Job Shop Scheduling Problem Instances Research Articles

A generic enhanced search framework based on genetic algorithm: Case study on job shop scheduling problem

Optimal allocation of production resources is an urgent need for the development of industrialization. Reasonable production scheduling algorithm and excellent scheduling scheme can efficiently plan production resources, reduce production costs and shorten order completion time. Genetic algorithm has become one of the most popular algorithms for solving job shop scheduling problem because of its simplicity, versatility and good robustness. However, the genetic algorithm for solving NP-hard problems such as job shop scheduling has the problem of falling into local optimum, which leads to the decrease of solution accuracy. This study focused on the problem and proposed a generic enhanced search framework based on genetic algorithm, which named niche adaptive genetic algorithm. The niche selection mechanism and adaptive genetic operators were used to enrich the diversity of population, balance the genetic probability and enhance the global search performance of the algorithm. The working mechanism of this algorithm is analysed by testing data, and the proposed algorithm was tested on job-shop scheduling problem instances. The results show that the performance of the proposed method is 0.79 percentage points higher than that of the standard genetic algorithm, and it has the ability to search for the global optimum.

Application of quantum approximate optimization algorithm to job shop scheduling problem

The Job Shop Scheduling Problem (JSSP) has always been considered as one of the most complex and industry essential scheduling problems. Optimizing the makespan of a given schedule generally involves using dedicated algorithms, local search strategies, or metaheuristics. These approaches, however, heavily rely on classical computational power, which is bounded by the physical limits of microcontrollers and power issues. Inspired by the promising results achieved for Quantum Annealing (QA) based approaches to solve JSSP instances, we propose a new approach that uses gate-model quantum architecture as an alternative to QA. We find that we can make use of the time-indexed JSSP instance representation to build a cost Hamiltonian, which can be embedded into Quantum Approximate Optimization Algorithm (QAOA) to find an optimal solution to a basic JSSP instance. We demonstrate the use of QAOA to solve the JSSP, and we evaluate its efficiency and accuracy for this problem from experimental results, as there is an increased urgency to demonstrate the applicability of quantum optimization algorithms. We also find that optimal variational parameters form patterns that can facilitate computation in bigger quantum circuits. Additionally, we compare the obtained noiseless simulation results of gate-model quantum circuits demonstrating the relationship between two evaluation criteria - makespan and energy. Finally, we analyze and present the overall performance of our approach with the increasing deadline and simulated depth of QAOA circuits.

Problem Decomposition and Multi-shot ASP Solving for Job-shop Scheduling

AbstractScheduling methods are important for effective production and logistics management, where tasks need to be allocated and performed with limited resources. In particular, the Job-shop Scheduling Problem (JSP) is a well known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. Given that already moderately sized JSP instances can be highly combinatorial, and neither optimal schedules nor the runtime to termination of complete optimization methods is known, efficient approaches to approximate good-quality schedules are of interest. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations so that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Regarding the feasibility and quality of solutions, problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.

A graph neural networks-based deep Q-learning approach for job shop scheduling problems in traffic management

A key problem in traffic management is to schedule the movements of vehicles to reduce unnecessary costs; this issue has arisen in applications such as train schedule management, air-traffic control, and urban traffic management. This problem can be modeled as a job shop scheduling problem (JSSP), which is an important combinatorial optimization problem that is widely applied in real-world scenarios. However, designing good approximation algorithms for JSSPs often requires significant specialized knowledge and trial-and-error. In this paper, we present an end-to-end framework for solving JSSPs by using graph neural networks (GNNs) and deep Q-Learning. This single-policy model is suitable for solving instances that have similar sizes and is trained only by observing reward signals and following feasible rules. The trained model behaves like a constructive heuristic algorithm that incrementally constructs a solution, and each action is determined by the output of a GNN, which captures the current state of the partial solution. We test the proposed approach on JSSP instances with multiple sizes and demonstrate its competitive performance in all cases (after training). Our proposed framework also has the potential to be applied to other JSS subproblems.

Switching strategy-based hybrid evolutionary algorithms for job shop scheduling problems

Since production efficiency and costs are directly affected by the ways in which jobs are scheduled, scholars have advanced a number of meta-heuristic algorithms to solve the job shop scheduling problem (JSSP). Although this JSSP is widely accepted as a computationally intractable NP-hard problem in combinatorial optimization, its solution is essential in manufacturing. This study proposes performance-driven meta-heuristic switching approaches that utilize the capabilities of multi-operator differential evolution (MODE) and particle swarm optimization (PSO) in a single algorithmic framework. The performance-driven switching mechanism is introduced to switch the population from an under-performing algorithm to other possibilities. A mixed selection strategy is employed to ensure the diversity and quality of the initial population, whereas a diversity check mechanism maintains population diversity over the generations. Moreover, a Tabu search (TS) inspired local search technique is implemented to enhance the proposed algorithm’s exploitation capability, avoiding being trapped in the local optima. Finally, this study presents two mixed population structure-based hybrid evolutionary algorithms (HEAs), such as a predictive sequence HEA (sHEA) and a random sequence HEA (rHEA), and one bi-population inspired HEA, called bHEA. The comparative impacts of these varied population structure-based approaches are assessed by solving 5 categories of the standard JSSP instances (i.e., FT, LA, ORB, ABZ and TA). The performance of these hybridized approaches (i.e., sHEA, rHEA and bHEA) is compared and contrasted with its constituent algorithms (MODE, PSO and TS) to validate the hybridization’s effectiveness. The statistical analysis shows that sHEA ranked first with mean value 1.84 compared to rHEA (1.96) and bHEA (2.21). Moreover, the proposed sHEA is compared with 26 existing algorithms and ranked first with a mean value 5.09 compared to the near-best algorithms. Thus, the simulation results and statistical analysis prove the supremacy of the sHEA.

Implementation of the Mushroom Picking Framework for Solving Flexible Job Shop Scheduling Problems in Parallel

The paper proposes a new version of the Mushroom Picking Framework (MPF) for solving the Flexible Job Shop Scheduling problem instances. The idea is to use a set of particles, representing a set of solutions, and a special scheme for a group of solution improving agents acting in parallel. The initial set of particles is partly generated by a heuristic procedure. The approach has been validated in the computational experiment. The proposed MPF implementation produces satisfactory quality solutions in a competitive time, especially for the tasks of bigger sizes.

Industrial-size job shop scheduling with constraint programming

The job shop scheduling problem is one of the most studied optimization problems to this day and it becomes more and more important in the light of the fourth industrial revolution (Industry 4.0) that aims at fully automated production processes. For a long time exact methods like constraint programming had problems to solve real large-scale problem instances and methods of choice were to be found in the area of (meta-) heuristics. However, developments during the last decade improved the performance of state-of-the-art constraint solvers dramatically, to the point that they can be applied also on large-scale instances. The presented work’s main target is to elaborate the performance of state-of-the-art constraint solvers with respect to industrial-size job shop scheduling problem instances. To this end, we analyze and compare the performance of two cutting-edge constraint solvers: OR-Tools, an open-source solver developed by Google and recurrent winner of the MiniZinc Challenge, and CP Optimizer, a proprietary constraint solver from IBM targeted at industrial optimization problems. In order to reflect real-world industrial scenarios with heavy workloads like found in the semi-conductor domain, we use novel benchmarks that comprise up to one million operations to be scheduled on up to one thousand machines. The comparison is based on the best makespan (i.e. completion time) achieved and the time required to solve the problem instances. We test the solvers on single-core and quad-core configurations.

Adaptive Population NSGA-III with Dual Control Strategy for Flexible Job Shop Scheduling Problem with the Consideration of Energy Consumption and Weight

The flexible job shop scheduling problem has always been the focus of research in the manufacturing field. However, most of the previous studies focused more on efficiency and ignored energy consumption. Energy, especially non-renewable energy, is an essential factor affecting the sustainable development of a country. To this end, this paper designs a flexible job shop scheduling problem model with energy consideration more in line with the production field. Except for the processing stage, the energy consumption of the transport, set up, unload, and idle stage are also included in our model. The weight property of jobs is also considered in our model. The heavier the job, the more energy it consumes during the transport, set up, and unload stage. Meanwhile, this paper invents an adaptive population non-dominated sorting genetic algorithm III (APNSGA-III) that combines the dual control strategy with the non-dominated sorting genetic algorithm III (NSGA-III) to solve our flexible job shop scheduling problem model. Four flexible job shop scheduling problem instances are formulated to examine the performance of our algorithm. The results achieved by the APNSGA-III method are compared with five classic multi-objective optimization algorithms. The results show that our proposed algorithm is efficient and powerful when dealing with the multi-objective flexible job shop scheduling problem model that includes energy consumption.

A Job-Shop Scheduling Problem with Bidirectional Circular Precedence Constraints

This paper introduces a job-shop scheduling problem (JSP) with bidirectional circular precedence constraints, called BCJSP. In the problem, each job can be started from any operation and continued by its remaining operations in a circular precedence-relation chain via either a clockwise or counterclockwise direction. To solve BCJSP, this paper proposes a multilevel metaheuristic consisting of top-, middle-, and bottom-level algorithms. The top- and middle-level algorithms are population-based metaheuristics, while the bottom-level algorithm is a local search algorithm. The top-level algorithm basically controls a start operation and an operation-precedence-relation direction of each job, so that BCJSP becomes a JSP instance that is a subproblem of BCJSP. Moreover, the top-level algorithm can also be used to control input parameters of the middle-level algorithm, as an optional extra function. The middle-level algorithm controls input parameters of the bottom-level algorithm, and the bottom-level algorithm then solves the BCJSP’s subproblem. The middle-level algorithm evolves the bottom-level algorithm’s parameter values by using feedback from the bottom-level algorithm. Likewise, the top-level algorithm evolves the start operations, the operation-precedence-relation directions, and the middle-level algorithm’s parameter values by using feedback from the middle-level algorithm. Performance of two variants of the multilevel metaheuristic (i.e., with and without the mentioned extra function) was evaluated on BCJSP instances modified from well-known JSP instances. The variant with the extra function performs significantly better in number than the other. The existing JSP-solving algorithms can also solve BCJSP; however, their results on BCJSP are clearly worse than those of the two variants of the multilevel metaheuristic.

A parallel memetic algorithm with explicit management of diversity for the job shop scheduling problem

The job shop scheduling problem (JSSP) is a very popular NP-hard optimization problem that involves assigning jobs to resources. Recent advances in the field of memetic algorithms show that explicitly managing the diversity of the population by taking into account the stopping criterion with the aim of dynamically adapting the balance between exploration and exploitation is key to their success. This is especially the case in long-term executions. However, this design principle has not yet been applied to the JSSP. This paper proposes a novel memetic algorithm that integrates some of the most advanced components devised in the literature for the JSSP with a replacement strategy that explicitly manages the diversity by considering a novel dissimilarity measure. To properly address large instances, a parallel master-worker model is used. Experimental validation shows the important advances attained by our proposal when compared to two state-of-the-art optimizers. The advantages are clear in both sequential and parallel cases, with more impressive achievements appearing in the parallel case. The parallel proposal has yielded new best-known solutions in 30 well-known JSSP instances, matching the lower bound in two of them, meaning that at least two new optimal solutions have been discovered.

Tailoring Job Shop Scheduling Problem Instances Through Unified Particle Swarm Optimization

Problem instances are paramount when testing the performance of any learning algorithm. For this reason, it is customary to use widespread problems known as benchmark instances. Nonetheless, these are usually generated disregarding heuristics and their nature. For Job Shop Scheduling problem, researchers have created such instances based on random distributions. This idea may bias conclusions about the algorithm under test since a practitioner can only observe performance from a limited perspective, which may not even reflect real-life situations. However, addressing this issue implies tackling the instance generation problem while considering the nature of the solution approach. Hence, in this work, we propose an instance generator based on the Unified Particle Swarm Optimization algorithm, which can tailor instances to different goals. To validate our approach, we include instances generated to different heuristics and instances tailored to a variety of features. In the first case, we seek to favor or hinder one heuristic whereas doing the opposite for the remaining ones. In the second one, we explore instances with specific feature values. Our data reveal that the proposed approach fulfills the expectations and can effectively deal with different kinds of instances. We analyse the nature of the generated instances and their insights, which can be used to further the study about heuristics and problem features.

Scatter search algorithm for the multiprocessor task job-shop scheduling problem

Abstract In this paper, we address the Multi-processor Task Job-shop Scheduling Problem (MTJSP) which extends the classical Job-shop Scheduling Problem (JSP): Each Job consists of a number of operations and each operation requires a set of machines to work simultaneously instead of a single one. Under the resource constraints, our goal is to minimize the makespan. Practically, MTJSP is usually found in the field of structure product manufacturing, grid computing as well as other fields with multi-step and multi-processor requirement. The problem optimization model is constructed using disjunctive formulation and solutions are represented as specific permutations for feasibility. Due to the NP-hardness of the problem, a Scatter Search (SS) based on the solution representation is developed which includes a new update scheme for the reference set to maintain diversification and an improvement method with a local search and a simulated annealing search to get better solutions. To evaluate the performance, we apply the SS procedure to both JSP benchmark instances and MTJSP instances, and the results are reported. The numerical results show that the SS has a very good performance on MTJSP instances as well as JSP instances.

Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times

In this paper, the job shop scheduling problem (JSP) with a makespan minimization criterion is investigated. Various approximate algorithms exist that can solve moderate JSP instances within a reasonable time limit. However, only a few exact algorithms are known in the literature. We have developed an exact algorithm by means of a bounded dynamic programming (BDP) approach. This approach combines elements of a dynamic programming with elements of a branch and bound method. In addition, a generalization is investigated: the JSP with sequence dependent setup times (SDST-JSP). The BDP algorithm is adapted for this problem. To the best of our knowledge, the dynamic programming approach has never been applied to the SDST-JSP before. The BDP algorithm can directly be used as a heuristic. Computational results show that the proposed algorithm can solve benchmark instances up to 20 jobs and 15 machines for the JSP. For the SDST-JSP, the proposed algorithm outperforms all the state-of-the-art exact algorithms and the best-known lower bounds are improved for 5 benchmark instances.

A tabu search/path relinking algorithm to solve the job shop scheduling problem

We present an algorithm that incorporates a tabu search procedure into the framework of path relinking to generate solutions to the job shop scheduling problem (JSP). This tabu search/path relinking (TS/PR) algorithm comprises several distinguishing features, such as a specific relinking procedure to effectively construct a path linking the initiating solution and the guiding solution, and a reference solution determination mechanism based on two kinds of improvement methods. We evaluate the performance of TS/PR on almost all of the benchmark JSP instances available in the literature. The test results show that TS/PR obtains competitive results compared with state-of-the-art algorithms for JSP in the literature, demonstrating its efficacy in terms of both solution quality and computational efficiency. In particular, TS/PR is able to improve the upper bounds for 49 out of the 205 tested instances and it solves a challenging instance that has remained unsolved for over 20years.

A Multi - Population Based Frog - Memetic Algorithm for Job Shop Scheduling Problem

The Job Shop Scheduling Problem (JSSP) is a well known practical planning problem in the manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this paper, we develop a three-stage hybrid approach called JSFMA to solve the JSSP. In JSFMA, considering a method similar to Shuffled Frog Leaping algorithm we divide the population in several sub populations and then solve the problem using a Memetic algorithm. The proposed approach have been compared with other algorithms for the Job Shop Scheduling and evaluated with satisfactory results on a set of the JSSP instances derived from classical Job Shop Scheduling benchmarks. We have solved 20 benchmark problems from Lawrence’s datasets and compared the results obtained with the results of the algorithms established in the literature. The experimental results show that JSFMA could gain the best known makespan in 17 out of 20 problems.

A hybrid Differential Evolution—Tabu Search algorithm for the solution of Job-Shop Scheduling Problems

The Job-Shop Scheduling Problem (JSSP) has drawn considerable interest during the last decades, mainly because of its combinatorial characteristics, which make it very difficult to solve. The good performances attained by local search procedures, and especially Nowicki and Smutnicki's i-TSAB algorithm, encouraged researchers to combine such local search engines with global methods. Differential Evolution (DE) is an Evolutionary Algorithm that has been found to be particularly efficient for continuous optimization, but which does not usually perform well when applied to permutation problems. We introduce in this paper the idea of hybridizing DE with Tabu Search (TS) in order to solve the JSSP. A competitive neighborhood is included within the TS with the aim of determining if DE is able to replace the re-start features that constitute the main strengths of i-TSAB (i.e., a long-term memory and a path-relinking procedure). The computational experiments reported for more than 100 JSSP instances show that the proposed hybrid DE–TS algorithm is competitive with respect to other state-of-the-art techniques, although, there is still room for improvement if the adequacy between the solution representation modes within DE and TS is properly stressed.

Pareto archived simulated annealing for job shop scheduling with multiple objectives

In this paper, the job shop scheduling problem is studied with the objectives of minimizing the makespan and the mean flow time of jobs. The simultaneous consideration of these objectives is the multi-objective optimization problem under study. A metaheuristic procedure based on the simulated annealing algorithm called Pareto archived simulated annealing (PASA) is proposed to discover non-dominated solution sets for the job shop scheduling problems. The seed solution is generated randomly. A new perturbation mechanism called segment-random insertion (SRI) scheme is used to generate a set of neighbourhood solutions to the current solution. The PASA searches for the non-dominated set of solutions based on the Pareto dominance or through the implementation of a simple probability function. The performance of the proposed algorithm is evaluated by solving benchmark job shop scheduling problem instances provided by the OR-library. The results obtained are evaluated in terms of the number of non-dominated schedules generated by the algorithm and the proximity of the obtained non-dominated front to the Pareto front.