for continuous-time dynamics arising in ant colony optimization

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is shown, and the speed of convergence is calculated explicitly and shown to be proportional to the difference between the reciprocals of the second shortest and the shortest paths.Comment: A short version of this paper was published in the preprints of the 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, 24-29 August 201

An ant colony optimization approach for maximizing the lifetime of heterogeneous wireless sensor networks

Maximizing the lifetime of wireless sensor networks (WSNs) is a challenging problem. Although some methods exist to address the problem in homogeneous WSNs, research on this problem in heterogeneous WSNs have progressed at a slow pace. Inspired by the promising performance of ant colony optimization (ACO) to solve combinatorial problems, this paper proposes an ACO-based approach that can maximize the lifetime of heterogeneous WSNs. The methodology is based on finding the maximum number of disjoint connected covers that satisfy both sensing coverage and network connectivity. A construction graph is designed with each vertex denoting the assignment of a device in a subset. Based on pheromone and heuristic information, the ants seek an optimal path on the construction graph to maximize the number of connected covers. The pheromone serves as a metaphor for the search experiences in building connected covers. The heuristic information is used to reflect the desirability of device assignments. A local search procedure is designed to further improve the search efficiency. The proposed approach has been applied to a variety of heterogeneous WSNs. The results show that the approach is effective and efficient in finding high-quality solutions for maximizing the lifetime of heterogeneous WSNs

A Deterministic Model for Analyzing the Dynamics of Ant System Algorithm and Performance Amelioration through a New Pheromone Deposition Approach

Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm. Traditionally, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. Thus the pheromone concentration remains uniform throughout the entire path of an ant. This article introduces an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of basic Ant System algorithm. The idea here is to introduce an additional attracting force to guide the ants towards destination more easily by constructing an artificial potential field identified by increasing pheromone concentration towards the goal. Apart from carrying out analysis of Ant System dynamics with both traditional and the newly proposed deposition rules, the paper presents an exhaustive set of experiments performed to find out suitable parameter ranges for best performance of Ant System with the proposed deposition approach. Simulations reveal that the proposed deposition rule outperforms the traditional one by a large extent both in terms of solution quality and algorithm convergence. Thus, the contributions of the article can be presented as follows: i) it introduces differential equation and explores a novel method of analyzing the dynamics of ant system algorithms, ii) it initiates an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of algorithm in terms of solution quality and convergence time, iii) exhaustive experimentation performed facilitates the discovery of an algebraic relationship between the parameter set of the algorithm and feature of the problem environment.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

An ant colony algorithm for the sequential testing problem under precedence constraints.

We consider the problem of minimum cost sequential testing of a series (parallel) system under precedence constraints that can be modeled as a nonlinear integer program. We develop and implement an ant colony algorithm for the problem. We demonstrate the performance of this algorithm for special type of instances for which the optimal solutions can be found in polynomial time. In addition, we compare the performance of the algorithm with a special branch and bound algorithm for general instances. The ant colony algorithm is shown to be particularly effective for larger instances of the problem