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Article

Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study †

Artificial Intelligence Research Institute (IIIA-CSIC), 08193 Bellaterra, Spain
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This paper is an extended version of our paper published in ANTS 2020—12th International Conference on Swarm Intelligence, Barcelona, Spain, 26–28 October 2020.
Academic Editor: Frank Werner
Mathematics 2021, 9(4), 361; https://doi.org/10.3390/math9040361
Received: 20 January 2021 / Revised: 8 February 2021 / Accepted: 9 February 2021 / Published: 11 February 2021
(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)
Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based metaheuristics such as evolutionary algorithms and particle swarm optimization. Examples from nature, however, indicate that negative learning—in addition to positive learning—can beneficially be used for certain purposes. Several research papers have explored this topic over the last decades in the context of ant colony optimization, mostly with limited success. In this work we present and study an alternative mechanism making use of mathematical programming for the incorporation of negative learning in ant colony optimization. Moreover, we compare our proposal to some well-known existing negative learning approaches from the related literature. Our study considers two classical combinatorial optimization problems: the minimum dominating set problem and the multi dimensional knapsack problem. In both cases we are able to show that our approach significantly improves over standard ant colony optimization and over the competing negative learning mechanisms from the literature. View Full-Text
Keywords: ant colony optimization; mathematical programming; negative learning; minimum dominating set; multi-dimensional knapsack problem ant colony optimization; mathematical programming; negative learning; minimum dominating set; multi-dimensional knapsack problem
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MDPI and ACS Style

Nurcahyadi, T.; Blum, C. Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study. Mathematics 2021, 9, 361. https://doi.org/10.3390/math9040361

AMA Style

Nurcahyadi T, Blum C. Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study. Mathematics. 2021; 9(4):361. https://doi.org/10.3390/math9040361

Chicago/Turabian Style

Nurcahyadi, Teddy, and Christian Blum. 2021. "Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study" Mathematics 9, no. 4: 361. https://doi.org/10.3390/math9040361

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