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.
The one-dimensional bin packing problem (1D-BPP) is a classical NP-hard combinatorial optimization problem with applications ranging from logistics and manufacturing to cloud resource management. Although deep reinforcement learning (DRL) has become a competitive paradigm for data-driven optimization, most learned packing methods target 2D and 3D variants, and intelligent learned solvers for 1D-BPP remain scarce. In this paper, we present a novel end-to-end, size-agnostic graph reinforcement learning framework for 1D-BPP. We formulate the packing process as a Markov decision process on an item-compatibility graph, serving as a structural knowledge representation in which every action merges two partial bins that fit together. A graph neural network actor-critic policy extracts relational features from this representation and is trained through reinforcement learning and decoded by stochastic beam search, enabling a single trained model to generalize zero-shot to instances of any size. We conduct a systematic empirical study across graph encoders, DRL algorithms, reward functions, training distributions, and hyperparameters. Evaluated zero-shot on the full BPPLIB benchmark against a constructive heuristic, a grouping genetic algorithm, and recent learned methods, our data-driven policy lowers the mean optimality gap of the constructive heuristic from 2.66% to 2.31%, with the largest gains on structured instances. Against learned baselines evaluated on the same benchmark, it attains a lower gap on most of the nine families and is far more stable across instance distributions. On the hardest benchmark family, it outperforms a state-of-the-art learned solver that relies on column generation and integer programming, while using no solver at all. A grouping genetic algorithm remains ahead overall, and we analyze where and why the residual gap arises.
Packing objects efficiently is a fundamental problem in logistics, warehouse automation, and robotics. When dealing with highly diverse 3D objects (household or grocery items), closed-form solutions are infeasible, and heuristic or model-free Reinforcement Learning~(RL) methods tend to focus solely on geometric optimization, relying on exhaustive searches of the discretized solution space. This leads to long training times (for pure RL) and high latency (heuristics), limited transferability to robotic scenarios, and ultimately ignores object characteristics (fragility, deformability) and human preferences. We propose HERB, a human-augmented RL framework for packing irregular objects, the first to explore the potential of learning from human demonstrations to solve this complex task. It leverages human demonstrations of packing strategies, which inherently exhibit latent factors such as space optimization, stability, and object properties that are difficult to model explicitly. The human-expert data is combined with RL exploration to provide the placement of each object inside the container. Experimental results show that our method outperforms heuristic, purely RL-based, and imitation learning approaches in packing efficiency and latency. Qualitative results highlight that our packing strategy produces more stable, human-like arrangements, which we expect to be more appropriate and widely accepted. Finally, we demonstrate the real-world feasibility of our method on a robotic system.
Selection Hyper-heuristics (HHs) automate algorithmic design by selecting from a set of low-level heuristics which one to apply at each stage of the optimisation process. Several impressive results have been recently rigorously proven regarding the performance of selection hyper-heuristics (HHs) for standard benchmark functions. However, the learning mechanisms employed by these HHs are considerably simplified compared to the machine learning techniques typically used in real world applications. In this paper we analyse a Reinforcement Learning Hyper-heuristic (RLHH) from the literature. The only previous result available proved that for a wide range of parameter settings, RLHH does not learn to select heuristics appropriately for the standard LeadingOnes benchmark function. In this paper, we rigorously prove that with appropriate parameter values RLHH equipped with two random local search operators, RLS_1 and RLS_2 optimises the LeadingOnes benchmark function in the best possible expected runtime achievable with the two operators up to lower order terms. Experiments show that for realistic problem sizes it is faster than the Generalised Random Gradient HH which was previously proven to also have optimal expected runtime up to lower order terms.