article · Scientific Reports
The Narwhal Optimization Algorithm is a population-based metaheuristic often limited by premature convergence, sensitivity to initial conditions, and rigid transitions between exploration and exploitation. Two improved versions resolve these limitations. One variant introduces opposition-based initialisation alongside dynamic restarts to preserve population diversity. The second variant incorporates a reinforcement learning controller using Q-learning to adjust search behaviour dynamically according to ongoing performance. Both approaches integrate an elite local search mechanism to provide finer refinement. Rigorous benchmarking across standard test suites and six constrained engineering design problems shows that the reinforcement-learning-guided variant delivers top-tier performance, matching the strongest benchmark competitors and outperforming several recent algorithms. Statistical testing confirms its capability to identify near-optimal solutions, with ablation analysis demonstrating that the elite local search component is the primary driver of these performance gains.
Complex engineering design problems require computational algorithms that can discover optimal solutions without getting trapped in suboptimal compromises. By incorporating reinforcement learning and targeted local search into swarm intelligence, this approach automates balance adjustments during problem-solving. This produces more dependable, robust computational tools for resolving challenging mathematical and physical design constraints.
The methods are applicable to computational design optimisation software used by engineers handling constrained physical systems, structural layouts, or complex numerical models. Tested on benchmark suites and simulated engineering problems, the algorithmic framework represents early-stage, foundational computational research. Commercial software vendors or engineering firms would need to integrate these algorithmic controllers into specialised design environments and validate them against real-world operational workflows before practical industry deployment.
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Abstract The Narwhal Optimization Algorithm is a recent swarm metaheuristic that, like most population-based optimisers, is prone to premature convergence, is sensitive to random initialisation, and relies on a rigid, schedule-driven exploration–exploitation balance. This paper develops and rigorously evaluates two enhanced variants that address these weaknesses. NWOA-OBL adds opposition-based initialisation and a stagnation-triggered, dynamic-opposition restart that replenishes population diversity, while NWOA-RL replaces the fixed exploration ratio with a Q-learning controller that selects the search behaviour online from the observed progress of the optimisation. Both variants are made memetic through a shared elite local search that supplies the local-refinement drive the original wave-based moves lack. The variants are compared against the baseline algorithm and seven established and recent optimisers on the CEC2017 suite at dimension thirty and the CEC2022 suite at dimensions ten and twenty, on six constrained engineering-design problems, and through parameter-sensitivity and ablation studies, all under a common evaluation budget with thirty independent runs and full nonparametric statistical analysis. Pooled over the benchmark functions, NWOA-RL attains the joint-best mean rank, statistically indistinguishable from the strongest competitor and significantly ahead of the remaining baselines, and reaches near-optimal engineering designs. The ablation identifies the elite local search as the decisive component of the design.
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DOI: 10.1038/s41598-026-66557-3
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