Multi-objective Job Shop Research Articles

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.

Ant colony algorithm for multi-criteria job shop scheduling to minimize makespan, mean flow time and mean tardiness

In the real world situation many scheduling problems faced by decision maker are involved more than one aspect and therefore multiple criteria analysis is required. This paper presents ant colony algorithm for solving the multi-objective Job Shop Scheduling Problem (JSP). The objectives considered in this study include the minimization of makespan, mean flow time, and mean tardiness. The proposed algorithm is tested on many benchmark problems up to 15 jobs × 10 machine. The results obtained have shown that the proposed algorithm is a feasible and effective approach for the multiple-objective problem.

Multi-objective Job Shop Rescheduling with Evolutionary Algorithm

Multi-objective Job Shop Rescheduling with Evolutionary Algorithm

Multi-objective job shop scheduling using hybrid differential evolution approach

Many real world scheduling problems involve simultaneous optimisation of multiple objectives and the trade-off between the objectives is crucial. The present work is an attempt to address the multi-objective job shop scheduling using a hybrid differential evolution approach. The objectives considered in the study are minimisation of makespan, mean flow time and mean tardiness. The operation schedule is generated using random keys encoding scheme which deals with the floating point vectors. A local search heuristic is embedded in the algorithm to achieve the best optimal solution. The proposed approach is tested on various job shop scheduling instances reported in the literature and it is observed that the proposed approach is performing well on all the test problems.

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.

A new dispatching rule based genetic algorithm for the multi-objective job shop problem

Hyper-heuristics or "methodologies to choose heuristics" are becoming increasingly popular given their suitability to solve hard real world combinatorial optimisation problems. Their distinguishing feature is that they operate in the space of heuristics or heuristic components rather than in the solution space. In Dispatching Rule Based Genetic Algorithms (DRGA) solutions are represented as sequences of dispatching rules which are called one at a time and used to sequence a number of operations onto machines. The number of operations that each dispatching rule in the sequence handles is a parameter to which DRGA is notoriously sensitive. This paper proposes a new hybrid DRGA which searches simultaneously for the best sequence of dispatching rules and the number of operations to be handled by each dispatching rule. The investigated DRGA uses the selection mechanism of NSGA-II when handling multi-objective problems. The proposed representation was used to solve different variants of the multi-objective job shop problem as well as the single objective problem with the sum of weighted tardiness objective. Our results, supported by the statistical analysis, confirm that DRGAs that use the proposed representation obtained better results in both the single and multi-objective environment overall and on each particular set of instances than DRGAs using the conventional dispatching rule representation and a GA that uses the more common permutation representation.

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 genetic solution based on lexicographical goal programming for a multiobjective job shop with uncertainty

In this work we consider a multiobjective job shop problem with uncertain durations and crisp due dates. Ill-known durations are modelled as fuzzy numbers. We take a fuzzy goal programming approach to propose a generic multiobjective model based on lexicographical minimisation of expected values. To solve the resulting problem, we propose a genetic algorithm searching in the space of possibly active schedules. Experimental results are presented for several problem instances, solved by the GA according to the proposed model, considering three objectives: makespan, tardiness and idleness. The results illustrate the potential of the proposed multiobjective model and genetic algorithm.

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.

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.

Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems

This paper addresses multi-objective job shop scheduling problems with fuzzy processing time and due-date in such a way to provide the decision-maker with a group of Pareto optimal solutions. A new priority rule-based representation method is proposed and the problems are converted into continuous optimization ones to handle the problems by using particle swarm optimization. The conversion is implemented by constructing the corresponding relationship between real vector and the chromosome obtained with the new representation method. Pareto archive particle swarm optimization is proposed, in which the global best position selection is combined with the crowding measure-based archive maintenance, and the inclusion of mutation into the proposed algorithm is considered. The proposed algorithm is applied to eight benchmark problems for the following objectives: the minimum agreement index, the maximum fuzzy completion time and the mean fuzzy completion time. Computational results demonstrate that the proposal algorithm has a promising advantage in fuzzy job shop scheduling.

Scheduling multi-objective job shops using a memetic algorithm based on differential evolution

In this paper, a memetic algorithm based on differential evolution (DE), named MODEMA, is proposed for multi-objective job shop scheduling problems (MJSSPs). To balance the exploration and exploitation abilities, both DE-based global search and an adaptive local search are designed and applied simultaneously in the proposed MODEMA. Firstly, a smallest-order-value (SOV) rule is presented to convert the continuous values of individuals (real vectors) in DE to job permutations. Secondly, after the exploration based on DE, several neighborhoods are 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. In addition, a solution set is used in MODEMA to hold and update the obtained nondominated solutions. Simulation results and comparisons with Ishibuchi and Murata’s multi-objective genetic local search (IMMOGLS) show the effectiveness and robustness of the proposed MODEMA.

Decision support tool for multi-objective job shop scheduling problems with linguistically quantified decision functions

This paper presents a new tool for multi-objective job shop scheduling problems. The tool encompasses an interactive fuzzy multi-objective genetic algorithm (GA) which considers aspiration levels set by the decision maker (DM) for all the objectives. The GA's decision (fitness) function is defined as a measure of truth of a linguistically quantified statement, imprecisely specified by the DM using linguistic quantifiers such as most, few, etc., that refer to acceptable distances between the achieved objective values and the aspiration levels. The linguistic quantifiers are modelled using fuzzy sets. The developed tool is used to analyse and solve a real-world problem defined in collaboration with a pottery company. The tool provides a valuable support in performing various what-if analyses, for example, how changes of batch sizes, aspiration levels, linguistic quantifiers and the measure of acceptable distances affect the final schedule.

Mathematical modelling of multi-objective job shop scheduling with dependent setups and re-entrant operations

For the last thirty years, in job shop scheduling, the setup times of operations have been either ignored or combined with their corresponding processing times, independent setups, to simplify the work of model construction. However, in practice, the setup times of an operation are usually considered be sequence-dependent. Moreover, the performance of a scheduling system is not evaluated to satisfy a single objective, but to obtain a trade-off solution regarding multiple objectives. Therefore, this paper investigates job shop scheduling problems with re-entrant operations where the setup times, which vary according to the preceding operation which is processed on the same machine, and which can be separated from their corresponding processing times, cannot be omitted. Three practical performance measures – minimum total job flow time, minimum total job tardiness and minimum machine idle time – are considered. An integer programming model is first developed to optimise each single objective and an acceptable trade-off schedule, which makes use of a multiple-decision-making technique, the global criterion method, is obtained by evaluating three objectives simultaneously .

Fuzzy programming for multiobjective job shop scheduling with fuzzy processing time and fuzzy duedate through genetic algorithms

In this paper, by considering the imprecise or fuzzy nature of the data in real-world problems, job shop scheduling with fuzzy processing time and fuzzy duedate is introduced. On the basis of the agreement index of fuzzy duedate and fuzzy completion time, multiobjective fuzzy job shop scheduling problems are formulated as three-objective ones which not only maximize the minimum agreement index but also maximize the average agreement index and minimize the maximum fuzzy completion time. Having elicited the linear membership functions for the fuzzy goals of the decision maker, we adopt the fuzzy decision of Bellman and Zadeh. By incorporating the concept of similarity among individuals into the genetic algorithms using the Gannt chart, a genetic algorithm which is suitable for solving the formulated problems are proposed. As illustrative numerical examples, both 6×6 and 10×10 three-objective job shop scheduling problems with fuzzy duedate and fuzzy processing time are considered, and the feasibility and effectiveness of the proposed method are demonstrated by comparing with the simulated annealing method.