A Comparison of Three Recent Nature-Inspired Metaheuristics for the Set Covering Problem

The Set Covering Problem (SCP) is a classic problem in combinatorial optimization. SCP has many applications in engineering,including problems involving routing, scheduling, stock cutting, electoral redistricting and others important real life situations. Because of its importance, SCP has attracted attention of many researchers. However,SCP instances are known as complex and generally NP-hard problems.Due to the combinatorial nature of this problem, during the last decades,several metaheuristics have been applied to obtain efficient solutions.This paper presents a metaheuristics comparison for the SCP. Three recent nature-inspired metaheuristics are considered: Shuffled Frog Leaping,Firefly and Fruit Fly algorithms. The results show that they can obtainn optimal or close to optimal solutions at low computational cost

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem

Particle Swarm Optimization is an evolutionary method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The evolution is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of the inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is illustrated on the minimum labelling Steiner tree problem: given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes, whose edges have the smallest number of distinct labels

Variable neighbourhood search for the minimum labelling Steiner tree problem

We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times

Preface: Swarm Intelligence, Focus on Ant and Particle Swarm Optimization

In the era globalisation the emerging technologies are governing engineering industries to a multifaceted state. The escalating complexity has demanded researchers to find the possible ways of easing the solution of the problems. This has motivated the researchers to grasp ideas from the nature and implant it in the engineering sciences. This way of thinking led to emergence of many biologically inspired algorithms that have proven to be efficient in handling the computationally complex problems with competence such as Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), etc. Motivated by the capability of the biologically inspired algorithms the present book on ""Swarm Intelligence: Focus on Ant and Particle Swarm Optimization"" aims to present recent developments and applications concerning optimization with swarm intelligence techniques. The papers selected for this book comprise a cross-section of topics that reflect a variety of perspectives and disciplinary backgrounds. In addition to the introduction of new concepts of swarm intelligence, this book also presented some selected representative case studies covering power plant maintenance scheduling; geotechnical engineering; design and machining tolerances; layout problems; manufacturing process plan; job-shop scheduling; structural design; environmental dispatching problems; wireless communication; water distribution systems; multi-plant supply chain; fault diagnosis of airplane engines; and process scheduling. I believe these 27 chapters presented in this book adequately reflect these topics

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

[EN] 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.The first author was supported by the Grant CONICYT/FONDECYT/INICIACION/11180056.García, J.; Astorga, G.; Yepes, V. (2021). An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics. Mathematics. 9(3):1-20. https://doi.org/10.3390/math9030225S12093Al-Madi, N., Faris, H., & Mirjalili, S. (2019). Binary multi-verse optimization algorithm for global optimization and discrete problems. International Journal of Machine Learning and Cybernetics, 10(12), 3445-3465. doi:10.1007/s13042-019-00931-8García, J., Moraga, P., Valenzuela, M., Crawford, B., Soto, R., Pinto, H., … Astorga, G. (2019). A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems. Computational Intelligence and Neuroscience, 2019, 1-16. doi:10.1155/2019/3238574Guo, H., Liu, B., Cai, D., & Lu, T. (2016). Predicting protein–protein interaction sites using modified support vector machine. International Journal of Machine Learning and Cybernetics, 9(3), 393-398. doi:10.1007/s13042-015-0450-6Korkmaz, S., Babalik, A., & Kiran, M. S. (2017). An artificial algae algorithm for solving binary optimization problems. International Journal of Machine Learning and Cybernetics, 9(7), 1233-1247. doi:10.1007/s13042-017-0772-7García, J., Martí, J. V., & Yepes, V. (2020). The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm. Mathematics, 8(6), 862. doi:10.3390/math8060862Yepes, V., Martí, J. V., & García, J. (2020). Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls. Sustainability, 12(7), 2767. doi:10.3390/su12072767Talbi, E.-G. (2015). Combining metaheuristics with mathematical programming, constraint programming and machine learning. Annals of Operations Research, 240(1), 171-215. doi:10.1007/s10479-015-2034-yJuan, A. A., Faulin, J., Grasman, S. E., Rabe, M., & Figueira, G. (2015). A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems. Operations Research Perspectives, 2, 62-72. doi:10.1016/j.orp.2015.03.001Chou, J.-S., & Nguyen, T.-K. (2018). Forward Forecast of Stock Price Using Sliding-Window Metaheuristic-Optimized Machine-Learning Regression. IEEE Transactions on Industrial Informatics, 14(7), 3132-3142. doi:10.1109/tii.2018.2794389Zheng, B., Zhang, J., Yoon, S. W., Lam, S. S., Khasawneh, M., & Poranki, S. (2015). Predictive modeling of hospital readmissions using metaheuristics and data mining. Expert Systems with Applications, 42(20), 7110-7120. doi:10.1016/j.eswa.2015.04.066De León, A. D., Lalla-Ruiz, E., Melián-Batista, B., & Marcos Moreno-Vega, J. (2017). A Machine Learning-based system for berth scheduling at bulk terminals. Expert Systems with Applications, 87, 170-182. doi:10.1016/j.eswa.2017.06.010García, J., Lalla-Ruiz, E., Voß, S., & Droguett, E. L. (2020). Enhancing a machine learning binarization framework by perturbation operators: analysis on the multidimensional knapsack problem. International Journal of Machine Learning and Cybernetics, 11(9), 1951-1970. doi:10.1007/s13042-020-01085-8García, J., Crawford, B., Soto, R., & Astorga, G. (2019). A clustering algorithm applied to the binarization of Swarm intelligence continuous metaheuristics. Swarm and Evolutionary Computation, 44, 646-664. doi:10.1016/j.swevo.2018.08.006García, J., Crawford, B., Soto, R., Castro, C., & Paredes, F. (2017). A k-means binarization framework applied to multidimensional knapsack problem. Applied Intelligence, 48(2), 357-380. doi:10.1007/s10489-017-0972-6Dokeroglu, T., Sevinc, E., Kucukyilmaz, T., & Cosar, A. (2019). 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A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem

[EN] The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental impact. From the point of view of computational complexity, the problem is challenging due to the large number of possible combinations in the solution space. In this article, a k-means cuckoo search hybrid algorithm is proposed where the cuckoo search metaheuristic is used as an optimization mechanism in continuous spaces and the unsupervised k-means learning technique to discretize the solutions. A random operator is designed to determine the contribution of the k-means operator in the optimization process. The best values, the averages, and the interquartile ranges of the obtained distributions are compared. The hybrid algorithm was later compared to a version of harmony search that also solved the problem. The results show that the k-mean operator contributes significantly to the quality of the solutions and that our algorithm is highly competitive, surpassing the results obtained by harmony search.The first author was supported by the Grant CONICYT/FONDECYT/INICIACION/11180056, the other two authors were supported by the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).García, J.; Yepes, V.; Martí Albiñana, JV. (2020). A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem. Mathematics. 8(4):1-22. https://doi.org/10.3390/math8040555S12284García, J., Altimiras, F., Peña, A., Astorga, G., & Peredo, O. (2018). A Binary Cuckoo Search Big Data Algorithm Applied to Large-Scale Crew Scheduling Problems. Complexity, 2018, 1-15. doi:10.1155/2018/8395193García, J., Moraga, P., Valenzuela, M., Crawford, B., Soto, R., Pinto, H., … Astorga, G. (2019). A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems. Computational Intelligence and Neuroscience, 2019, 1-16. doi:10.1155/2019/3238574Al-Madi, N., Faris, H., & Mirjalili, S. (2019). Binary multi-verse optimization algorithm for global optimization and discrete problems. International Journal of Machine Learning and Cybernetics, 10(12), 3445-3465. doi:10.1007/s13042-019-00931-8Kim, M., & Chae, J. (2019). Monarch Butterfly Optimization for Facility Layout Design Based on a Single Loop Material Handling Path. Mathematics, 7(2), 154. doi:10.3390/math7020154García, J., Crawford, B., Soto, R., & Astorga, G. (2019). A clustering algorithm applied to the binarization of Swarm intelligence continuous metaheuristics. Swarm and Evolutionary Computation, 44, 646-664. doi:10.1016/j.swevo.2018.08.006García, J., Lalla-Ruiz, E., Voß, S., & Droguett, E. L. (2020). 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