symmetry S S Article MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm Mohammad H. Nadimi-Shahraki 1,2, * , Shokooh Taghian 1,2 , Seyedali Mirjalili 3,4, * , Ahmed A. Ewees 5 , Laith Abualigah 6,7 and Mohamed Abd Elaziz 8,9,10,11   Citation: Nadimi-Shahraki, M.H.; Taghian, S.; Mirjalili, S.; Ewees, A.A.; Abualigah, L.; Abd Elaziz, M. MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm. Symmetry 2021, 13, 2388. https:// doi.org/10.3390/sym13122388 Academic Editor: Mihai Postolache Received: 13 November 2021 Accepted: 6 December 2021 Published: 10 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran; sh.taghian@sco.iaun.ac.ir 2 Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran 3 Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, QLD 4006, Australia 4 Yonsei Frontier Lab, Yonsei University, Seodaemun-gu, Seoul 03722, Korea 5 Department of Computer, Damietta University, Damietta 34511, Egypt; ewees@du.edu.eg 6 Faculty of Computer Sciences and Informatics, Amman Arab University, Amman 11953, Jordan; aligah.2020@gmail.com 7 School of Computer Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia 8 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt; abd_el_aziz_m@yahoo.com 9 Artificial Intelligence Research Center (AIRC), Ajman University, Ajman 346, United Arab Emirates 10 Department of Artificial Intelligence Science & Engineering, Galala University, Suze 435611, Egypt 11 School of Computer Science and Robotics, Tomsk Polytechnic University, 634050 Tomsk, Russia * Correspondence: nadimi@iaun.ac.ir (M.H.N.-S.); ali.mirjalili@torrens.edu.au (S.M.) Abstract: The moth-flame optimization (MFO) algorithm is an effective nature-inspired algorithm based on the chemical effect of light on moths as an animal with bilateral symmetry. Although it is widely used to solve different optimization problems, its movement strategy affects the convergence and the balance between exploration and exploitation when dealing with complex problems. Since movement strategies significantly affect the performance of algorithms, the use of multi-search strategies can enhance their ability and effectiveness to solve different optimization problems. In this paper, we propose a multi-trial vector-based moth-flame optimization (MTV-MFO) algorithm. In the proposed algorithm, the MFO movement strategy is substituted by the multi-trial vector (MTV) approach to use a combination of different movement strategies, each of which is adjusted to accom- plish a particular behavior. The proposed MTV-MFO algorithm uses three different search strategies to enhance the global search ability, maintain the balance between exploration and exploitation, and prevent the original MFO’s premature convergence during the optimization process. Furthermore, the MTV-MFO algorithm uses the knowledge of inferior moths preserved in two archives to prevent premature convergence and avoid local optima. The performance of the MTV-MFO algorithm was evaluated using 29 benchmark problems taken from the CEC 2018 competition on real parameter op- timization. The gained results were compared with eight metaheuristic algorithms. The comparison of results shows that the MTV-MFO algorithm is able to provide competitive and superior results to the compared algorithms in terms of accuracy and convergence rate. Moreover, a statistical analysis of the MTV-MFO algorithm and other compared algorithms was conducted, and the effectiveness of our proposed algorithm was also demonstrated experimentally. Keywords: optimization; metaheuristic algorithms; moth-flame optimization; global numerical opti- mization 1. Introduction Metaheuristic algorithms have been shown to be effective due to complex charac- teristics of difficult optimization problems such as dimensionality, multimodality, and Symmetry 2021, 13, 2388. https://doi.org/10.3390/sym13122388 https://www.mdpi.com/journal/symmetry