An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call ant system (AS). 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 quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics-global data structure revision, distributed communication and probabilistic transitions of the AS.

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Ant system: optimization by a colony of cooperating agents

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 TSPs. 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 nature-inspired algorithms such as simulated annealing and evolutionary computation, and we conclude comparing ACS-3-opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSPs.

http://www-igm.univ-mlv.fr/~lombardy/ens/JavaTTT0708/fourmis.pdf

Ant colony system: a cooperative learning approach to the traveling salesman problem

https://leeds-faculty.colorado.edu/glover/TS%20-%20Future%20Paths%20for%20Integer%20Programming.pdf

Future paths for integer programming and links to artificial intelligence

Ants colonies exhibit very interesting behaviours: even if a single ant only has simple capabilities, the behaviour of a whole ant colony is highly structured. This is the result of coordinated interactions. But, as communication possibilities among ants are very limited, interactions must be based on very simple flows of information. In this paper we explore the implications that the study of ants behaviour can have on problem solving and optimization. We introduce a distributed problem solving environment and propose its use to search for a solution to the travelling salesman problem.

Distributed Optimization by Ant Colonies

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.

https://people.idsia.ch/~luca/acs-bio97.pdf

Ant colonies for the travelling salesman problem

We express the Quadratic Assignment Problem in terms of graph multiplication of a flow graph G f with a distance graph G d . By decomposing G f into simpler graphs, we give a general unified procedure to calculate bounds. This procedure generates the two previously known bounds as special cases and also generates some new bounds. By enumerating all practical decompositions, we show that no better bounds can be computed in reasonable time—by solving linear assignment subproblems—other than the bounds pointed out in this paper.

Nicos Christofides

Papers

A Graph Theoretic Analysis of Bounds for the Quadratic Assignment Problem

An optimal algorithm for the straight segment approximation of digital arcs

Zero-one programming using non-binary tree-search

A graph-theoretic approach to distance transformations

The optimal discretization of probability density functions