A Graph-based Ant system and its convergence
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Information Processing Letters
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Natural Computing: an international journal
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Theoretical Computer Science
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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Proceedings of the 12th annual conference on Genetic and evolutionary computation
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Algorithmica - Special Issue: Theory of Evolutionary Computation
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Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
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IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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Proceedings of the 14th annual conference on Genetic and evolutionary computation
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Proceedings of the 14th annual conference on Genetic and evolutionary computation
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Proceedings of the 15th annual conference on Genetic and evolutionary computation
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We study the behavior of a Max-Min Ant System (MMAS) on the stochastic single-destination shortest path (SDSP) problem. Two previous papers already analyzed this setting for two slightly different MMAS algorithms, where the pheromone update fitness-independently rewards edges of the best-so-far solution. The first paper showed that, when the best-so-far solution is not reevaluated and the stochastic nature of the edge weights is due to noise, the MMAS will find a tree of edges successfully and efficiently identify a shortest path tree with minimal noise-free weights. The second paper used reevaluation of the best-so-far solution and showed that the MMAS finds paths which beat any other path in direct comparisons, if existent. For both results, for some random variables, this corresponds to a tree with minimal expected weights. In this work we analyze a variant of MMAS that works with fitness-proportional update on stochastic-weight graphs with arbitrary random edge weights from [0,1]. For δ such that any suboptimal path is worse by at least δ than an optimal path, then, with suitable parameters, the graph will be optimized after O(n3 ln n/δ over δ3 iterations (in expectation). In order to prove the above result, the multiplicative and the variable drift theorem are adapted to continuous search spaces.