Whale Optimization Algorithms in Global Optimization Problems

Whale Optimization Algorithms (WOA) represent a class of bio-inspired metaheuristic methods that emulate the bubble-net feeding behaviour of humpback whales to tackle complex global optimisation problems. By modelling two primary behaviours—encircling of prey and spiral bubble-net attack—WOA achieves a balance between global exploration of the search space and local exploitation of high-quality solutions. Since its introduction, the algorithm has spawned numerous variants incorporating adaptive weight strategies, chaotic sequences, hybrid operators and multi-strategy collaboration to address limitations such as premature convergence and slow optimisation speed. WOA and its enhanced forms have been applied to continuous and discrete optimisation challenges, ranging from engineering design and resource allocation to hyperparameter tuning in machine learning. Recent developments focus on integrating dynamic control parameters, adaptive search mechanisms and memory-based operators to further refine convergence accuracy and computational efficiency. These advances underscore the global significance of WOA in offering flexible, robust solutions across scientific, industrial and environmental domains.

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Several studies in diverse engineering and computational settings have proposed novel enhancements to the basic WOA framework. One approach introduced a nonlinear adaptive weight together with a golden sine operator to guide search agents along sine-based trajectories, thereby improving both convergence speed and global search capability. Comparative analyses against standard WOA, particle swarm optimisation and firefly algorithms demonstrated superior performance on high-dimensional benchmark functions. Another line of work presented an enhanced variant that embeds a dynamic opposite learning mechanism and an adaptive inertia weight strategy. This method adaptively alternates between exploration and exploitation phases, preventing premature stagnation and delivering robust results on unimodal, multimodal and real-world engineering problems. A third advancement fused thermal exchange optimisation and genetic crossover operators within a hybrid framework, enabling memory-based retention of elite solutions and thermal exchange-inspired perturbation for global exploration. Evaluations on standard benchmark suites and classification tasks confirmed the hybrid algorithm’s competitive accuracy and efficiency, highlighting its potential for general-purpose global optimisation.

Whale Optimization Algorithms in Global Optimization Problems publication trend

The graph below shows the total number of articles in whale optimization algorithms in global optimization problems across all publications each year (not limited to Nature Index journals).

Technical terms

Metaheuristic algorithm: A high-level procedure designed to find near-optimal solutions for complex optimisation problems through iterative trial-and-error strategies.

Swarm intelligence: Collective problem-solving behaviour emerging from the interactions of decentralised, autonomous agents, as seen in natural systems.

Exploration: The process by which an algorithm investigates diverse regions of the search space to avoid premature convergence.

Exploitation: The refinement of solutions in promising regions of the search space to enhance precision and convergence speed.

Bubble-net feeding: The inspirative foraging strategy of humpback whales, modelled in WOA as a spiral-based movement and encircling behaviour to simulate prey capture.

References

1. Improved Whale Optimization Algorithm Based on Nonlinear Adaptive Weight and Golden Sine Operator. IEEE Access (2020).
2. A Hybrid Whale Optimization Algorithm for Global Optimization. Mathematics (2021).
3. An enhanced whale optimization algorithm with improved dynamic opposite learning and adaptive inertia weight strategy. Complex & Intelligent Systems (2022).