## 1 Introduction
For instance, [PERSON] introduced a comprehensive hyper-heuristic algorithm utilizing genetic algorithms, specifically designed to address the challenges posed by two-dimensional regular (rectangular) and irregular (convex polygon) bin packing problems [10]. [PERSON] proposed a greedy adaptive search algorithm that involves the construction of an evaluation function and the introduction of a restricted local search strategy [11]. [PERSON] proposed a novel algorithm called Sequence Transfer-Based Particle Swarm Optimization (ST-PSO) to address the challenges of multi-constraint layout problems. This algorithm was inspired by transfer learning and takes into account the characteristics of two-dimensional irregular layouts [12]. [PERSON] proposed a hybrid search algorithm (BSTS) to solve the irregular packing problem. The algorithm combines beam search (BS) and tabu search (TS) to search for an optimal sequence of irregular pieces on a plate [13]. [PERSON] introduced a dynamic hierarchical hyper-heuristic approach that involves the utilization of low-level heuristics. These heuristics are combined in various manners using the main hyper-heuristic in order to determine the most effective heuristic operators for solving the two-dimensional irregular bin packing problem [14]. [PERSON] presented a random-key genetic algorithm (RKGA) for solving the nesting problem. This algorithm combines the power of a metaheuristic approach, the random-key genetic algorithm, with well-known placement strategies, such as the bottom-left strategy [15]. In recent years, researchers have begun to explore machine learning methods to solve two-dimensional irregular packing problems. These techniques forecast the potential packing solutions based on historical data. For instance, [PERSON] proposed a deep hierarchical reinforcement learning approach to effectively plan the packing order and placement of irregular objects [16]. In a similar vein, [PERSON] investigated a deep reinforcement learning hyper-heuristic with feature fusion to address online packing problems [17]. Despite the advantages associated with these techniques, they also possess several drawbacks and limitations. Insufficient computational resources and lengthy solution durations for larger problems are two challenges that may arise when employing mathematical programming approaches. These challenges can significantly diminish the effectiveness of problem-solving efforts. Heuristic algorithms necessitate a gradual improvement in algorithm performance through the incorporation of additional variable elements and the adjustment of algorithm parameters. This is essential as heuristic algorithms are susceptible to becoming trapped in local optimal solutions. The effectiveness of machine learning techniques in processing heavily depends on the training set. This particular dataset necessitates a substantial quantity of meticulously curated samples for the purposes of training and algorithm refinement. Consequently, a longer duration is required to acquire a more refined set of samples. For packing problems on a large scale, the utilization of machine learning-based searches can result in significant time consumption. To tackle the aforementioned challenges, this study presents a pioneering and inventive solution: the GA-LP optimization algorithm. By integrating genetic algorithms (GAs) with linear programming (LP), our algorithm presents a distinctive and robust solution that surpasses the constraints of current methodologies. In contrast to prior research, the GA-LP algorithm capitalizes on the synergistic capabilities of genetic algorithms (GAs) and linear programming (LP). This approach enables a more streamlined and successful optimization of packing configurations, effectively balancing efficiency and utilization in the resolution of irregular two-dimensional packing problems.