A Multi-Strategy Improved Horned Lizard Optimization Algorithm and Its Application in Engineering Optimization

To address NP-hard optimization challenges prevalent in engineering applications, meta-heuristic algorithms are highly regarded for their ability to provide high-quality solutions. In this study, a multi-strategy improved horned lizard optimization algorithm (MSHLOA) is proposed to overcome the limitations of the standard HLOA in terms of premature convergence and slow optimization search. The algorithm is innovated through four synergistic strategies: (1) logistic chaotic population initialization to enhance initial solution diversity; (2) dynamic lens imaging-based adversarial learning to enhance global search capability; (3) sub-linear probability decay selection-based crisscross strategy to effectively break through dimensional local optima; and (4) golden sine factor-guided local exploitation to balance the trade-off between exploration and exploitation. Experimental validation on 15 benchmark functions and the CEC2021 test set demonstrates the superior performance of MSHLOA, with an overall effectiveness improvement of 53.35% compared to standard HLOA. Statistical analyses including the Wilcoxon rank sum test (p < 0.05), Friedman’s test, and solution distribution visualization validate the robustness of the algorithm against local optimal stagnation. In the engineering optimization example, the average cost of the pressure vessel problem was reduced by 55.6%, while the optimal value with the lowest standard deviation verified its stability in terms of solution accuracy, convergence speed, and stability. These advances establish the computational efficiency and reliability of MSHLOA for engineering problems, providing a general example of an augmented meta-heuristic algorithm that offers a new, more efficient solution to engineering structural optimization problems.