Enhanced approach to permutation flow-shop scheduling problem using convolutional neural networks

This paper presents an enhanced approach to solving the Permutation Flow-Shop Scheduling Problem (PFSP) using Convolutional Neural Networks (CNNs). The PFSP is a well-known NP-hard combinatorial optimization problem where the objective is to find an optimal job sequence to minimize the makespan or total completion time in a flow-shop environment. Given the complexity and computational intensity of solving PFSP, traditional methods, such as heuristics and metaheuristics, have been widely employed. However, these methods are often limited in handling large-scale problems and do not guarantee optimal solutions. To address these challenges, this paper proposes using deep learning techniques, specifically CNNs, to predict optimal or near-optimal schedules for PFSP instances. The approach transforms the scheduling task into an image classification problem, where each PFSP instance is represented as an image, and CNNs are trained to output the makespan or job completion time for given instances. The proposed methodology includes data collection from various sources, including industrial scenarios and public benchmark datasets. A dataset of 30,000 instances was generated to train, validate, and test the CNN model. The paper outlines the data preprocessing steps, model architecture, and the training process, which uses K-fold cross-validation for model validation. The CNN architecture consists of input, convolutional, global max pooling, fully connected, and output layers, with appropriate activation functions at each stage. The model’s performance is evaluated using standard metrics such as mean absolute error (MAE) and training loss, with comparisons made to traditional metaheuristic approaches.