An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical Traveling Salesman Problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the Ant System (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadrat...

In this paper we give a programmatic overview of parameterized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how fixed-parameter tractability techniques can deliver practical algorithms in two different ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT kernelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artificial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W [1]. As a corollary, this implies that k-Step Reachability for Petri Nets is complete for W [1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph k-Coloring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.

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 so-called Ant System (AS) [1],[2],[5],[7] and in Ant-Q [8] an extension of AS with Q-learning [12], a reinforcement learning technique. In particular, ACS is a revisited version of Ant-Q 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 simple mechanism is presented, based on ant-like agents, for routing and load balancing in telecommunications networks, following the initial works of Appleby and Stewart (1994) and Schoonderwoerd et al. (1997). In the present work, agents are very similar to those proposed by Schoonderwoerd et al. (1997), but a r e supplemented with a simplified dynamic programming capability, initially experimented by Gurin (1997) with more complex agents, which is shown to significantly improve the network's relaxation and its response to perturbations. Topic area: Intelligent agents and network management 2 1. Introduction 1.1 Routing in telecommunications networks Routing is a mechanism that allows calls to be transmitted from a source to a destination through a sequence of intermediate switching stations or nodes, because not all points are directly connected: the cost of completely connecting a network becomes prohibitive for more than a few nodes. Routing selects routes that meet the o...

The ant system is a new meta-heuristic for hard combinatorial optimization problems. It is a population-based approach that uses exploitation of positive feedback as well as greedy search. It was first proposed for tackling the well known Traveling Salesman Problem (TSP), but has been also successfully applied to problems such as quadratic assignment, job-shop scheduling, vehicle routing and graph colouring. In this paper we introduce a new rank based version of the ant system and present results of a computational study, where we compare the ant system with simulated annealing and a genetic algorithm on several TSP instances. It turns out that our rank based ant system can compete with the other methods in terms of average behavior, and shows even better worst case behavior.

. Social insects provide us with a powerful metaphor to create decentralized systems of simple interacting, and often mobile, agents. The emergent collective intelligence of social insects -- swarm intelligence -- resides not in complex individual abilities but rather in networks of interactions that exist among individuals and between individuals and their environment. In particular, a recently proposed model of division of labor in a colony of primitively eusocial wasps, based on a simple reinforcement of response thresholds, can be transformed into a decentralized adaptive algorithm of task allocation. An application of such an algorithm is proposed in the context of a mail company, but virtually any type of flexible task allocation can be described within the same framework. 1 Introduction Evidence of the ecological success of social insects can be found almost everywhere [56]. Some of the main reasons for this success are to be looked for in the organization of insect societies, ...

Machine scheduling is a central task in production planning. In general it means the problem of scheduling job operations on a given number of available machines. In this paper we consider a machine scheduling problem with one machine, the Single Machine Total Tardiness Problem. To solve this NP-hard problem, we apply the ant colony optimization metaphor, a recently developed meta-heuristic that has proven its potential for various other combinatorial optimization problems. We test our algorithm using 125 benchmark problems and present computational results. 1 Introduction Ant Colony Optimization (ACO) is a rather new meta-heuristic introduced in the early nineties (cf. [6, 7, 11, 15]) and has successfully been applied to several combinatorial optimization problems (cf. e.g. [4, 5, 8, 9, 16, 21, 25]). In this paper we apply ACO to the Single Machine Total Tardiness Problem y We would like to thank Herbert Dawid and Marco Dorigo for their contributions to this research. Financial sup...

The paper analyses recent developments of a number of memory-based metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the name of Adaptive Memory Programming (AMP). A number of methods recently developed for the quadratic assignment, vehicle routing and graph colouring problems are reviewed and presented under the adaptive memory programming point of view. AMP presents a number of interesting aspects such as a high parallelization potential and the ability of dealing with real and dynamic applications.

In this paper we try to describe the main characters of Heuristics "derived" from Nature, a border area between Operations Research and Artificial Intelligence, with applications to graph optimization problems. These algorithms take inspiration from physics, biology, social sciences, and use a certain amount of repeated trials, given by one or more "agents" operating with a mechanism of competition-cooperation. Two introductory sections, devoted respectively to a presentation of some general concepts and to a tentative classification of Heuristics from Nature open the work. The paper is then composed of six review sections: each of them concerns a heuristic and its application to an NP-hard combinatorial optimization problem. We consider the following topics: genetic algorithms with timetable problems, simulated annealing with dial-a-ride problems, sampling & clustering with communication spanning tree problems, tabu search with job-shop-scheduling problems, neural nets with ...

Ant Colony Optimisation (ACO) is applied to the problem of routing and wavelength-allocation in a multi-wavelength all-optical virtual-wavelength-path routed transport network. Three variants of our ACO algorithm are proposed: local update (LU), global update/ distance (GU/D) and global update/occupancy (GU/O). All three extend the usual practice that ants are attracted by the pheromone trail of ants from their own colony: in our work, the artificial ants are also repelled by the pheromone of other colonies. Overall, the best ACO variant, GU/O, provides results that approach those of an earlier problem-specific heuristic on small- and medium-sized networks. 1 Introduction Multi-wavelength all-optical transport networks have attracted considerable interest in recent years, because of their potential, by using multiple wavelengths in both optical transmission and optical switching, to provide the huge bandwidths necessary if broadband services are to be widely adopted [1]. In addition,...