ACO algorithms with guaranteed convergence to the optimal solution

By Walter J. Gutjahr. Information Processing Letters, 2002

308 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/bfc6800560a4135b50a511c0dc790e6006f10f0e

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Citations in the corpus

A novel decentralized platform for peer-to-peer energy trading market with blockchain technology (2021, methodology): “The ACO method is a highly efficient algorithm with the ability to achieve optimal solutions given suitable parameters and design schemes [60–62].”
A short convergence proof for a class of ant colony optimization algorithms (2002, background): “Gutjahr’s proof is stronger than ours (it implies our result, but the reverse is not true), but our proof holds for any ACO algorithm as far as a lower bound and an upper bound to the pheromone trails exist.”
Ant Colony Optimization: Overview and Recent Advances (2018, background): “Later, he proved convergence to any optimal solution [84] with probability one for two extended versions of GBAS.”
Heuristic Solution of an Extended Double-Coverage Ambulance Location Problem for Austria (2005, background): “[10]), and convergence of specific ACO algorithms to optimal solutions has been shown in [12].”
Fundamentals of natural computing: an overview (2007, methodology): “Theoretical investigations into ACO include convergence analysis [128]; the comparison with other approaches, like optimal control [31] and gradientbased search [193]; and the hybridization with more classical artificial intelligence and operations research methods [34].”
Ant colony optimization (2006, unknown): “Gutjahr proved convergence with probability 1 − ǫ to the optimal solution [36], and more in general to any optimal solution [37].”
Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection (2004, background): “, 2002a) and a convergence proof for a generalized Ant System algorithm has been established (Gutjahr, 2002).”
Evolutionary optimization as applied to inverse scattering problems (2009, background): “A first proof on the convergence of an ACO-based algorithm, named the graph-based ant system (GBAS), was reported in [72, 73] where it has been shown that the global solution can be found at least once throughout the optimization process.”
A survey on metaheuristics for stochastic combinatorial optimization (2009, methodology): “The first convergence proofs have been provided for an ACO algorithm called GBAS by Gutjahr in (2000) and (2002).”
Ant colony optimization theory: A survey (2005, methodology): “The proof of convergence in solution as presented in [24] was inspired by an earlier work of Gutjahr [38].”
Swarm Intelligence in Optimization (2008, background): “They deal with the question of algorithm convergence [75, 76, 163].”
Ant colony optimization: Introduction and recent trends (2005, background): “The first convergence proofs concerning an algorithm called graph-based ant system (GBAS) were presented by Gutjahr in [53,54].”