Multi-objective Job Shop Scheduling Problem Research Articles

A Pareto archive floating search procedure for solving multi-objective flexible job shop scheduling problem

Flexible job shop scheduling problem is a key factor of using efficiently in production systems. This paper attempts to simultaneously optimize three objectives including minimization of the make span, total workload and maximum workload of jobs. Since the multi objective flexible job shop scheduling problem is strongly NP-Hard, an integrated heuristic approach has been used to solve it. The proposed approach was based on a floating search procedure that has used some heuristic algorithms. Within floating search procedure utilize local heuristic algorithms; it makes the considered problem into two sections including assigning and sequencing sub problem. First of all search is done upon assignment space achieving an acceptable solution and then search would continue on sequencing space based on a heuristic algorithm. This paper has used a multi-objective approach for producing Pareto solution. Thus proposed approach was adapted on NSGA II algorithm and evaluated Pareto-archives. The elements and parameters of the proposed algorithms were adjusted upon preliminary experiments. Finally, computational results were used to analyze efficiency of the proposed algorithm and this results showed that the proposed algorithm capable to produce efficient solutions.

Self-evolution Algorithm with Multi-objective for Scheduling a Job-shop-like Knowledgeable Manufacturing Cell

It is difficult to find the global optimal solution for the multi-objective job-shop scheduling problem and the solutions obtained usually belong to the Pareto optimal ones. A multi-objective scheduling optimization model is given for the Job-shop-like knowledgeable manufacturing cell and the relationship between the multi objectives is analyzed. The properties of key arcs of tasks are presented through the analysis of its disjunctive graph and the conclusion is obtained that it is helpless to improve the function value by changing the direction of the middle key arc of job. A simplified neighborhood is proposed based on the conclusion which can reduce greatly the number of feasible solutions to be searched. A self-evolution algorithm for multi-objective scheduling problem is proposed based on the properties of the simplified neighborhood by the use of adaptive heuristic critic method whose associate search module can find the best action for the concurrent solution to obtain a better solution by learning and training, and such ability of the module will be improved continuously with the training increasing. The numerical simulation results show that the algorithm proposed has the excellent ability to search the optimal solution for the proposed scheduling problem and possesses obvious evolution capacities through learning.

An improved particle swarm optimization with decline disturbance index (DDPSO) for multi-objective job-shop scheduling problem

As same with many evolutional algorithms, performance of simple PSO depends on its parameters, and it often suffers the problem of being trapped in local optima so as to cause premature convergence. In this paper, an improved particle swarm optimization with decline disturbance index (DDPSO), is proposed to improve the ability of particles to explore the global and local optimization solutions, and to reduce the probability of being trapped into the local optima. The correctness of the modification, which incorporated a decline disturbance index, was proved. The key question why the proposed method can reduce the probability of being trapped in local optima was answered. The modification improves the ability of particles to explore the global and local optimization solutions, and reduces the probability of being trapped into the local optima. Theoretical analysis, which is based on stochastic processes, proves that the trajectory of particle is a Markov processes and DDPSO algorithm converges to the global optimal solution with mean square merit. After the exploration based on DDPSO, neighborhood search strategy is used in a local search and an adaptive meta-Lamarckian strategy is employed to dynamically decide which neighborhood should be selected to stress exploitation in each generation. The multi-objective combination problems with DDPSO for finding the pareto front was presented under certain performance index. Simulation results and comparisons with typical algorithms show the effectiveness and robustness of the proposed DDPSO.

An improved intelligent water drops algorithm for solving multi-objective job shop scheduling

Multi-objective job shop scheduling (MOJSS) problems can be found in various application areas. The efficient solution of MOJSS problems has received continuous attention. In this research, a new meta-heuristic algorithm, namely the Intelligent Water Drops (IWD) algorithm is customized for solving the MOJSS problem. The optimization objective of MOJSS in this research is to find the best compromising solutions (Pareto non-dominance set) considering multiple criteria, namely makespan, tardiness and mean flow time of the schedules. MOJSS-IWD, which is a modified version of the original IWD algorithm, is proposed to solve the MOJSS problem. A scoring function which gives each schedule a score based on its multiple criteria values is embedded into the MOJSS-IWD’s local search process. Experimental evaluation shows that the customized IWD algorithm can identify the Pareto non-dominance schedules efficiently.

Fuzzy optimisation of multi-objective job shop scheduling based on inventory information

Job shop scheduling problems are one of the oldest combinatorial optimisation problems being studied. In this paper, fuzzy processing times of operations and fuzzy due dates of jobs are considered to incorporate fuzziness in the problem. Percentage of inventory consumption and profit earned form the orders are also considered in this fuzzy multi-objective job shop scheduling problem. Fuzzy inference system (FIS) is used to calculate the job weights based on the percentage of inventory consumption for a particular job and profit can be earned from the jobs. Average weighted tardiness, number of tardy jobs, total flow time and idle times of machines are considered as objectives which should be minimised. In this paper, genetic algorithm (GA) is used as a heuristic technique with specially encoded chromosomes that denotes the complete schedule of the jobs. A local search technique, simulated annealing (SA) is also used to compare the results obtained in two different methods. Different problem sizes has been tested and the fitness function values and computation times of the problems for each method is compared.

A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems

This paper presents a hybrid Pareto-based local search (PLS) algorithm for solving the multi-objective flexible job shop scheduling problem. Three minimisation objectives are considered simultaneously, i.e. the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine. In this study, several well-designed neighbouring approaches are proposed, which consider the problem characteristics and thus can hold fast convergence ability while keep the population with a certain level of quality and diversity. Moreover, a variable neighbourhood search (VNS) based self-adaptive strategy is embedded in the hybrid algorithm to utilise the neighbouring approaches efficiently. Then, an external Pareto archive is developed to record the non-dominated solutions found so far. In addition, a speed-up method is devised to update the Pareto archive set. Experimental results on several well-known benchmarks show the efficiency of the proposed hybrid algorithm. It is concluded that the PLS algorithm is superior to the very recent algorithms, in term of both search quality and computational efficiency.

A PSO-based procedure for a bi-level multi-objective TOC-based job-shop scheduling problem

This study presents an application of particle swarm optimisation (PSO) algorithm for a bi-level multi-objective job-shop scheduling problem. The bi-level decision-making requirement stems from the concept of theory of constraints. At the first level, the decision is made by concentrating on minimising idle time on the system bottleneck. The second-level decision is made to plan other machines while maintaining the maximum use of the bottleneck and gaining improvements in other performance measures. This paper proposed a PSO-based procedure for solving the bi-level programming problem. The proposed procedure simplifies the solution method by simultaneously providing solutions for the objective of both levels. In addition, during the schedule generation process, the job-shop case applied in this study also considers the machine set-up time, transfer lot size and product demands to make the model more realistic. The numerical examples are given to demonstrate how this approach works. The results from this procedure are compared with the solutions obtained by a commercial optimiser, the LINGO 10 software package. This proposed PSO is implemented in C# programming language in order to obtain the final solution within the short computational time.

Research of Multi-Objective Optimization Study for Job Shop Scheduling Problem Based on Grey Ant Colony Algorithm

In order to resolve Multi-objective job shop scheduling problem, an optimization method of many goals scheduling based on grey relation theory and ant colony algorithm is proposed. Firstly, this paper introduces the relevant mathematical theory. AHP and Grey relational analysis, and they are combined to solve the choice of pre-processing equipment under the multi-objective conditions. What's more, ant colony algorithm is discussed to solve problem of processing order for machine. The effectiveness of multi-objective algorithm for job shop scheduling problem is verified through applying example.

The Optimization of Flexible Job Shop Scheduling Problem Based on Improved Dual Coding Non-Dominated Sorting Genetic Algorithm

In order to optimize the multi-objective flexible job shop scheduling problem (FJSP) roundly, multi-objective mathematical model is established, including makespan, maximal workload, total workload and total tardiness. In this paper a dual coding method which takes operation arrangement and machine selection into account is employed, and designed new crossover and mutation methods, the infeasible solutions are avoided. In order to deal with the multi-objective optimization problem, a new non-dominated sorting method is introduced, which can get the Pareto optimal solutions quickly and correctly by dividing the whole population into three parts. Example shows that the algorithm is efficient.

The Improved Genetic Algorithm for Multi-Objective Flexible Job Shop Scheduling Problem

To solve the multi-objective flexible job shop scheduling problem, an improved non-dominated sorting genetic algorithm is proposed. Multi-objective mathematical model is established, four objectives, makespan, maximal workload, total workload and total tardiness are considered together. In this paper a dual coding method is employed, and infeasible solutions were avoided by new crossover and mutation methods. Pareto optimal set was taken to deal with multi-objective optimization problem, in order to reduce computational complexity, the non-dominated sorting method was improved. The niche technology is adopted to increase the diversity of solutions, and a new self adaptive mutation rate computing method is designed. The proposed algorithm is tested on some instances, and the computation results demonstrate the superiority of the algorithm.

Research on Optimization Algorithm for MFJSSP

A method combined ant colony algorithm with particle swarm optimization algorithm was designed for solving multi-objective flexible job shop scheduling problem in this paper. In the combined algorithm the start position of ants was marked by particles optimum position obtained by particle swarm optimization algorithm. Then the traditional ant colony algorithm was improved and was used to search the global optimum scheduling. The combined algorithm was validated by practical instances. The results obtained have shown the proposed approach is feasible and effective for the multi-objective flexible job shop scheduling problem.

A two-stage hybrid memetic algorithm for multiobjective job shop scheduling

In this paper we address multiobjective job shop scheduling problems. After several decades of research in scheduling problems, a variety of heuristics have been developed. The proposed algorithm is a hybrid of three frequently applied ones: the dispatching rule, the shifting bottleneck procedure, and the evolutionary algorithm. It is a two-stage algorithm, which integrates a rule-based memetic algorithm in the first stage and a re-optimization procedure of shifting bottleneck in the second. We conduct experiments using benchmark instances found in the literature to assess the performance of the proposed method. The experimental results show that the proposed method is effective and efficient for multiobjective scheduling problems.

Study on Job Shop Scheduling Optimization with Multi-Objective

A new multi-objective scheduling method based on the GA is proposed to the job-shop scheduling problem (JSP) constrained by machines, workers. Function objectives of the proposed method are to minimize the completion time, the maximum load of machines and the total expense of machines and workers. Firstly, the mathematical model is constructed. Then, on the basis of the mathematical model, the genetic algorithm (GA) based on Pareto is applied, and an optimal or suboptimal scheduling plan can be obtained. The optimal solutions are not unique due to the multi-objective of JSP. Finally, a scheduling example is employed to illustrate that the proposed method could solve multi-objective job shop scheduling problem effectively.

Improved precedence preservation crossover for multi-objective job shop scheduling problem

Over the last three decades, a great deal of research has been focused on solving the job-shop scheduling problem (JSSP). Researchers have emerged with a wide variety of approaches to solve this stubborn problem. Recently much effort has been concentrated on evolutionary techniques to search for the near-optimal solutions optimizing multiple criteria simultaneously. The choice of crossover operator is very important in the aspect of genetic algorithms (GA), and consequently a wide range of crossover operators have been proposed for JSSP. Most of them represent a solution by a chromosome containing the sequence of all the operations and decode the chromosome to a real schedule from the first gene to the last gene. However, these methods introduce high redundancy at the tail of the chromosome. In this paper, we address this problem in case of precedence preservation crossover (PPX) which is regarded as one of the better crossover operators and propose an improved version, termed as improved precedence preservation crossover (IPPX). Experimental results reveal that our proposed approach finds the near-optimal solutions by optimizing multiple criteria simultaneously with better results and also reduces the execution time significantly.

Solving a multi-objective job shop scheduling problem with sequence-dependent setup times by a Pareto archive PSO combined with genetic operators and VNS

In this paper, we present a combination of particle swarm optimization (PSO) and genetic operators for a multi-objective job shop scheduling problem that minimizes the mean weighted completion time and the sum of the weighted tardiness/earliness costs, simultaneously. At first, we propose a new integer linear programming for the given problem. Then, we redefine and modify PSO by introducing genetic operators, such as crossover and mutation operators, to update particles and improve particles by variable neighborhood search. Furthermore, we consider sequence-dependent setup times. We then design a Pareto archive PSO, where the global best position selection is combined with the crowding measure-based archive updating method. To prove the efficiency of our proposed PSO, a number of test problems are solved. Its reliability based on some comparison metrics is compared with a prominent multi-objective genetic algorithm (MOGA), namely non-dominated sorting genetic algorithm II (NSGA-II). The computational results show that the proposed PSO outperforms the above MOGA, especially for large-sized problems.

Study on Scheduling Optimization for Flexible Job Shop

A hybrid genetic algorithm based on Pareto was proposed and applied to flexible job shop scheduling problem (FJSP) with multi-objective, and the multi-objective FJSP optimization model was built, where the make-span and the machine utilization rate were concerned. The algorithm embeds Pareto ranking strategy into Pareto competition method. The operation-based encoding and an active scheduling decoding method are employed. In order to promote solution diversity, the niche technology and many kinds of crossover operations are used. Pareto filter saves the optimum individual occurring in the course of evolution, which avoids losing the optimum solutions. Three simulation experiments are carried out to illustrate that the proposed method could solve multi-objective job shop scheduling problem effectively.

Multi-objective decision making and search space for the evaluation of production process scheduling

Multi-objective decision making and search space for the evaluation of production process schedulingOver the years, various approaches have been proposed in order to solve the multi-objective job-shop scheduling problem - particularly a hard combinatorial optimization problem. The paper presents an evaluation of job shop scheduling problem under multiple objectives (mean flow time, max lateness, mean tardiness, mean weighted tardiness, mean earliness, mean weighted earliness, number of tardy tasks). The formulation of the scheduling problem has been presented as well as the evaluation schedules for various optimality criteria. The paper describes the basic mataheuristics used for optimization schedules and the approaches that use domination method, fuzzy method, and analytic hierarchy proccess (AHP) for comparing schedules in accordance with multiple objectives. The effectiveness of the algorithms has been tested on several examples and the results have been shown. New search space for evaluation and generation of schedules has been created. The three-dimensional space can be used for the analysis and control of the production processes.

A two-stage genetic algorithm for multi-objective job shop scheduling problems

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.

A multi-objective PSO for job-shop scheduling problems

Most previous research into the job-shop scheduling problem has concentrated on finding a single optimal solution (e.g., makespan), even though the actual requirement of most production systems requires multi-objective optimization. The aim of this paper is to construct a particle swarm optimization (PSO) for an elaborate multi-objective job-shop scheduling problem. The original PSO was used to solve continuous optimization problems. Due to the discrete solution spaces of scheduling optimization problems, the authors modified the particle position representation, particle movement, and particle velocity in this study. The modified PSO was used to solve various benchmark problems. Test results demonstrated that the modified PSO performed better in search quality and efficiency than traditional evolutionary heuristics.

Hybrid Evolutionary Approach for Multi-Objective Job-Shop Scheduling Problem

Over the years, various evolutionary approaches have been proposed in efforts to solve the Job-Shop Scheduling Problem (JSSP), a particularly hard combinatorial optimization problem. Unfortunately, most of these approaches are limited to a single objective only, and often fail to meet the requirements for real-world applications. Previously, we proposed several evolutionary approaches for multi-objective JSSP using the Jumping Genes Genetic Algorithm (JGGA) [1], [2]. Simulation results indicated that these approaches are capable of maintaining consistency and convergence of the trade-off, non-dominated solutions. In some rare cases, however, the solutions may be too diverse due to the additional diversity that occurs naturally from the jumping operations introduced in JGGA. This paper extends the idea by describing a hybrid approach that alleviates the difficulty outlined above. Experimental results reveal that our proposed hybrid approach can search for the nearly-optimal and non-dominated solutions with better convergence by optimizing multiple criteria simultaneously. Concurrently, it is capable of producing a set of controlled, diverse solutions that provide a wide range of alternative scheduling choices.