Journal of Bionic Engineering (2024) 21:1465–1495 https://doi.org/10.1007/s42235-024-00493-8

Multi?trial Vector?based Whale Optimization Algorithm

Mohammad H. Nadimi?Shahraki1,2  · Hajar Farhanginasab1,2 · Shokooh Taghian1,2 · Ali Safaa Sadiq3 · Seyedali Mirjalili4

1 Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran

2 Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran

3 Department of Computer Science, Nottingham Trent University, Nottingham NG11 8NS, UK

4 Centre for Artifcial Intelligence Research and Optimisation, Torrens University, Brisbane 4006, Australia

Abstract

The Whale Optimization Algorithm (WOA) is a swarm intelligence metaheuristic inspired by the bubble-net hunting tactic of humpback whales. In spite of its popularity due to simplicity, ease of implementation, and a limited number of parameters, WOA’s search strategy can adversely afect the convergence and equilibrium between exploration and exploitation in complex problems. To address this limitation, we propose a new algorithm called Multi-trial Vector-based Whale Optimization Algorithm (MTV-WOA) that incorporates a Balancing Strategy-based Trial-vector Producer (BS_TVP), a Local Strategy-based Trial-vector Producer (LS_TVP), and a Global Strategy-based Trial-vector Producer (GS_TVP) to address real-world optimization problems of varied degrees of difculty. MTV-WOA has the potential to enhance exploitation and exploration, reduce the probability of being stranded in local optima, and preserve the equilibrium between exploration and exploitation. For the purpose of evaluating the proposed algorithm's performance, it is compared to eight metaheuristic algorithms utilizing CEC 2018 test functions. Moreover, MTV-WOA is compared with well-stablished, recent, and WOA variant algorithms. The experimental results demonstrate that MTV-WOA surpasses comparative algorithms in terms of the accuracy of the solutions and convergence rate. Additionally, we conducted the Friedman test to assess the gained results statistically and observed that MTV-WOA signifcantly outperforms comparative algorithms. Finally, we solved fve engineering design problems to demonstrate the practicality of MTV-WOA. The results indicate that the proposed MTV-WOA can efciently address the complexities of engineering challenges and provide superior solutions that are superior to those of other algorithms.

Keywords Swarm intelligence algorithms · Metaheuristic algorithms · Optimization · Engineering design problems · Whale optimization algorithm