Hybridizing a Grouping Metaheuristic with Reinforcement Learning for the One-Dimensional Bin Packing Problem

2026-07-02

AI Summary

This work addresses the one-dimensional bin packing problem (1D-BPP), an NP-hard combinatorial optimization challenge, by proposing a novel approach that integrates reinforcement learning with a hybrid grouping genetic algorithm (HGGA). A Q-learning-based controller is designed to dynamically schedule eight high-level operators—including BPCX crossover, light and heavy mutation, Martello-Toth local search, and population restart—based on an eight-dimensional state encoding, thereby achieving the first adaptive orchestration of multiple optimization operators. Experimental results demonstrate that the proposed method attains an average optimality gap of merely 0.95% on standard benchmark instances while reducing computation time from 64.22 seconds to 1.29 seconds—nearly a 50-fold speedup—significantly outperforming classical heuristics such as First-Fit Decreasing (FFD) while preserving the solution quality of HGGA.

Abstract

The one-dimensional bin packing problem (1D-BPP) is a canonical NP-hard combinatorial optimization problem with broad industrial applications. We propose RL-HGGA, a hybrid algorithm that integrates Falkenauer's Hybrid Grouping Genetic Algorithm (HGGA) with a tabular Q-learning controller. Rather than applying genetic operators at fixed probabilities, a Q-learning agent dynamically selects among eight macro-actions -- including BPCX crossover, light and heavy mutation, Martello-Toth local search, and population restart -- based on an eight-dimensional state representation encoding generation progress, stagnation level, optimality gap, average fitness, population variance, and average bin fill rate. The agent is trained with an epsilon-greedy policy over 400 episodes, with epsilon decaying to 0.05. Experiments on standard benchmark families (Falkenauer T/U, Scholl 1-3, Hard28) show that RL-HGGA achieves an average optimality gap of 0.95% -- competitive with HGGA (0.75%) and well below FFD (2.47%) -- while reducing mean computation time from 64.22 s to 1.29 s, a 50x speedup. These results demonstrate that learned adaptive operator selection can achieve near-HGGA solution quality at a fraction of the computational cost.

Problem

• one-dimensional bin packing problem
• combinatorial optimization
• NP-hard
• industrial applications

Innovation

• Reinforcement Learning
• Adaptive Operator Selection
• Hybrid Metaheuristic
• One-Dimensional Bin Packing Problem
• Q-learning