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

Effect of Population Structures on Quantum-Inspired Evolutionary Algorithm

Quantum-inspired evolutionary algorithm (QEA) has been designed by integrating some quantum mechanical principles in the framework of evolutionary algorithms. They have been successfully employed as a computational technique in solving difficult optimization problems. It is well known that QEAs provide better balance between exploration and exploitation as compared to the conventional evolutionary algorithms. The population in QEA is evolved by variation operators, which move the Q-bit towards an attractor. A modification for improving the performance of QEA was proposed by changing the selection of attractors, namely, versatile QEA. The improvement attained by versatile QEA over QEA indicates the impact of population structure on the performance of QEA and motivates further investigation into employing fine-grained model. The QEA with fine-grained population model (FQEA) is similar to QEA with the exception that every individual is located in a unique position on a two-dimensional toroidal grid and has four neighbors amongst which it selects its attractor. Further, FQEA does not use migrations, which is employed by QEAs. This paper empirically investigates the effect of the three different population structures on the performance of QEA by solving well-known discrete benchmark optimization problems

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. 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Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms