Search Results (177)

This study addresses a critical gap in Energy-Efficient Permutation Flow Shop Scheduling (EPFSP) by integrating the often-overlooked time-accumulative equipment degradation inherent in practical manufacturing. This research formalizes and solves the EPFSP with machine deterioration (EPFSP-DEM), aiming to simultaneously minimize the makespan and total energy consumption. To achieve this objective, this study proposes a Diversity-Constrained Imperialist Competitive Algorithm (DCICA) featuring several novel mechanisms. In DCICA, a differentiated assimilation is developed to improve diversity of the population; a knowledge-guided revolution is designed to allocate computing resources efficiently; the convergence and diversity metrics are defined to evaluate the search quality on assimilation and revolution; a novel imperialist competition is also given to enhance information exchanges among empires and strengthen the search for some worse solutions. Finally, extensive experiments are conducted, and the results demonstrate that DCICA outperforms the existing algorithms in solving the investigated problem. Full article

Production scheduling that involves distributed factories, machine maintenance, and resource constraints plays a crucial role in manufacturing. However, these realistic constraints have rarely been considered simultaneously in the hybrid flow shop (HFS). To address this issue, a distributed resource-constrained hybrid flow shop scheduling problem with machine breakdowns (DRCHFSP-MB) is studied. There are two optimization objectives, i.e., makespan and total energy consumption (TEC). To solve the strongly NP-hard problem, a mathematical model is established and a block–neighborhood-based multi-objective evolutionary algorithm (BNMOEA) is developed. In the proposed algorithm, an efficient hybrid initialization method is adopted to obtain high-quality individuals to participate in the evolutionary process of the population. Next, to enhance the search capability of the BNMOEA, three well-designed crossover operators are used in the global search. Then, the convergence of the proposed algorithm is improved by utilizing eight critical factory-based local search operators combined with block–neighborhood. Finally, the BNMOEA is compared with several of the most advanced multi-objective algorithms; the results indicate that the BNMOEA has an outstanding performance in solving DRCHFSP-MB. Full article

Highly customized requirements in smart manufacturing result in the unavoidable manual execution of complex operational procedures. Physical and mental fatigue from long work periods for assembly-line operators induces production issues, such as defective work-in-processes or equipment failure. An effective production schedule should account for worker fatigue. This study investigates a three-machine flowshop scheduling problem with the objective of makespan minimization, in which a linear fatigue effect function provides an approximate mathematical representation of fatigue and recovery processes in workers. A mixed integer programming (MIP) model is developed to optimize the integration of automated and human-operated production in manufacturing systems. Given its NP-hardness, an improved tabu search (ITS) algorithm is designed to obtain high-quality solutions, incorporating multiple initial solutions, a well-designed encoding-decoding strategy, and a tabu-based adaptive search mechanism to enhance efficiency. Numerical simulations indicate the veracity of the MIP model and the effectiveness of the ITS algorithm. Full article

This study proposes an improved Fruit Fly Optimization Algorithm integrated with Simulated Annealing (SA-FOA) for hybrid flow shop scheduling problems with dual objectives of minimizing makespan and total tardiness. The algorithm adopts a three-stage integration strategy to generate high-quality initial populations, surpassing random initialization. During olfactory search, insertion-based neighborhood operations expand search scope, while visual search incorporates simulated annealing acceptance criteria to escape local optima. Validation employs three scalable instances, comparing SA-FOA against basic FOA and classical scheduling rules. Experimental results demonstrate significant superiority in Inverted Generational Distance (IGD), Non-dominant rate (NR), and Convergence Matrix (C-matrix metrics), highlighting enhanced convergence, distribution, and diversity. Notably, performance advantages amplify with problem scale growth. Full article

The permutation flow shop scheduling problem (PFSP) is one of the hot issues in current research, and its production methods are widely used in steel, medicine, semiconductor, and other industries. Due to the characteristics of permutation flow (optimize the production process through the principle of symmetry to achieve efficient allocation and balance of resources), its task processes only need to be sorted on the first machine, and the subsequent machines are completely symmetrical with the first machine. This paper proposes an enhanced particle swarm optimization algorithm (EPSO) for the PFSP. Firstly, in order to enhance the diversity of the algorithm, a new dynamic inertia weight method was introduced to dynamically adjust the search range of particles. Secondly, a new speed update strategy was proposed, which makes full use of the information of high-quality solutions and further improves the convergence speed of the algorithm. Subsequently, an interference strategy based on individual mutations was designed, which improved the universality of the model’s global search. Finally, to verify the effectiveness of the EPSO algorithm, six benchmark functions were tested, and the results proved the superiority of the EPSO algorithm. In addition, the average relative error of the improved algorithm is at least 21.6% higher than that of the unimproved algorithm when solving large-scale PFSPs. Full article

This paper introduces a novel scheduling model that integrates weather-based productivity coefficients into multi-unit construction projects, aiming to enhance profit and reduce delays. The method is suitable especially for renewable energy, open-area projects. The authors propose a flow-shop optimization framework that considers key aspects of construction contracts, e.g., contractual penalties, downtime losses, and cash flow constraints. A proprietary Tabu Search (TS) metaheuristic algorithm variant is used to solve the resulting NP-hard problem. Numerical experiments on multiple test sets indicate that the TS algorithm consistently outperforms other methods in finding higher-profit schedules. A real-world wind farm case study further demonstrates substantial improvements, transforming an initially loss-making operation into a profitable venture. By explicitly accounting for weather disruptions within a formalized scheduling model, this work advances the understanding of reliable project planning under uncertain environmental conditions. The solution framework offers contractors an effective tool for mitigating scheduling risks and optimizing resource usage. The integration of weather data and cash flow management increases the likelihood of on-time and on-budget project delivery. Full article

In this paper, we propose a formulation of the permutation flow and job shop scheduling problems using special recursive functions and show its equivalence to the existing classical formulation. Equivalence is understood in the sense that both ways of defining the problem describe the same set of feasible schedules for each pair of jobs and machine numbers. In this paper, the apparatus of recursive functions is used to describe and solve three problems: permutation flow shop; permutation flow shop with the addition of the ‘and’ predicate extending the machine chain to an acyclic graph; and permutation job shop. The predicate ‘and’ allows the description of the flow shop with assembly operation tasks. Recursive functions have a common domain and range. To calculate an optimal schedule for each of these three problems, a branch and bound method is considered based on a recursive function that implements a job swapping algorithm. The complexity of the optimization algorithm does not increase compared to the non-recursive description of the PFSP. This article presents some results for the calculation of optimal schedules on several test instances. It is expected that the new method, based on the description of recursive functions and their superposition, will be productive for formulating and solving some extensions of scheduling problems that have practical significance. Full article

In distributed manufacturing systems, minimizing completion time and improving resource utilization are critical for enhancing operational efficiency. Conventional scheduling models for centralized flowshops struggle to capture the complexity of distributed heterogeneous systems, while existing studies often overlook the combined challenges of heterogeneous factories, no-wait constraints, and sequence-dependent setup times (SDST). This study focuses on the distributed heterogeneous no-wait permutation flowshop scheduling problem with SDST (DHNPFSP-SDST), which is proven NP-hard via polynomial reduction to the classic permutation flowshop scheduling problem (PFSP). We first establish a bi-objective optimization model to simultaneously minimize makespan and total machine non-working time, serving as a standard experimental foundation. The core innovation is a large language model-assisted non-dominated sorting genetic algorithm (LLM-NSGAII), Through a structured prompt framework, LLM-NSGAII leverages LLM’s zero-shot in-context learning to dynamically orchestrate selection, crossover, and mutation operations—replacing the fixed operators of traditional NSGAII. Experiments on extended benchmarks show that when compared with mainstream, multi-objective algorithms demonstrate competitiveness across most instances and provide a proof of concept for integrating LLMs with evolutionary algorithms, opening new avenues for algorithmic optimization. Full article

Efficient scheduling is critical for the success of any organization. Researchers have proposed numerous strategies for addressing various scheduling problems. The hybrid flow shop (HFS) scheduling is a complex and NP-hard problem that arises in many manufacturing and service industries. This work introduces an optimization technique that utilizes atomic orbitals to address issues in HFS scheduling. Our objective is to reduce makespan (Cmax). Makespan minimization is critical for improving productivity and resource utilization. The standard atomic orbital search optimization algorithm (AOSOA) is hybridized with constructive heuristics to enhance solution quality. The scheduling problem of an electrical panel board manufacturing industry is solved using the hybrid AOSOA (HAOSOA). The results were better than those previously reported. A variety of random test situations of varying sizes and configurations were devised to assess the efficacy of the suggested algorithm. The proposed algorithm’s outcomes were compared against well-known algorithms discussed in the literature. Friedman and Wilcoxon test results indicate that the proposed methodology improves the solution quality in each test instance compared to all the metaheuristics used for comparison. The performance of the proposed algorithm is also evaluated using benchmark problems from the literature. In the first test, the algorithm has a rank value of 1, indicating it performs better than each of the comparing algorithms. In the second test, it is able to find the best makespan for 65 of the 77 problems. Full article

The Distributed No-Wait Flow Shop Scheduling Problem (DNWFSP) arises in various manufacturing contexts, such as chemical production and electronic assembly, where strict no-wait constraints and multi-factory coordination are required. Solving the DNWFSP involves determining the allocation of jobs to factories and the no-wait processing sequences within each factory, making it a highly complex combinatorial problem. To address the limitations of existing methods—including poor initial solution quality, limited neighborhood exploration, and a tendency to converge prematurely—this paper proposes a Multi-Neighborhood Adaptive Tabu Search Algorithm (MNATS). The MNATS integrates a balance–lookahead NEH initializer (BL-NEH), an adaptive neighborhood local search (ANLS) strategy, and an Adaptive Tabu-Guided Perturbation (ATP) strategy. Experimental results on multiple benchmark instances demonstrate that MNATS algorithm significantly outperforms several state-of-the-art algorithms in terms of solution quality and robustness. Full article

Advances in satellite miniaturisation have led to a steep rise in the number of Earth-observation platforms, turning the downlink of the resulting high-volume remote-sensing data into a critical bottleneck. Low-Earth-Orbit (LEO) communication constellations offer a high-throughput relay for these data, yet also introduce intricate scheduling requirements. We term the associated task the Remote Sensing Data Transmission in Communication Constellations (DTIC) problem, which comprises two sequential stages: inter-satellite routing, and satellite-to-ground delivery. This problem can be cast as a Hybrid Flow Shop Scheduling Problem (HFSP). Unlike the classical HFSP, every processor (e.g., ground antenna) in DTIC can simultaneously accommodate multiple jobs (data packets), subject to two-dimensional spatial constraints. This gives rise to a new variant that we call the Hybrid Flow Shop Problem with Two-Dimensional Processor Space (HFSP-2D). After an in-depth investigation of the characteristics of this HFSP-2D, we propose a constructive heuristic, denoted NEHedd-2D, and a Two-Stage Memetic Algorithm (TSMA) that integrates an Inter-Processor Job-Swapping (IPJS) operator and an Intra-Processor Job-Swapping (IAJS) operator. Computational experiments indicate that when TSMA is initialized with the solution produced by NEHedd-2D, the algorithm attains the optimal solutions for small-sized instances and consistently outperforms all benchmark algorithms across problems of every size. Full article

Efficient production scheduling is a key challenge in industrial operations and continues to attract significant interest within the field of operations research. This paper investigates a range of methodological approaches designed to solve the permutation flow shop scheduling problem (PFSP) with sequence-dependent setup times (SDST). The main objective is to minimize the total weighted flow time (TWFT) while ensuring a no-wait production environment. The proposed solution strategy is based on using algorithms with a mixed integer linear programming (MILP) formulation, heuristics, and their combination. The heuristics utilized in this paper include an advanced greedy randomized adaptive search procedure (GRASP) based on a priority rule and Hybrid-GRASP-NEH (HGRASP), where Nawaz-Enscore-Ham (NEH) takes place to initiate solutions, based on iterative global and local search methods to refine exploration capabilities and improve solution quality. These approaches were validated using a comprehensive set of experiments across diverse instance sizes that proved the efficiency of HGRASP, with the results showing a high-performance level that closely matched that of the exact MILP approach. Statistical analysis via the Friedman test (χ² = 46.75, p = 7.04 × 10⁻¹¹) confirmed significant performance differences among MILP, GRASP, and HGRASP. While MILP guarantees theoretical optimality, its practical effectiveness was limited by imposed computational time constraints, and HGRASP consistently achieved near-optimal solutions with superior computational efficiency, as demonstrated across diverse instance sizes. Full article

This study developed a simple genetic algorithm (SGA) enhanced by a random forest (RF) surrogate model, namely ${SGA}_{RF}$, to solve the permutation flow-shop scheduling problem with order acceptance under the conditions of limited capacity, weighted-tardiness, and past-sequence-dependent (PSD) setup times (PFSS-OAWT with PSD). To the best of our knowledge, this is the first study to investigate this problem. Our proposed algorithm increases the setup time for each successive job by a constant proportion of the cumulative processing time of preceding jobs to capture the progressive slowdown that often occurs on real production lines. In the developed algorithm with maximum ${10}^5$ fitness evaluations, the RF surrogate model predicts objective function values and guides crossover and mutation. On the PFSS-OAWT with PSD benchmark (up to 500 orders and 20 machines, 160 instances), ${SGA}_{RF}$ represents improvements of 0.9% over SGA, 0.8% over ${SGA}_{LS}$, and 5.6% over SABPO. Although the surrogate incurs additional runtime, the gains in both profit and order-acceptance rates justify its use for high-margin, offline planning. Overall, the results of this study suggest that integrating evolutionary search into data-driven prediction is an effective strategy for solving complex capacity-constrained scheduling problems. Full article

Distributed permutation flowshop scheduling is an NP-hard problem that has become a hot research topic in the fields of optimization and manufacturing in recent years. Multimodal optimization finds multiple global and local optimal solutions of a function. This study proposes a harmony search algorithm with iterative optimization operators to solve the NP-hard problem for multimodal optimization with the objective of makespan minimization. First, the initial solution set is constructed by using a distributed NEH operator. Second, after generating new candidate solutions, efficient iterative optimization operations are applied to optimize these solutions, and the worst solutions in the harmony memory (HM) are replaced. Finally, the solutions that satisfy multimodal optimization of the harmony memory are obtained when the stopping condition of the algorithm is met. The constructed algorithm is compared with three meta-heuristics: the iterative greedy meta-heuristic algorithm with a bounded search strategy, the improved Jaya algorithm, and the novel evolutionary algorithm, on 600 newly generated datasets. The results show that the proposed method outperforms the three compared algorithms and is applicable to solving distributed permutation flowshop scheduling problems in practice. Full article

Mixed-flow assembly lines are widely employed in industrial manufacturing to handle diverse production tasks. For mixed flow assembly lines that involve mold changes and greater processing difficulties, there are currently two approaches: batch production and production according to order sequence. The first approach struggles to meet the processing constraints of workpieces with higher production difficulty, while the second approach requires the development of suitable scheduling schemes to balance mold changes and continuous processing. Therefore, under the second approach, developing an excellent scheduling scheme is a challenging problem. This study addresses the mixed-flow assembly shop scheduling problem, considering continuous processing and mold-changing constraints, by developing a multi-objective optimization model to minimize additional production time and customer waiting time. As this NP-hard problem poses significant challenges in solution space exploration, the conventional NSGA-II algorithm suffers from limited local search capability. To address this, we propose an enhanced NSGA-II algorithm (RLVNS-NSGA-II) integrating deep reinforcement learning. Our approach combines multiple neighborhood search operators with deep reinforcement learning, which dynamically utilizes population diversity and objective function data to guide and strengthen local search. Simulation experiments confirm that the proposed algorithm surpasses existing methods in local search performance. Compared to VNS-NSGA-II and SVNS-NSGA-II, the RLVNS-NSGA-II algorithm achieved hypervolume improvements ranging from 19.72% to 42.88% and 12.63% to 31.19%, respectively. Full article