A hybrid metaheuristic solution approach for the cobot assignment and job shop scheduling problem

Motivated by recent developments to deploy collaborative robots in industrial production systems, we investigate the assembly line balancing problem with collaborative robots. The problem is characterized by the possibility that human and robots can simultaneously execute tasks at the same workpiece either in parallel or in collaboration. For this novel problem type, we present a mixed-integer programming formulation for balancing and scheduling of assembly lines with collaborative robots. The model decides on both the assignment of collaborative robots to stations and the distribution of workload to workers and robotic partners, aiming to minimize the cycle time. Given the high problem complexity, a hybrid genetic algorithm is presented as a solution procedure. Based on extensive computational experiments, the algorithm reveals promising results in both computational time and solution quality. Moreover, the results indicate that substantial productivity gains can be utilized by deploying collaborative robots in manual assembly lines. This holds especially true for a high average number of robots and tasks to be assigned to every station as well as a high portion of tasks that can be executed by the robot and in collaboration.

Motivated by recent developments to deploy collaborative robots in industrial production systems, we investigate the assembly line balancing problem with collaborative robots. The problem is characterized by the possibility that human and robots can simultaneously execute tasks at the same workpiece either in parallel or in collaboration. For this novel problem type, we present a mixed-integer programming formulation for balancing and scheduling of assembly lines with collaborative robots. The model decides on both the assignment of collaborative robots to stations and the distribution of workload to workers and robotic partners, aiming to minimize the cycle time. Given the high problem complexity, a hybrid genetic algorithm is presented as a solution procedure. Based on extensive computational experiments, the algorithm reveals promising results in both computational time and solution quality. Moreover, the results indicate that substantial productivity gains can be utilized by deploying collaborative robots in manual assembly lines. This holds especially true for a high average number of robots and tasks to be assigned to every station as well as a high portion of tasks that can be executed by the robot and in collaboration.

Collaborative robots are progressively employed to support human workers in assembly tasks or independently assigned to one station to complete assembly tasks in U-shaped assembly lines. This study develops two exact methods, based on constraint programming (CP) model and Combinatorial Benders’ decomposition algorithm (CBDA), to tackle the U-shaped assembly line balancing problem with collaborative robots. The CBDA is based on distinct decomposition strategies that address the master problem and the subproblem, formulated by a mixed integer linear programming (MILP) model and a CP model, which is designed to obtain a real objective value and generate cuts that refine the master problem. Additionally, MILP-based and CP-based local search techniques are proposed to improve the algorithm's performance. The computational study demonstrates that both the proposed methods, namely CP and CBDA, outperform the current state-of-the-art methods (the MILP model and simulated annealing algorithm). Furthermore, the CP outperforms the CBDA in terms of the number of optimal solutions, achieving the optimal solutions for 574 out of 1500 test instances, and might be regarded as the new state-of-the-art methodology.

As collaborative robots begin to appear on factory floors, there is a need to consider how these robots can best help their human partners. In this paper, we propose an optimization framework that generates task assignments and schedules for a human-robot team with the goal of improving both time and ergonomics and demonstrate its use in six real-world manufacturing processes that are currently performed manually. Using the strain index method to quantify human physical stress, we create a set of solutions with assigned priorities on each goal. The resulting schedules provide engineers with insight into selecting the appropriate level of compromise and integrating the robot in a way that best fits the needs of an individual process.

In this study, the U-type assembly line balancing problem (UALBP) with assignment restrictions (AR-UALBP) is considered. Linked and incompatible distance and station restrictions are taken into account. New mathematical programming (MP) and constraint programming (CP) models are proposed. The objective function of the models is minimizing the cycle time for a given number of workstations. In addition to this objective, line efficiency and CPU time are also considered as other performance measurements. Numerical experiments on some problems from the literature are performed to evaluate the effectiveness of the proposed models. The results are compared with the results of the CP model of the straight ALBP with assignment restrictions and also the results from MP and CP models are compared with each other. The numerical results indicate that the proposed CP and MP models are more effective in obtaining better and optimal results when solving the AR-UALBP.

A variable neighborhood search heuristic algorithm for production routing problems

Job shop scheduling problem (JSSP) has drawn a lot of attention as it is one of the vital combinational optimization problems in manufacturing systems. In this paper, a differential-based harmony search (DHS) algorithm with variable neighborhood search (VNS) is proposed for solving JSSP with the objective of minimized makespan. Since the standard harmony search algorithm is constructed for global optimization problems, the smallest position value is introduced to map a harmony vector to an active schedule. The active decoding scheme is employed to improve the search efficiency of DHS. In the pitch-adjustment process, the best individual of the current harmony memory is employed to accelerate the convergence speed. After the pitch-adjustment process, the differential-based enhanced mechanism is designed to maintain the diversity of the population. The modified VNS, which is based on the blocks on the critical path, is embedded into DHS to search for a better solution around the current harmony vector. Besides, the runtime of DHS is analyzed according to the level-based theorem. Compared with various HS-based algorithms and other state-of-the-art algorithms on a set of typical benchmark instances, the DHS is superior to the compared algorithms in terms of solution quality, convergence speed, and stability. The DHS lays a solid foundation for solving optimization problems of expert and intelligent systems.

Large Language Models (LLMs) have emerged as a promising technology for solving combinatorial optimization problems. However, their direct application to scheduling problems remains limited due to the inherent complexity of these problems. This paper proposes an LLMs-based neighborhood search method that leverages LLMs to tackle the job shop scheduling problem (JSP) and its variants. The main contributions of this work are threefold. First, we introduce a novel LLMs-guided neighborhood evaluation strategy that guides local search by dynamically adjusting operation weights. Second, we develop a verification evolution (VeEvo) framework to mitigate the hallucination effects of LLMs, enabling the generation of high-quality heuristics for weight updates. Third, we integrate this framework with the weighted neighborhood evaluation strategy to effectively guide the search towards promising regions. Extensive experiments are conducted on 349 benchmark instances across three classical scheduling problems. The results demonstrate that our algorithm significantly outperforms existing state-of-the-art methods. For JSP, our algorithm reduces the average optimality gap from 10.46% to 1.35% on Taillard's instances compared to reinforced adaptive staircase curriculum learning. For flexible JSP (FJSP), it reduces the gap from 13.24% to 0.05% on Brandimarte's instances compared to deep reinforcement learning methods. Furthermore, for FJSP with sequence dependent setup time, our algorithm updates 9 upper bounds for benchmark instances.

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP.

Production scheduling problems are typically combinational optimization problems named bases on the processing routes of jobs on different machines. In this paper, the flexible job shop scheduling problem aimed to minimize the maximum completion times of operations or makespan is considered. To solve such an NP-hard problem, variable neighborhood search (VNS) based on genetic algorithm is proposed to enhance the search ability and to balance the intensification and diversification. VNS algorithm has shown excellent capability of local search with systematic neighborhood search structures. External library is improved to save the optimal or near optimal solutions during the iterative process, and when the objective value of the optimal solutions are the same, the scheduling Gantt charts need to be considered. To evaluate the performance of our proposed algorithm, benchmark instances in different sizes are optimized. Consequently, the computational results and comparisons illustrate that the proposed algorithm is efficiency and effectiveness.

In the just-in-time job-shop scheduling (JIT–JSS) problem every operation has a distinct due-date, and earliness and tardiness penalties. Any deviation from the due-date incurs penalties. The objective of JIT–JSS is to obtain a schedule, i.e., the completion time for performing the operations, with the smallest total (weighted) earliness and tardiness penalties. This paper presents a matheuristic algorithm for the JIT–JSS problem, which operates by decomposing the problem into smaller sub-problems, optimizing the sub-problems and delivering the optimal schedule for the problem. By solving a set of 72 benchmark instances ranging from 10 to 20 jobs and 20 to 200 operations we show that the proposed algorithm outperforms the state-of-the-art methods and the solver CPLEX, and obtains new best solutions for nearly 56% of the instances, including for 79% of the large instances with 20 jobs.

To tackle the balancing and sequencing problems of flexible mixed model assembly lines with alternative precedence relations, If–then rules and AND/OR graphs are adopted as modelling tools to replace precedence graphs that have limitations in representing alternative precedence relations. Mixed integer linear programming (MILP) and constraint programming (CP) models are established respectively. Moreover, an iterative decomposition method is developed to deal with large-sized problems. Computational experiments on different scales are carried out to test those methods. The computational results reveal that the performance of CP is better than MILP especially when more OR relations exist. And the iterative decomposition method outperforms MILP and CP in terms of solution quality and time.

The Job shop scheduling problem with generic time lags is a generalization of the job shop problem. It is defined as a job shop problem with minimal and maximal delays between starting times of operations of different jobs. In this paper, we propose a combination of genetic algorithm and tabu search to solve Job Shop Problem with Generic Time Lags. Benchmark instances are used to investigate the performance of the proposed metaheuristic. The results show that the proposed combination of metaheuristics improves the efficiency.

Ant colony optimization combined with taboo search for the job shop scheduling problem

The Flexible Job Shop scheduling Problem (FJSP) is a generalization of the classical Job Shop scheduling Problem (JSP) allowing to process operations on one machine out of a set of alternative machines. The FJSP is an NP-hard problem consisting of two sub-problems, which are the machine assignment and the operation scheduling problems. In this paper, we propose how to solve the FJSP by metaheuristics based on clustering in a holonic multiagent model. Firstly, a Neighborhood-based Genetic Algorithm (NGA) is applied by a scheduler agent for a global exploration of the search space. Secondly, a local search technique is used by a set of cluster agents to guide the research in promising regions of the search space and to improve the quality of the NGA final population. To evaluate our approach, numerical tests are made based on three sets of well known benchmark instances from the literature of the FJSP, which are Kacem, Brandimarte, Hurink. The experimental results show the efficiency of our approach in comparison to other approaches.