Search Results (43)

In this paper, a Multiple-Objective Memetic Algorithm (MOMA) is proposed to address the Energy-Efficient Distributed Assembly Permutation Flow-Shop Scheduling Problem (EEDAPFSP) by explicitly exploiting the structural and objective symmetries inherent in the scheduling process, with the dual objectives of minimizing the maximum completion time (makespan) and total energy consumption (TEC). The EEDAPFSP is a complex NP-hard optimization problem in modern sustainable manufacturing that balances production efficiency and environmental sustainability. During the global search phase, a symmetry-preserving dual-search framework is constructed, in which diverse and potential regions in the solution space are explored by symmetrically generating time-dominant product sub-sequences (TDPSs) and energy-dominant product sub-sequences (EDPSs) in the individuals of each iteration, enabling complementary exploration from time- and energy-oriented perspectives. This is accomplished through the incorporation of a variable-weight metric technique and a first product fixed strategy into an estimation distributed algorithm-based hyper-heuristic (EDAHH), so as to maintain a balanced and symmetric probabilistic modeling of decision patterns with respect to the makespan and energy consumption. In the local search phase, two problem-specific designed neighborhood structures are proposed to refine the job sequences corresponding to the TDPS and EDPS in the superior sub-population, effectively reducing both the makespan and TEC. A box-level $\epsilon$ dominance technique based on the crowding distance is proposed for Pareto archive updating. Additionally, an energy-saving strategy is embedded throughout the algorithm, incorporating three mechanisms—job processing delay, machine shutdown and restart control, and speed regulation—to further optimize TEC during both the global and local search phases. Finally, extensive computational experiments are carried out, and the results demonstrate that the MOMA achieves significantly better performance in terms of the inverted generational distance ($IGD$) and the quality metric $\rho$ compared with state-of-the-art algorithms. The resulting Pareto front of non-dominated solutions provides a comprehensive set of trade-offs between energy consumption and the makespan, offering decision makers flexible and efficient scheduling options. Full article

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

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

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

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

In order to address the Distributed Displacement Flow Shop Scheduling Problem (DPFSP) with uncertain processing times in real production environments, Plant Simulation is employed to construct a simulation model for the MSRDPFSP. The model conducts quantitative analyses of workshop layout, assembly line design, worker status, operating status of robotic arms and AGV vehicles, and production system failure rates. A hybrid NEH-DDQN algorithm is integrated into the simulation model via a COM interface and DLL, where the NEH algorithm ensures the model maintains optimal performance during the early training phase. Four scheduling strategies are designed for workpiece allocation across different workshops. A deep neural network replaces the traditional Q-table for greedy selection among these four scheduling strategies, using each workshop’s completion time as a simplified state variable. This approach reduces algorithm training complexity by abstracting away intricate workpiece allocation details. Experimental comparisons show that for the data of 500 workpieces, the NEH algorithm in 3 s demonstrates equivalent quality to that produced by the GA algorithm in 300 s. After 2000 iterations, the DDQN algorithm achieves a 15% reduction in makespan with only a 2.5% increase in computational time compared to random search, this joint simulation system offers an efficient and stable solution for the modeling and optimization of the MSRDPFSP issue. Full article

The Mixed No-Idle Permutation Flow Shop Scheduling Problem (MNPFSSP) represents a specific case within regular flow scheduling problems. In this problem, some machines allow idle times between consecutive jobs or operations while other machines do not. Traditionally, the MNPFSSP has been addressed using the metaheuristics and exact methods. This work proposes an Evolutionary Strategy Based on the Generalized Mallows Model (ES-GMM) to solve the issue. Additionally, its advanced version, ES-GMMc, is developed, incorporating operating conditions to improve execution times without compromising solution quality. The proposed approaches are compared with algorithms previously used for the problem under study. Statistical tests of the experimental results show that the ES-GMMc achieved reductions in execution time, especially standing out in large instances, where the shortest computing times were obtained in 23 of 30 instances, without affecting the quality of the solutions. Full article

The no-idle permutation flow shop scheduling problem (NIPFSP), as a current hot topic, is widely present in practical production scenarios in industries such as aviation and electronics. However, existing methods may face challenges such as excessive computational time or insufficient solution quality when solving large-scale NIFSSP instances. In this paper, a discrete fruit fly optimization algorithm (DFFO) is proposed for solving the NIPFSP. DFFO consists of three phases, i.e., the smell search phase based on the variable neighborhood, the visual search phase based on the probabilistic model, and the local search phase. In the smell search phase, multiple perturbation operators are constructed to further expand the search range of the solution; in the visual search phase, a probabilistic model is constructed to generate a series of positional sequences using some elite groups, and the concept of shared sequences is adopted to generate new individuals based on the positional sequences and shared sequences. In the local search stage, the optimal individuals are refined with the help of an iterative greedy algorithm, so that the fruit flies are directed to more promising regions. Finally, the test results show that DFFO’s performance is at least 28.1% better than other algorithms, which verifies that DFFO is an efficient method to solve NIPFSP. Full article

This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the PFSP is modeled using an end-to-end deep reinforcement learning (DRL) approach, named PFSP_NET, which is designed based on the characteristics of the PFSP, with the actor–critic algorithm employed to train the model. Once trained, this model can quickly and directly produce relatively high-quality solutions. Secondly, to further enhance the quality of the solutions, the outputs from PFSP_NET are used as the initial population for the improved genetic algorithm (IGA). Building upon the traditional genetic algorithm, the IGA utilizes three crossover operators, four mutation operators, and incorporates hamming distance, effectively preventing the algorithm from prematurely converging to local optimal solutions. Then, to optimize energy consumption, an energy-saving strategy is proposed that reasonably adjusts the job scheduling order by shifting jobs backward without increasing the maximum completion time. Finally, extensive experimental validation is conducted on the 120 test instances of the Taillard standard dataset. By comparing the proposed method with algorithms such as the standard genetic algorithm (SGA), elite genetic algorithm (EGA), hybrid genetic algorithm (HGA), discrete self-organizing migrating algorithm (DSOMA), discrete water wave optimization algorithm (DWWO), and hybrid monkey search algorithm (HMSA), the results demonstrate the effectiveness of the proposed method. Optimal solutions are achieved in 28 test instances, and the latest solutions are updated in instances Ta005 and Ta068 with values of 1235 and 5101, respectively. Additionally, experiments on 30 instances, including Taillard 20-10, Taillard 50-10, and Taillard 100-10, indicate that the proposed energy strategy can effectively reduce energy consumption. Full article

This paper addresses the green permutation flow shop scheduling problem (GPFSP) with energy consumption consideration, aiming to minimize the maximum completion time and total energy consumption as optimization objectives, and proposes a new method that integrates end-to-end deep reinforcement learning (DRL) with the multi-objective evolutionary algorithm based on decomposition (MOEA/D), termed GDRL-MOEA/D. To improve the quality of solutions, the study first employs DRL to model the PFSP as a sequence-to-sequence model (DRL-PFSP) to obtain relatively better solutions. Subsequently, the solutions generated by the DRL-PFSP model are used as the initial population for the MOEA/D, and the proposed job postponement energy-saving strategy is incorporated to enhance the solution effectiveness of the MOEA/D. Finally, by comparing the GDRL-MOEA/D with the MOEA/D, NSGA-II, the marine predators algorithm (MPA), the sparrow search algorithm (SSA), the artificial hummingbird algorithm (AHA), and the seagull optimization algorithm (SOA) through experimental tests, the results demonstrate that the GDRL-MOEA/D has a significant advantage in terms of solution quality. Full article

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies. Full article

The permutation flow-shop scheduling problem is a classical problem in scheduling that aims at identifying the optimal sequence of jobs that should be processed in a number of machines in an effort to minimize makespan or some other performance criterion. The distributed permutation flow-shop scheduling problem adds multiple factories where copies of the machines exist and asks for minimizing the makespan on the longest-running location. In this paper, the problem is approached using Constraint Programming and its specialized scheduling features, such as interval variables and non-overlap constraints, while a novel heuristic is proposed for computing lower bounds. Two constraint programming models are proposed: one that solves the Distributed Permutation Flow-shop Scheduling problem, and another one that drops the constraint of processing jobs under the same order for all machines of each factory. The experiments use an extended public dataset of problem instances to validate the approach’s effectiveness. In the process, optimality is proved for many problem instances known in the literature but has yet to be proven optimal. Moreover, a high speed of reaching optimal solutions is achieved for many problems, even with moderate big sizes (e.g., seven factories, 20 machines, and 20 jobs). The critical role that the number of jobs plays in the complexity of the problem is identified and discussed. In conclusion, this paper demonstrates the great benefits of scheduling problems that stem from using state-of-the-art constraint programming solvers and models that capture the problem tightly. Full article

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a “decomposition” style (in the abstract of the well-known “Transformer” article “Attention is All You Need”, they use “attention” instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or “gathered” for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two “where to go” strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation. Full article

The permutation flow shop scheduling problem (PFSP) stands as a classic conundrum within the realm of combinatorial optimization, serving as a prevalent organizational structure in authentic production settings. Given that conventional scheduling approaches fall short of effectively addressing the intricate and ever-shifting production landscape of PFSP, this study proposes an end-to-end deep reinforcement learning methodology with the objective of minimizing the maximum completion time. To tackle PFSP, we initially model it as a Markov decision process, delineating pertinent states, actions, and reward functions. A notably innovative facet of our approach involves leveraging disjunctive graphs to represent PFSP state information. To glean the intrinsic topological data embedded within the disjunctive graph’s underpinning, we architect a policy network based on a graph isomorphism network, subsequently trained through proximal policy optimization. Our devised methodology is compared with six baseline methods on randomly generated instances and the Taillard benchmark, respectively. The experimental results unequivocally underscore the superiority of our proposed approach in terms of $makespan$ and computation time. Notably, the $makespan$ can save up to 183.2 h in randomly generated instances and 188.4 h in the Taillard benchmark. The calculation time can be reduced by up to 18.70 s for randomly generated instances and up to 18.16 s for the Taillard benchmark. Full article