Adaptive multi-step path planning for multi-robot in dynamic environments based on hybrid optimization approach

The multi-robot path planning problem requires algorithms with high convergence speed and accuracy, as well as the completeness of the search probability for the optimal path. The integration of metaheuristic algorithms in path planning has proven to be remarkably efficient. This paper introduces a novel hybrid metaheuristic algorithm, Beluga Whale-Crayfish Optimization (BWCOA), for enhanced global optimization in path planning applications. While the Crayfish Optimization (COA) demonstrates superior convergence speed, its inherent probabilistic path completeness remains suboptimal. To address this limitation, we present three key innovations: a dynamic probability completion mechanism, adaptive convergence acceleration factors, and balanced exploration–exploitation trade-off parameters. The proposed BWCOA synergizes Beluga Whale Optimization (BWO)’s basin-hopping capability with COA’s swarm intelligence through parallel combined exploration strategies. To prove its powerfulness, a series of comparative analyses were conducted between BWCOA and other leading algorithms across two comprehensive test function suites. The numerical experiment results underscore the significant superiority of BWCOA over its counterparts. In the context of path planning simulations, BWCOA demonstrated notable improvements over COA within the same number of function evaluations, with average enhancement rates of 6.49 %, 7.42 %, 15.09 %, 76.42 %, and 0.73 % across five evaluation metrics. Similarly, when compared to BWO on the same set of indicators, BWCOA showed average improvement rates of 22.39 %, 27.71 %, 70.53 %, 260.86 %, and 41.22 %. Furthermore, the running time of BWCOA is comparable to that of similar algorithms.