Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

The identifying code problem for a given graph involves finding a minimum subset of vertices such that each vertex of the graph is uniquely specified by its nonempty neighborhood within the identifying code. The combinatorial optimization problem has a wide variety of applications in location and detection schemes. Finding an identifying code of minimum possible size is a difficult task. In fact, it has been proven to be computationally intractable (NP-complete). Therefore, the use of heuristics to provide good approximations in a reasonable amount of time is justified. In this work, we present a new population-based local search algorithm for finding identifying codes of minimum cost. Computational experiments show that the proposed approach was found to be more effective than other state-of-the-art algorithms at generating high-quality solutions in different types of graphs with varying numbers of vertices.

Section: Configuration Checking Strategymentioning

confidence: 99%

A Population-Based Local Search Algorithm for the Identifying Code Problem

Lara-Caballero,

González-Moreno

2023

“…In the literature, there are many variants of the MDS problem. Examples include the minimum connected dominating set problem [34], the minimum total dominating set problem [35] and the minimum vertex weight dominating set problem [36]. The currently best metaheuristic approach for solving the MDS problem is a two-goal local search with inference rules from [37].…”

Section: Minimum Dominating Setmentioning

confidence: 99%

Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

Nurcahyadi

Blum

2021

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 node-weighted versions of these problems are also often considered. The latest algorithms for the minimum weight (vertex) independent dominating set problem include a local search approach that makes use of a reinforcement learning based repair procedure [17] and a memetic algorithm [18]. Next, it is worth mentioning the so-called minimum total dominating set problem, which was solved by means of a hybrid evolutionary algorithm in [19].…”

Section: Literature Review On Related Problemsmentioning

confidence: 99%

Barrakuda: A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem

Pinacho-Davidson

Blum

2020

The minimum capacitated dominating set problem is an NP-hard variant of the well-known minimum dominating set problem in undirected graphs. This problem finds applications in the context of clustering and routing in wireless networks. Two algorithms are presented in this work. The first one is an extended version of construct, merge, solve and adapt, while the main contribution is a hybrid between a biased random key genetic algorithm and an exact approach which we labeled BARRAKUDAmathsizesmall. Both algorithms are evaluated on a large set of benchmark instances from the literature. In addition, they are tested on a new, more challenging benchmark set of larger problem instances. In the context of the problem instances from the literature, the performance of our algorithms is very similar. Moreover, both algorithms clearly outperform the best approach from the literature. In contrast, BARRAKUDAmathsizesmall is clearly the best-performing algorithm for the new, more challenging problem instances.