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.
The overwhelming majority of ant colony optimization approaches from the literature is exclusively based on learning from positive examples. Natural examples from biology, however, indicate the potential usefulness of negative learning. Several research works have explored this topic over the last two decades in the context of ant colony optimization, with limited success. In this work we present an alternative proposal for the incorporation of negative learning in ant colony optimization. The results obtained for the capacitated minimum dominating set problem indicate that this approach can be quite useful. More specifically, our extended ant colony algorithm clearly outperforms the standard approach. Moreover, we were able to improve the current stateof-the-art results in 10 out of 36 cases.
Recently, a new negative learning variant of ant colony optimization (ACO) has been used to successfully tackle a range of combinatorial optimization problems. For providing stronger evidence of the general applicability of negative learning ACO, we investigate how it can be adapted to solve the Maximum Satisfiability problem (MaxSAT). The structure of MaxSAT is different from the problems considered to date and there exists only a few ACO approaches for MaxSAT. In this paper, we describe three negative learning ACO variants. They differ in the way in which sub-instances are solved at each algorithm iteration to provide negative feedback to the main ACO algorithm. In addition to using IBM ILOG CPLEX, two of these variants use existing MaxSAT solvers for this purpose. The experimental results show that the proposed negative learning ACO variants significantly outperform the baseline ACO as well as IBM ILOG CPLEX and the two MaxSAT solvers. This result is of special interest because it shows that negative learning ACO can be used to improve over the results of existing solvers by internally using them to solve smaller sub-instances.
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