An Improved Crested Porcupine Optimization Algorithm Incorporating Butterfly Search and Triangular Walk Strategies.

The Crested Porcupine Optimizer (CPO), as a newly emerging swarm intelligence algorithm, demonstrates advantages in balancing global exploration and local exploitation but still suffers from limitations in convergence speed and local exploitation precision. To address these issues, this paper proposes an enhanced variant, the Butterfly Search and Triangular Walk Crested Porcupine Optimizer (BTCPO). The method achieves a dynamic balance between exploration and exploitation by combining triangular walk to boost local exploitation and butterfly search to increase global variety. Experimental results on 23 classical benchmark functions and the CEC2021 test suite show that BTCPO outperforms CPO as well as seven state-of-the-art algorithms (DBO, HBA, BKA, HHO, GWO, GOOSE, and SSA). Specifically, BTCPO achieves the best performance on more than 80% of CEC2021 functions, with convergence speed improved by approximately 25% compared to CPO. Furthermore, BTCPO exhibits higher efficiency and usefulness in engineering design problems such as trusses, welded beams, and cantilever beams. These findings demonstrate the theoretical and practical advantages of BTCPO, making it a workable approach to solving difficult optimization problems.