Improving the Bin Packing Heuristic thro

In recent years, Grammatical Evolution (GE) has emerged as a representation of Genetic Programming (GP) applied to various optimization issues, including symbolic regression and algorithmic challenges. This paper explores the integration of Swarm Intelligence (SI) strategies, specifically Particle Swarm Optimization (PSO) and the novel Particle Evolutionary Swarm Optimization (PESO), within the GE framework to enhance bin packing problem (BPP) solutions. Given PSO’s limitations—such as premature convergence and lack of diversity—PESO introduces innovative perturbations to ameliorate these issues. To evaluate the effectiveness of these strategies, a nonparametric Friedman test is conducted, comparing the performance of PESO, PSO, and traditional BPP heuristics. The study's principal contribution lies in proposing a grammar for generating both online and offline heuristics based on test instances, thereby improving upon existing heuristics developed by other grammars and human interventions. This methodology presents a versatile approach, transferable to various optimization problems beyond the BPP. The findings demonstrate that applying PESO within the GE framework can yield superior results compared to the conventional PSO alone.