This paper proposes a novel approach based on deep reinforcement learning (DRL) for the 2D+1 packing problem with spatial constraints. This problem is an extension of the traditional 2D packing problem, incorporating an additional constraint on the height dimension. Therefore, a simulator using the OpenAI Gym framework has been developed to efficiently simulate the packing of rectangular pieces onto two boards with height constraints. Furthermore, the simulator supports multidiscrete actions, enabling the selection of a position on either board and the type of piece to place. Finally, two DRL-based methods (Proximal Policy Optimization -- PPO and the Advantage Actor-Critic -- A2C) have been employed to learn a packing strategy and demonstrate its performance compared to a well-known heuristic baseline (MaxRect-BL). In the experiments carried out, the PPO-based approach proved to be a good solution for solving complex packaging problems and highlighted its potential to optimize resource utilization in various industrial applications, such as the manufacturing of aerospace composites.

Balanced circular bin packing problems consist in positioning a given number of weighted circles in order to minimize the radius of a circular container while satisfying equilibrium constraints. These problems are NP-hard, highly constrained and dimensional. This paper describes a swarm algorithm based on a virtual-force system in order to solve balanced circular bin packing problems. In the proposed approach, a system of forces is applied to each component allowing to take into account the constraints and minimizing the objective function using the fundamental principle of dynamics. The proposed algorithm is experimented and validated on benchmarks of various balanced circular bin packing problems with up to 300 circles. The reported results allow to assess the effectiveness of the proposed approach compared to existing results from the literature.

Cutting and Packing problems are occurring in different industries with a direct impact on the revenue of businesses. Generally, the goal in Cutting and Packing is to assign a set of smaller objects to a set of larger objects. To solve Cutting and Packing problems, practitioners can resort to heuristic and exact methodologies. Lately, machine learning is increasingly used for solving such problems. This paper considers a 2D packing problem from the furniture industry, where a set of wooden workpieces must be assigned to different modules of a trolley in the most space-saving way. We present an experimental setup to compare heuristics, constraint optimization, and deep reinforcement learning for the given problem. The used methodologies and their results get collated in terms of their solution quality and runtime. In the given use case a greedy heuristic produces optimal results and outperforms the other approaches in terms of runtime. Constraint optimization also produces optimal results but requires more time to perform. The deep reinforcement learning approach did not always produce optimal or even feasible solutions. While we assume this could be remedied with more training, considering the good results with the heuristic, deep reinforcement learning seems to be a bad fit for the given use case.

In this article, we introduce PackingSolver, a new solver for two-dimensional two- and three-staged guillotine Packing Problems. It relies on a simple yet powerful anytime tree search algorithm called Memory Bounded A* (MBA*). This algorithm was first introduced in libralesso2020 for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php), for which it had been ranked first during the final phase. In this article, we generalize it for a large variety of Cutting and Packing problems. The resulting program can tackle two-dimensional Bin Packing, Multiple Knapsack, and Strip Packing Problems, with two- or three-staged exact or non-exact guillotine cuts, the orientation of the first cut being imposed or not, and with or without item rotation. Despite its simplicity and genericity, computational experiments show that this approach is competitive compared to the other dedicated algorithms from the literature. It even returns state-of-the-art solutions on several variants. The combination of efficiency, ability to provide good solutions fast, simplicity and versatility makes it particularly suited for industrial applications, which require quickly developing algorithms implementing several business-specific constraints.

This work aims to study and explore the use of Gene Expression Programming (GEP) in solving the on-line Bin-Packing problem. The main idea is to show how GEP can automatically find acceptable heuristic rules to solve the problem efficiently and economically. One dimensional Bin-Packing problem is considered in the course of this work with the constraint of minimizing the number of bins filled with the given pieces. Experimental Data includes instances of benchmark test data taken from Falkenauer (1996) for One-dimensional Bin-Packing Problems. Results show that GEP can be used as a very powerful and flexible tool for finding interesting compact rules suited for the problem. The impact of functions is also investigated to show how they can affect and influence the success of rates when they appear in rules. High success rates are gained with smaller population size and fewer generations compared to previous work performed using Genetic Programming.