Search Results (35)

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

Flow-shop scheduling problems are classic examples of multi-resource and multi-operation scheduling problems where the objective is to minimize the makespan. Because of the high complexity and intractability of the problem, apart from some exceptional cases, there are no explicit algorithms for finding the optimal permutation in multi-machine environments. Therefore, different heuristic approaches, including evolutionary and memetic algorithms, are used to obtain the solution—or at least, a close enough approximation of the optimum. This paper proposes a novel approach: a novel combination of two rather efficient such heuristics, the discrete bacterial memetic evolutionary algorithm (DBMEA) proposed earlier by our group, and a conveniently modified heuristics, the Monte Carlo tree method. By their nested combination a new algorithm was obtained: the hybrid discrete bacterial memetic evolutionary algorithm (HDBMEA), which was extensively tested on the Taillard benchmark data set. Our results have been compared against all important other approaches published in the literature, and we found that this novel compound method produces good results overall and, in some cases, even better approximations of the optimum than any of the so far proposed solutions. Full article

Estimation of distribution algorithms (EDAs) is a subset of evolutionary algorithms widely used in various optimization problems, known for their favorable results. Each generation of EDAs builds a probabilistic model to represent the most promising individuals, and the next generation is created by sampling from this model. The primary challenge in designing such algorithms lies in effectively constructing the probabilistic model. The mutual exclusivity constraint imposes an additional challenge for EDAs to approach permutation-based problems. In this study, we propose a new EDA called Position-Guided Sampling Estimation of Distribution Algorithm (PGS-EDA) specifically designed for permutation-based problems. Unlike conventional approaches, our algorithm focuses on the positions rather than the elements during the sampling phase. We evaluate the performance of our algorithm on the Permutation Flow-shop Scheduling Problem (PFSP). The experiments conducted on various sizes of Taillard instances provide evidence of the effectiveness of our algorithm in addressing the PFSP, particularly for small and medium-sized problems. The comparison results with other EDAs designed to handle permutation problems demonstrate that our PSG-EDA algorithm consistently achieves the lowest Average Relative Percentage Deviation (ARPD) values in 19 out of the 30 instances of sizes 20 and 50 used in the study. These findings validate the superior performance of our algorithm in terms of minimizing the makespan criterion of the PFSP. Full article

Permutation flow-shop scheduling is the strategy that ensures the processing of jobs on each subsequent machine in the exact same order while optimizing an objective, which generally is the minimization of makespan. Because of its NP-Complete nature, a substantial portion of the literature has mainly focused on computational efficiency and the development of different AI-based hybrid techniques. Particle Swarm Optimization (PSO) has also been frequently used for this purpose in the recent past. Following the trend and to further explore the optimizing capabilities of PSO, first, a standard PSO was developed during this research, then the same PSO was hybridized with Variable Neighborhood Search (PSO-VNS) and later on with Simulated Annealing (PSO-VNS-SA) to handle Permutation Flow-Shop Scheduling Problems (PFSP). The effect of hybridization was validated through an internal comparison based on the results of 120 different instances devised by Taillard with variable problem sizes. Moreover, further comparison with other reported hybrid metaheuristics has proved that the hybrid PSO (HPSO) developed during this research performed exceedingly well. A smaller value of 0.48 of ARPD (Average Relative Performance Difference) for the algorithm is evidence of its robust nature and significantly improved performance in optimizing the makespan as compared to other algorithms. Full article

This feasibility study utilized regression models to predict makespan robustness in dynamic production processes with uncertain processing times. Previous methods for robustness determination were computationally intensive (Monte Carlo experiments) or inaccurate (surrogate measures). However, calculating robustness efficiently is crucial for field-synchronous scheduling techniques. Regression models with multiple input features considering uncertain processing times on the critical path outperform traditional surrogate measures. Well-trained regression models internalize the behavior of a dynamic simulation and can quickly predict accurate robustness (correlation: $r>0.98$). The proposed method was successfully applied to a permutation flow shop scheduling problem, balancing makespan and robustness. Integrating regression models into a metaheuristic model, schedules could be generated that have a similar quality to using Monte Carlo experiments. These results suggest that employing machine learning techniques for robustness prediction could be a promising and efficient alternative to traditional approaches. This work is an addition to our previous extensive study about creating robust stable schedules based on deep reinforcement learning and is part of the applied research project, Predictive Scheduling. Full article

Single-objective to multi-objective/many-objective optimization (SMO) is a new paradigm in the evolutionary transfer optimization (ETO), since there are only “1 + 4” pioneering works on SMOs so far, that is, “1” is continuous and is firstly performed by Professors L. Feng and H.D. Wang, and “4” are firstly proposed by our group for discrete cases. As a new computational paradigm, theoretical insights into SMOs are relatively rare now. Therefore, we present a proposal on the fine brushworks of SMOs for theoretical advances here, which is based on a case study of a permutation flow shop scheduling problem (PFSP) in manufacturing systems via lenses of building blocks, transferring gaps, auxiliary task and asynchronous rhythms. The empirical studies on well-studied benchmarks enrich the rough strokes of SMOs and guide future designs and practices in ETO based manufacturing scheduling, and even ETO based evolutionary processes for engineering optimization in other cases. Full article

The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software’s applicability. Full article