Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems

Jorge M. Cruz-Duarte, José C. Ortiz-Bayliss, Iván Amaya, Yong Shi, Hugo Terashima-Marín and Nelishia Pillay
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Jorge M. Cruz-Duarte: School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, NL 64849, Mexico
José C. Ortiz-Bayliss: School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, NL 64849, Mexico
Iván Amaya: School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, NL 64849, Mexico
Yong Shi: Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Zhongguancun East Road 80, Haidian District, Beijing 100190, China
Hugo Terashima-Marín: School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, NL 64849, Mexico
Nelishia Pillay: Department of Computer Science, University of Pretoria, Lynnwood Rd, Hatfield, Pretoria 0083, South Africa

Mathematics, 2020, vol. 8, issue 11, 1-23

Abstract: Metaheuristics have become a widely used approach for solving a variety of practical problems. The literature is full of diverse metaheuristics based on outstanding ideas and with proven excellent capabilities. Nonetheless, oftentimes metaheuristics claim novelty when they are just recombining elements from other methods. Hence, the need for a standard metaheuristic model is vital to stop the current frenetic tendency of proposing methods chiefly based on their inspirational source. This work introduces a first step to a generalised and mathematically formal metaheuristic model, which can be used for studying and improving them. This model is based on a scheme of simple heuristics, which perform as building blocks that can be modified depending on the application. For this purpose, we define and detail all components and concepts of a metaheuristic (i.e., its search operators), such as heuristics. Furthermore, we also provide some ideas to take into account for exploring other search operator configurations in the future. To illustrate the proposed model, we analyse search operators from four well-known metaheuristics employed in continuous optimisation problems as a proof-of-concept. From them, we derive 20 different approaches and use them for solving some benchmark functions with different landscapes. Data show the remarkable capability of our methodology for building metaheuristics and detecting which operator to choose depending on the problem to solve. Moreover, we outline and discuss several future extensions of this model to various problem and solver domains.

Keywords: metaheuristic; continuous optimisation; mathematical model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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