Multi-objective Flexible Job Shop Research Articles

Minimizing total carbon footprint and total late work criterion in flexible job shop scheduling by using an improved multi-objective genetic algorithm

In scheduling, previous research attention has been directed towards classical-based objective functions, while ignoring environmental-based objective functions. The purpose of this research is to present a multi-objective flexible job shop scheduling problem with the objectives of minimizing total carbon footprint and total late work criterion, simultaneously, as sustainability-based and classical-based objective functions, respectively. In order to solve the presented problem effectively, an improved multi-objective genetic algorithm is proposed to obtain high quality non-dominated schedules. This work has three main scientific contributions that are: (1) This is a novel and pioneer research that addresses carbon footprint reduction in flexible job shop scheduling, (2) This is also the first research that addresses the total late work criterion in multi-objective flexible job shop scheduling, and (3) This research proposes an improved multi-objective evolutionary algorithm for solving the newly extended bi-objective problem. Stepwise delineation of the proposed algorithm is provided and fifteen newly extended test instances are solved by the proposed approach. Computational outcomes of the proposed algorithm are compared with two most representative and well-known multi-objective evolutionary algorithms, namely, non-dominated sorting genetic algorithm II and strength Pareto evolutionary algorithm 2. The principal results show that: (1) The proposed algorithm is superior in finding high quality non-dominated schedules, (2) It performs better in four averaged comparison metrics as compared to the other algorithms, and (3) Carbon footprint has an impact on the optimum solutions. As conclusions, the proposed algorithm is useful for production managers to schedule their operations in a way that can reduce carbon emission while minimizing late work. Production managers will also have the flexibility in selecting a schedule from amongst a set of non-dominated schedules.

Particle swarm optimization with variable neighborhood search for multiobjective flexible job shop scheduling problem

The simulation on benchmarks is a very simple and efficient method to evaluate the performance of the algorithm for solving flexible job shop scheduling model. Due to the assignment and scheduling decisions, flexible job shop scheduling problem (FJSP) becomes extremely hard to solve for production management. A discrete multi-objective particle swarm optimization (PSO) and simulated annealing (SA) algorithm with variable neighborhood search is developed for FJSP with three criteria: the makespan, the total workload and the critical machine workload. Firstly, a discrete PSO is designed and then SA algorithm performs variable neighborhood search integrating two neighborhoods on public critical block to enhance the search ability. Finally, the selection strategy of the personal-best individual and global-best individual from the external archive is developed in multi-objective optimization. Through the experimental simulation on matlab, the tests on Kacem instances, Brdata instances and BCdata instances show that the modified discrete multi-objective PSO algorithm is a promising and valid method for optimizing FJSP with three criteria.

Balancing setup workers load of flexible job shop scheduling using hybrid genetic algorithm with tabu search strategy

This paper describes optimisation of a multi-objective flexible job shop scheduling problem (MO-FJSP) in small and medium-sized enterprises (SMEs) where widely various products are manufactured in make-to-order (MTO) mode. A genetic algorithm using tabu search strategy was applied to solve the MO-FJSP incorporating weighted tardiness, setup worker load balance, and work-in-process. From experiments using data based on real-world SME, the solutions obtained using the proposed method are compared with those obtained by conventional earliest due date (EDD), and GA using multi-island. The results confirmed the effectiveness of the proposed method. Results imply that the proposed approach is applicable not only for production scheduling but also for estimating the investment of resources such as machine and worker capacity.

Hybrid Discrete Bat Algorithm for Solving the Multi-objective Flexible Job Shop Scheduling Problem

Hybrid Discrete Bat Algorithm for Solving the Multi-objective Flexible Job Shop Scheduling Problem

Particle swarm optimization algorithm embedded with maximum deviation theory for solving multi-objective flexible job shop scheduling problem

Due to intense competition in the market place, effective scheduling has now become an important issue for the growth and survival of manufacturing firms. To sustain in the current competitive environment, it is essential for the manufacturing firms to improve the schedule based on simultaneous optimization of performance measures such as makespan, flow time, and tardiness. The current paper presents a novel particle swarm optimization (PSO) algorithm for solving multi-objective flexible job shop scheduling problem with the goal of finding approximations of the optimal Pareto front. The Pareto-optimal solutions obtained through multi-objective particle swarm optimization (MOPSO) have been ranked by the composite scores obtained through maximum deviation theory (MDT) to avoid subjectiveness and impreciseness in the decision-making. The results are compared with non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective evolutionary algorithm (MOEA) in terms of four performance metrics. Twenty-eight benchmark instances from literature are solved by the proposed algorithm. It is observed that MOPSO outperforms NSGA-II and MOEA in four performance metrics in most of the instances.

Multiobjective Flexible Job Shop Scheduling Using A Modified Invasive Weed Optimization

Recently, many studies are carried out with inspirations from ecological phenomena for developing optimization techniques. The new algorithm that is motivated by a common phenomenon in agriculture is colonization of invasive weeds. In this paper, a modified invasive weed optimization (IWO) algorithm is presented for optimization of multiobjective flexible job shop scheduling problems (FJSSPs) with the criteria to minimize the maximum completion time (makespan), the total workload of machines and the workload of the critical machine. IWO is a bio-inspired metaheuristic that mimics the ecological behaviour of weeds in colonizing and finding suitable place for growth and reproduction. IWO is developed to solve continuous optimization problems that’s why the heuristic rule the Smallest Position Value (SPV) is used to convert the continuous position values to the discrete job sequences. The computational experiments show that the proposed algorithm is highly competitive to the state-of-the-art methods in the literature since it is able to find the optimal and best-known solutions on the instances studied.

Applying an Intelligent Dynamic Genetic Algorithm for Solving a Multi-Objective Flexible Job Shop Scheduling Problem with Maintenance Considerations

In this paper, a multi-objective flexible dynamic job shop scheduling problem (MO-FDJSPM) with maintenance constraint is studied. The objectives of the scheduling are maximizing the completion time, mean job rotation time and mean components' tardiness. Also, in order to adapt with the internal disruptions of the manufacturing system, such as breakdown of existing machines, we consider the machines availability (so called maintenance) as a constraint. The multi-objective mathematical model is formulated and a genetic algorithm (GA) with dynamic bidimensional chromosomes along with a heuristic algorithm to handle maintenance sub-problem is developed as solution approach. In proposed algorithm, since the control parameters change intelligently and dynamically during implementation and optimization process, the early convergence and trapping in local optimum are reduced leading to performance improvement. The performance of the proposed approach is evaluated with respect to convergence speed and solutions quality. The results of computations verify and confirm both two evaluation criteria.

A hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problems

Firefly algorithm (FA) is a nature-inspired optimisation algorithm that can be successfully applied to continuous optimisation problems. However, lot of practical problems are formulated as discrete optimisation problems. In this paper a hybrid discrete firefly algorithm (HDFA) is proposed to solve the multi-objective flexible job shop scheduling problem (FJSP). FJSP is an extension of the classical job shop scheduling problem that allows an operation to be processed by any machine from a given set along different routes. Three minimisation objectives - the maximum completion time, the workload of the critical machine and the total workload of all machines are considered simultaneously. This paper also proposes firefly algorithms discretisation which consists of constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. In the proposed algorithm discrete firefly algorithm (DFA) is combined with local search (LS) method to enhance the searching accuracy and information sharing among fireflies. The experimental results on the well-known benchmark instances and comparison with other recently published algorithms shows that the proposed algorithm is feasible and an effective approach for the multi-objective flexible job shop scheduling problems.

Multiobjective Flexible Job Shop Scheduling Using Memetic Algorithms

In this paper, we propose new memetic algorithms (MAs) for the multiobjective flexible job shop scheduling problem (MO-FJSP) with the objectives to minimize the makespan, total workload, and critical workload. The problem is addressed in a Pareto manner, which aims to search for a set of Pareto optimal solutions. First, by using well-designed chromosome encoding/decoding scheme and genetic operators, the nondominated sorting genetic algorithm II (NSGA-II) is adapted for the MO-FJSP. Then, our MAs are developed by incorporating a novel local search algorithm into the adapted NSGA-II, where some good individuals are chosen from the offspring population for local search using a selection mechanism. Furthermore, in the proposed local search, a hierarchical strategy is adopted to handle the three objectives, which mainly considers the minimization of makespan, while the concern of the other two objectives is reflected in the order of trying all the possible actions that could generate the acceptable neighbor. In the experimental studies, the influence of two alternative acceptance rules on the performance of the proposed MAs is first examined. Afterwards, the effectiveness of key components in our MAs is verified, including genetic search, local search, and the hierarchical strategy in local search. Finally, extensive comparisons are carried out with the state-of-the-art methods specially presented for the MO-FJSP on well-known benchmark instances. The results show that the proposed MAs perform much better than all the other algorithms.

Using the gravitational emulation local search algorithm to solve the multi-objective flexible dynamic job shop scheduling problem in Small and Medium Enterprises

Scheduling problems are naturally dynamic. Increasing flexibility will help solve bottleneck issues, increase production, and improve performance and competitive advantage of Small Medium Enterprises (SMEs). Maximum make span, as well as the average work- flow time and latency time of parts are considered the objectives of scheduling, which are compatible with the philosophy of on-time production and supply chain management goals. In this study, these objectives were selected to optimize the resource utilization, minimize inventory turnover, and improve commitment to customers; simultaneously controlling these objectives improved system performance. In the job-shop scheduling problem considered in this paper, the three objectives were to find the best total weight of the objectives, maximize the number of reserved jobs and improve job-shop performance. To realize these targets, a multi-parametric objective function was introduced with dynamic and flexible parameters. The other key accomplishment is the development of a new method called TIME_GELS that uses the gravitational emulation local search algorithm (GELS) for solving the multi- objective flexible dynamic job-shop scheduling problem. The proposed algorithm used two

A hybrid multi-objective genetic algorithm based on the ELECTRE method for a capacitated flexible job shop scheduling problem

In this paper, a multi-objective flexible job shop scheduling problem with machines capacity constraints is studied. Minimizing the makespan and overtime costs of machines are considered as two objectives for evaluating solutions. First, a new nonlinear integer programming model is presented to formulate the problem. Inasmuch as this problem is well-known as a NP-hard problem, a hybrid meta-heuristic algorithm (CFJSP II) is developed to overcome its complexity. Regarding to the solution space of the problem, for assigning and sequencing operations, a multi-objective genetic algorithm based on the ELECTRE method is presented. Also, a powerful heuristic approach to tradeoff the objective functions is developed. Finally, the proposed algorithm is compared with some well-known multi-objective algorithms such as NSGAII, SPEA2, and VEGA. Regarding to the computational results, it is clear that the proposed algorithm has a better performance especially in the closeness of the solutions to the Pareto optimal front.

An Improved Immune Algorithm for Multi-objective Flexible Job-shop Scheduling

Flexible job-shop scheduling problem derived from the job-shop scheduling problem, and is more realistic than the job-shop scheduling problem in the manufacturing enterprise. It should be utilized with high efficiency. But it is a multi-objective optimal problem. Three minimization objectives (Maximum completion time (makespan), Total workload of machines and Workload of the critical machine) are considered simultaneously. This multi-objective flexible job-shop scheduling problem is one of the hardest combinatorial optimization problems, and is a strongly NP-hard problem. To solve the multi-objective flexible job-shop scheduling problem, a quantum immune algorithm based on the quantum and immune principles is proposed. According to the analysis of the experimental results, this algorithm is feasible and effective to solve the multi-objective flexible job-shop scheduling problem. It effectively relieves some disadvantages of the quantum and immune optimization

A Novel Quantum Immune Algorithm for Multiobjective Flexible Job Shop Scheduling

In this study, a hybrid of Quantum Evolutionary and Artificial Immune Algorithms (QIA) is proposed for solving Multiobjective Flexible Job Shop Scheduling Problem (MFJSSP). This problem is formulated as three-objective problem which minimizes completion time (makespan), critical machine workload and total work load of all machines. The quantum coding is shown to improve the immune strategy. The proposed algorithm overcomes the problem by increasing the speed of convergence and diversity of population. Three benchmarks of Kacem and Brandimart are examined to evaluate the performance of the proposed algorithm. The experimental results show a better performance in comparison to other approaches.

Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling

This paper proposes a Pareto-based grouping discrete harmony search algorithm (PGDHS) to solve the multi-objective flexible job shop scheduling problem (FJSP). Two objectives, namely the maximum completion time (makespan) and the mean of earliness and tardiness, are considered simultaneously. Firstly, two novel heuristics and several existing heuristics are employed to initialize the harmony memory. Secondly, multiple harmony generation strategies are proposed to improve the performance of harmony search algorithm. The operation sequence in a new harmony is produced based on the encoding method and the characteristics of FJSP. Thirdly, two local search methods based on critical path and due date are embedded to enhance the exploitation capability. Finally, extensive computational experiments are carried out using well-known benchmark instances. Three widely used performance measures, number of non-dominated solutions, diversification metric and quality metric, are employed to test the performance of PGDHS algorithm. Computational results and comparisons show the efficiency and effectiveness of the proposed PGDHS algorithm for solving multi-objective flexible job-shop scheduling problem.

Study on multi-objective flexible job-shop scheduling problem considering energy consumption

Purpose: Build a multi-objective Flexible Job-shop Scheduling Problem(FJSP) optimization model, in which the makespan, processing cost, energy consumption and cost-weighted processing quality are considered, then Design a Modified Non-dominated Sorting Genetic Algorithm (NSGA-II) based on blood variation for above scheduling model. Design/methodology/approach: A multi-objective optimization theory based on Pareto optimal method is used in carrying out the optimization model. NSGA-II is used to solve the model. Findings: By analyzing the research status and insufficiency of multi-objective FJSP, Find that the difference in scheduling will also have an effect on energy consumption in machining process and environmental emissions. Therefore, job-shop scheduling requires not only guaranteeing the processing quality, time and cost, but also optimizing operation plan of machines and minimizing energy consumption. Originality/value: A multi-objective FJSP optimization model is put forward, in which the makespan, processing cost, energy consumption and cost-weighted processing quality are considered. According to above model, Blood-Variation-based NSGA-II (BVNSGA-II) is designed. In which, the chromosome mutation rate is determined after calculating the blood relationship between two cross chromosomes, crossover and mutation strategy of NSGA-II is optimized and the prematurity of population is overcome. Finally, the performance of the proposed model and algorithm is evaluated through a case study, and the results proved the efficiency and feasibility of the proposed model and algorithm.

A Hybrid Discrete Firefly Algorithm for Multi-Objective Flexible Job Shop Scheduling Problems with Maintenance Activity

This paper presents a novel hybrid discrete firefly algorithm (HDFA) for solving the multi-objective flexible job shop scheduling problem with non fixed availability constraints (FJSP-nfa) due to maintenance activity. Three minimization objectives-the maximum completion time, the workload of the critical machine and the total workload of all machines are considered simultaneously. In this study, the discrete firefly algorithm is adopted to solve the problem, in which the machine assignment and operation sequence are processed by constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. In addition the decoding mechanism considering the maintenance activity is presented. A neighbourhood based local search is hybridized to enhance the exploitation capability. Representative benchmark problems are solved in order to evaluate and study the performance of the proposed algorithm.

A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints

In this paper, a hybrid discrete firefly algorithm is presented to solve the multi-objective flexible job shop scheduling problem with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow a process sequence and each operation must be processed on an assigned machine. These constraints are used to balance between the resource limitation and machine flexibility. Three minimisation objectives—the maximum completion time, the workload of the critical machine and the total workload of all machines—are considered simultaneously. In this study, discrete firefly algorithm is adopted to solve the problem, in which the machine assignment and operation sequence are processed by constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. Meanwhile, local search method with neighbourhood structures is hybridised to enhance the exploitation capability. Benchmark problems are used to evaluate and study the performance of the proposed algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.

Path-relinking Tabu search for the multi-objective flexible job shop scheduling problem

The multi-objective flexible job shop scheduling problem is solved using a novel path-relinking algorithm based on the state-of-the-art Tabu search algorithm with back-jump tracking. A routing solution is identified by problem-specific neighborhood search, and is then further refined by the Tabu search algorithm with back-jump tracking for a sequencing decision. The resultant solution is used to maintain the medium-term memory where the best solutions are stored. A path-relinking heuristics is designed to generate diverse solutions in the most promising areas. An improved version of the algorithm is then developed by incorporating an effective dimension-oriented intensification search to find solutions that are located near extreme solutions. The proposed algorithms are tested on benchmark instances and its experimental performance is compared with that of algorithms in the literature. Comparison results show that the proposed algorithms are competitive in terms of its computation performance and solution quality.

Multi-objective flexible job shop scheduling using hybrid differential evolution algorithm

The authors addressed multi objective flexible job shop scheduling problems using hybrid differential evolution algorithm for minimisation of makespan, total machine load and critical machine load. The differential evolution algorithm is a stochastic-based adaptive scheme used for global optimisation over continuous space and to apply it for flexible job shop scheduling problem a suitable encoding mechanism is required. In this work random keys encoding mechanism is used to generate schedules that deals with floating point vectors. A non-dominated sorting algorithm is used to find the set of non-dominated solutions for the given scheduling problem. The proposed approach is extensively tested on a set of standard flexible job shop scheduling instances reported in the literature and it is found that the proposed algorithm is performing well on all the test problems.

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.