A Hybrid Symmetry Strategy Improved Binary Planet Optimization Algorithm with Theoretical Interpretability for the 0-1 Knapsack Problem

The Planet Optimization Algorithm (POA) is a meta-heuristic inspired by celestial mechanics, drawing on Newtonian gravitational principles to simulate planetary dynamics in optimization search spaces. While the POA demonstrates a strong performance in continuous domains, we propose an Improved Binary Planet Optimization Algorithm (IBPOA) tailored to the classical 0-1 knapsack problem (0-1 KP). Building upon the POA, the IBPOA introduces a novel improved transfer function (ITF) and a greedy repair operator (GRO). Unlike general binarization methods, the ITF integrates theoretical foundations from branch-and-bound (B&B) and reduction algorithms, reducing the search space while guaranteeing optimal solutions. This improvement is strengthened further through the incorporation of the GRO, which significantly improves the searching capability. Extensive computational experiments on large-scale instances demonstrate the IBPOA’s effectiveness for the 0-1 KP, showing a superior performance in its convergence rate, population diversity, and exploration–exploitation balance. The results from 30 independent runs confirm that the IBPOA consistently obtains the optimal solutions across all 15 benchmark instances, spanning three categories. Wilcoxon’s rank-sum tests against seven state-of-the-art algorithms reveal that the IBPOA significantly outperforms all competitors (p<0.05), though it is occasionally matched in its solution quality by the binary reptile search algorithm (BinRSA). Crucially, the IBPOA achieves solutions 4.16 times faster than the BinRSA on average, establishing an optimal balance between solution quality and computational efficiency.