An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

Abstract

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

Initialization and Local Search Methods Applied to the Set Covering Problem: A Systematic Mapping

“…The main characteristics of the methods found are described below. Studies [15]- [16] show population-based MH algorithms where the initialization stage integrates the random generation of solutions, a heuristic operator applied to solutions that do not meet the covering conditions, and a redundant column reduction operator, which removes rows covered by more than one column seeking to improve solutions. These last two operators are applied again in later stages of the algorithms, validating compliance with the covering conditions.…”

“…Meanwhile, [17] and [18] show a similar approach, except for the initialization stage, where only the random generation of solutions is performed. As in [15]- [16], the heuristic and column reduction operators are applied in later stages of the algorithms. In the variant of the binary monkey algorithm [17], it is applied after the watch jump process, and in the binary version of the fruit fly algorithm [18], it is then applied to the global view-based search stage.…”

“…technique is implemented [15], which seeks to perturb the list of solutions when a perturbation criterion is met. If the solution is within 25% of the best solutions of the iteration, a perturbation probability is defined for each element of the solution.…”

“…Population-based MH algorithms were found applied in continuous domains using binarization methods [15,[17][18], a percentile operator [28][29][30][31], and operators based on machine learning [15][16][32][33][34][35] to resolve binary domains problems such as SCP. These methods facilitate the adoption of algorithms that have not been applied to the SCP or that were recently proposed.…”

A Binary Machine Learning Cuckoo Search Algorithm Improved by a Local Search Operator for the Set-Union Knapsack Problem

“…There are examples of integration between machine learning and metaheuristics in this domain. In [16,17], the binary versions of the cuckoo search algorithm were generated using the k-nearest neighbor technique. These binary versions were applied to multidimensional knapsack and set covering problems, respectively.…”