# Nesting Process Automation in the Footwear Industry: A Hybrid Approach to Minimize Material Waste
## 2 State of the Art
Through a series of iterations, particles--representing candidate solutions--navigate the search space with defined velocities and directions, aiming for convergence on optimal solutions. The aim is for the swarm to converge toward the best solutions. Analyses of this technique can be found in studies such as [17] and the original authors' own review [18]. * Greedy Randomized Adaptive Search Procedure (GRASP): Proposed by [PERSON] and [PERSON] [19], it is a greedy randomized search method based on the repetition of two phases: a greedy construction followed by local search. * Simulated Annealing (SA): As demonstrated in studies [20; 21], this strategy explores the search for a solution in the neighborhood of a current solution, allowing probabilistic acceptance of suboptimal solutions. This strategy is especially effective in discrete search spaces. Recent advancements in robust solutions for the nesting problem have increasingly focused on advanced image processing techniques [22] and neural networks [23]. Several recent studies regarding the application of artificial intelligence on nesting/packing are worth mentioning. In [24], a novel hierarchical reinforcement learning (RL) approach is proposed for packing irregular objects. The system employs a two-level architecture: a manager network that plans the packing sequence using object heightmaps, and a worker network that executes the placement of individual objects. This hierarchical structure is trained with a self-supervised Q-learning framework, using packing results to reward efficient packing (low top height, high volume utilization, and stable placements). The proposed method is demonstrated in both simulated and real-world robotic packing scenarios. [PERSON] et al. [25] explore the application of RL for packing 2D irregular patterns. A mathematical model is formulated, and RL algorithms based on Monte Carlo, Q-learning, and Sarsa learning are implemented, incorporating a custom reward and strategy update mechanism tied to packing outcomes. Combining these RL-based sequence generation methods with a classical Bottom-Left positioning algorithm, the system achieves effective packing. Standard test cases validate the proposed method, showing competitive performance against traditional heuristic approaches. This work lays the groundwork for future packing solutions based on Deep Reinforcement Learning (DRL) and offers the potential for improved material efficiency. In [26], an end-to-end RL strategy for arranging scattered irregular objects within a crate using a series of pushing actions is proposed. A sparse reward function, based on object connectivity, guides the learning process. Proximal Policy Optimization is used to simultaneously train a convolutional neural network encoder and a fully connected actor-network. Evaluated in both simulation and real-world experiments with varying object numbers, shapes, and materials, the proposed method demonstrates efficient and flexible arrangement, achieving an 85% success rate in simulation and 75% in the real world. The trained network exhibits strong generalization capabilities to previously unconsidered objects. [PERSON] et al. [27] propose a novel robotic system for high-performance 3D bin packing using DRL. The system comprises three key components: first, a DRL agent that tackles the 3D bin packing problem, formulated as a Markov Decision Process, using a heightmap-based environment; second, a candidate map mechanism to efficiently explore the action space and improve DRL training; and third, a robotic system with a motion primitive and vision module to ensure robust real-world execution. The experimental results on two datasets show significant improvements in space utilization (over 2.7% and 3.8%) compared to baselines, with performance scaling to different container sizes. In [28], the first DL approach to predict scrap generated during nesting-based manufacturing is presented. The proposed framework estimates scrap based solely on part geometries, without needing prior nesting arrangements.