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Ant colony optimization on a limited budget of evaluations


Ant colony optimization (ACO) is a successful method for solving difficult combinatorial optimization problems. Following Ant System, the first ACO algorithm, a large number of algorithmic variants have been developed that showed significantly better performance on a wide range of optimization problems. Typically, performance was measured according to the solution quality achieved for a given computation time limit, which usually allowed the evaluation of a very large number of candidate solutions, often in the range of millions. However, there are practical applications where the number of evaluations that can be done is very restricted due to tight real-time constraints or to the high computational cost of evaluating a solution. Since these situations are quite different from those for which ACO algorithms were initially designed, current knowledge on good parameter settings or the most promising search strategies may not be directly applicable. In this paper, we examine the performance of different ACO algorithms under a strongly limited budget of 1000 evaluations. We do so using default parameter settings from the literature and parameter settings tuned for the limited-budget scenario. In addition, we compare the performance of the ACO algorithms to algorithms that make use of surrogate modeling of the search landscapes. We show that tuning algorithms for the limited-budget case is of uttermost importance, that direct search through the ACO algorithms keeps an edge over techniques using surrogate modeling, and that the ACO variants proposed as improvements over Ant System remain preferable.

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  1. All experiments were performed on a single core of cluster nodes each equipped with two AMD Opteron 6272 16 cores CPUs running at 2.1 GHz and with 64 GB RAM. Note that the heavy computation needs for the model update, and other computations in EGO make this approach an option in case the actual real evaluation of a candidate solution involves very high computation times but not for the case of very tight real-time constraints.

  2. In what follows, we use the problem name to identify results specific to a problem, e.g., EGOTSP-AS refers to the TSP results obtained by using AS to search the landscape of the expected improvement.


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The research leading to the results presented in this paper received support from the COMEX project within the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office and from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement No. 246939. Manuel López-Ibáñez and Thomas Stützle acknowledge support from the Belgian F.R.S.-FNRS, of which they are a postdoctoral researcher and a senior research associate, respectively. Leslie Pérez Cáceres acknowledges support of CONICYT Becas Chile.

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Correspondence to Thomas Stützle.

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Pérez Cáceres, L., López-Ibáñez, M. & Stützle, T. Ant colony optimization on a limited budget of evaluations. Swarm Intell 9, 103–124 (2015).

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  • Ant colony optimization
  • Expensive optimization problems
  • Parameter tuning
  • Automatic configuration
  • Surrogate modeling