SPNOA: An Improved Nutcracker Optimizer Based on Specular Reflection Learning and Probability-Driven Hybrid Mutation Strategy for Global Optimization

The nutcracker optimization algorithm (NOA) is a novel swarm intelligence algorithm, inspired by the different natural behaviors of nutcrackers during two periods. Compared with many classical algorithms, NOA performs competitively on various test suites and optimization problems. NOA still suffers from local-optimum entrapment, an imbalance between exploration and exploitation, and insufficient convergence accuracy. To address these deficiencies, this paper proposes a multi-strategy enhanced NOA, termed SPNOA. The proposed method incorporates specular reflection learning, a nonlinear convergence factor, a diversity attack strategy, and a probability-driven hybrid mutation strategy. First, the specular reflection learning strategy is employed to enhance the diversity of the initial population. Second, the nonlinear convergence factor is introduced to balance the exploration and exploitation of SPNOA. Then, to augment the exploitation ability of the algorithm and improve its convergence accuracy, the diversity attack strategy is used to replace the storage phase in the foraging and storage strategy. Finally, the probability-driven hybrid mutation strategy is used before the end of each iteration, which helps SPNOA to break free from the local optimum. Subsequently, NOA, the newly proposed algorithm, the high-performance improved algorithm, and the CEC competition-winning algorithms are chosen as the comparison algorithms. Experiments are conducted across various dimensions of the CEC2020 test suite to assess the performance of SPNOA. The outcomes demonstrate that the proposed SPNOA exhibits superior convergence accuracy and robustness. Finally, 27 real-world engineering problems in different domains are selected to validate the ability of SPNOA to handle realistic optimization problems. The experimental results indicate that SPNOA retains its competitive edge in tackling complex, real-world optimization problems with diverse dimensions.