Enhancing the Whale Optimisation Algorithm with sub-population and hybrid techniques for single- and multi-objective optimisation

The Whale Optimisation Algorithm (WOA) is a meta-heuristic model inspired by the hunting behaviours of humpback whales. Similar to many other meta-heuristic models, e.g., Particle Swarm Optimisation (PSO), Artificial Bee Colony (ABC), and Ant Colony Optimisation (ACO), the WOA is susceptible to the issues of slow convergence and local optima. In this study, we address these short comings by first proposing an Enhanced WOA (EWOA) model for tackling single-objective optimisation. Specifically, EWOA integrates the WOA and Differential Evolution (DE). DE is a population-based algorithm that generates new candidate solutions by combining the existing ones, employing a simple yet robust formula. This amalgamation aids in generating diverse solutions during the exploration stage by utilising a non-linear coefficient vector, adaptive weight, and sub-population strategies. Furthermore, fast non-dominated sorting and crowding distance techniques from the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are incorporated into EWOA, resulting in a multi-objective EWOA (MOEWOA) model. We evaluate both EWOA and MOEWOA with a broad spectrum of benchmark functions. The results from 51 single-objective optimisation problems indicate the usefulness of EWOA in terms of a fast convergence rate and with increased performance. On the other hand, MOEWOA demonstrates a better convergence rate and an effective balance between convergence and diversity in 12 multi-objective optimisation problems. In addition, MOEWOA successfully solves 21 complex multi-objective constrained mechanical design problems, outperforming other compared algorithms at the 95% confidence level. The empirical outcomes of our study indicate the potential of EWOA and MOEWOA for undertaking complex, real-world optimisation problems.

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