Multi-Objective Goods Loading Problem: A Complex Combinatorial Optimization Challenge

The multi-objective goods loading problem constitutes a highly complex combinatorial optimization challenge falling within the NP-hard problem category. In this research, we implement a hybrid particle swarm optimization algorithm to address this problem. The hybrid PSO algorithm enhances the basic particle swarm framework by integrating crossover and mutation strategies from genetic algorithms, effectively preventing convergence to local optima while significantly accelerating convergence velocity toward global optimal solutions. From an implementation perspective, the algorithm maintains particle velocity and position updates through standard PSO equations while periodically applying genetic operators to diversify the solution space. Additionally, we introduce a weighting coefficient mechanism that dynamically balances multiple objectives during optimization, enabling the achievement of relatively optimal results across all target functions through adaptive parameter adjustment and fitness evaluation.