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Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems

1
School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey, NL 64849, Mexico
2
Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Zhongguancun East Road 80, Haidian District, Beijing 100190, China
3
Department of Computer Science, University of Pretoria, Lynnwood Rd, Hatfield, Pretoria 0083, South Africa
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(11), 2046; https://doi.org/10.3390/math8112046
Received: 6 October 2020 / Revised: 11 November 2020 / Accepted: 16 November 2020 / Published: 17 November 2020
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. View Full-Text
Keywords: metaheuristic; continuous optimisation; mathematical model metaheuristic; continuous optimisation; mathematical model
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MDPI and ACS Style

Cruz-Duarte, J.M.; Ortiz-Bayliss, J.C.; Amaya, I.; Shi, Y.; Terashima-Marín, H.; Pillay, N. Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems. Mathematics 2020, 8, 2046. https://doi.org/10.3390/math8112046

AMA Style

Cruz-Duarte JM, Ortiz-Bayliss JC, Amaya I, Shi Y, Terashima-Marín H, Pillay N. Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems. Mathematics. 2020; 8(11):2046. https://doi.org/10.3390/math8112046

Chicago/Turabian Style

Cruz-Duarte, Jorge M., José C. Ortiz-Bayliss, Iván Amaya, Yong Shi, Hugo Terashima-Marín, and Nelishia Pillay. 2020. "Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems" Mathematics 8, no. 11: 2046. https://doi.org/10.3390/math8112046

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