The hybrid flow shop scheduling (HFS) model has significant practical applicability in fields, such as manufacturing, transportation, service, and communication. However, learning effects, refer to the phenomenon of processors spending less processing time with more familiar operations, which are common constraints in actual production while often ignored in HFS research despite their significant impact on processing efficiency. In this article, an HFS problem with learning effects and release dates is investigated from a practical application perspective. For large-scale instances, a dispatching rule-based heuristic is developed with theoretical performance guarantees by demonstrating the asymptotic optimality and the tight worst-case bound. For small-scale instances, a branch-and-boun3d algorithm is designed to obtain an exact solution. An elaborate branching scheme, an idle-time-based pruning rule, and a task-splitting-based lower bound effectively reduce the search space. For medium-scale instances, a hybrid shuffled frog-leaping algorithm combined with macro evolution and local intensification is presented to search for high-quality solutions. Extensive experiments demonstrate the superiority of the developed algorithms against the state-of-the-art algorithms.

Cloud computing is widely applied in modern industrial areas due to its technological advancement, cost reduction, and applicability. Packets (tasks) belonging to different applications (agents) compete to share the common cloud resource through a series of edge nodes (processors) in pursuit of fast transmission. This paper abstracts the cloud computing system as a multi-agent flow-shop scheduling (MAFS) problem. The objective is to minimise the total completion time of several agents with the restriction that the maximum lateness cannot exceed a given bound. Given the complexity of the considered problem, a branch and bound algorithm combined with several pruning rules and lower bounds is proposed to obtain optimal solutions. Furthermore, the considered problem is generalised to a bi-scenario version, and a bi-population cooperative co-evolutionary (BCCE) algorithm is proposed to solve it. A reinforcement learning-based method is presented to generate the initial population. Several problem-specific intensification strategies are constructed to explore promising solutions. Comprehensive experiments verified the effectiveness of the proposed algorithms. The industrial data from the China Earthquake Network Centre further confirmed the superiority of the BCCE algorithm. Overall, the MAFS model and the proposed algorithms effectively enhance the user experience and reasonably guarantee revenue.

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

Flow-shop scheduling is an extremely popular optimization model in industrial production, where each job must be scheduled on a series of machines following an identical process. The optimal criteria, makespan and maximum delivery–completion time, are investigated separately. A mixed integer programming model is built to evaluate the exact algorithm in simulation experiments. Given that these problems are NP hard and cannot be solved in polynomial time, exact and metaheuristic methods are proposed for different problem sizes. For small-scale instances, optimal schedules are achieved using an effective branch-and-bound algorithm, in which elaborately designed lower bound and branching rules significantly improve computational efficiency. For medium-scale instances, satisfactory solutions are obtained using a hybrid discrete differential evolution algorithm with improvement schemes to promote its performance. The experimental results show the effectiveness of the proposed algorithms.