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

The multi-objective goods loading problem represents a complex combinatorial optimization challenge classified as NP-hard. This paper employs a hybrid particle swarm optimization (PSO) algorithm enhanced with genetic algorithm strategies to solve this problem. The hybrid approach integrates crossover and mutation operations from genetic algorithms into the standard PSO framework, preventing premature convergence to local optima while accelerating convergence toward global optimum solutions. Furthermore, the implementation incorporates weight coefficients to balance multiple objectives, ensuring relatively optimal outcomes across all target functions through strategic parameter tuning.