Multi-objective Flow Shop Scheduling Problem Research Articles

An interactive algorithm for multi-objective flow shop scheduling with fuzzy processing time through resolution method and TOPSIS

This paper develops a method for solving a multi-objective flow shop scheduling in a fuzzy environment where processing times are fuzzy numbers. The objective functions are designed to simultaneously minimize the makespan (completion time), the mean flow time, and the machine idle time. For each objective function, a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal is defined. Then, technique for order preference by similarity to an ideal solution (TOPSIS) method finds the nondominated solution in a multiple objective state. The TOPSIS method and the interactive resolution method are integrated in the proposed method to solve the multi-objective flow shop scheduling problem. One of the new contributions of this research is combining these two methods in solving this problem. The proposed algorithm provides a way to find a crisp solution for the fuzzy flow shop scheduling in a multi-objective state. Also, the proposed method yields a reasonable solution that represents the balance between the feasibility of a decision vector and the optimality for an objective function by the interactive participation of the decision maker in all steps of decision process. Application of the proposed method to flow shop scheduling is shown with two numerical examples. The results show that the algorithm could be applied for determining the most preferable sequence by finding a nondominated solution for different degrees of satisfaction of constraints, and with regard to objective value, where processing time is fuzzy.

Multi-objective no-wait flowshop scheduling problems: models and algorithms

This article studies multi-objective no-wait flowshop scheduling problems to minimise both makespan and total tardiness. This problem is commonly denoted by . This article mathematically formulates the problem using two effective multi-objective mixed integer linear programming models. The multi-objective mathematical models are then solved by a multiple criteria decision making approach, called Fuzzy programming method. Moreover, the article proposes a novel multi-objective iterated local search algorithm incorporating three types of local search engine: greedy, moderate and curtailed fashions. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.

Multi-objective no-wait hybrid flowshop scheduling problem with transportation times

This paper studies multi-objective no-wait hybrid flowshop scheduling problems to minimise both makespan and total tardiness. Furthermore, we consider transportation times between machines. This transportation time can be either job-dependent or job-independent. We consider that all transportations are job-independent; and transportations between two machines have to be done by one transporter. This paper presents a new multi-objective electromagnetism algorithm (MOEA). Electromagnetism algorithm is known as a flexible and effective population-based algorithm utilising an attraction/repulsion mechanism to move the particles towards optimality. The algorithm is carefully evaluated for its performance against two available algorithms by means of multi-objective performance measures and statistical tools. The results show that the proposed solution method outperforms the others.

Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.

Multi-objective optimization algorithms for flow shop scheduling problem: a review and prospects

Since multi-objective flow shop scheduling problem (MFSP) plays a key role in practical scheduling, there has been an increasing interest in MFSP according to the literature. However, there still have been wide gaps between theories and practical applications, and the review research of multi-objective optimization algorithms in MFSP (objectives > 2) field is relatively scarce. In view of this, this paper provides a comprehensive review of both former and the state-of-the-art approaches on MFSP. Firstly, we introduce a broad description and the complexity of MFSP. Secondly, a taxonomy of multi-objective optimizations and an analysis of the publications on MFSP are presented. It is noteworthy that heuristic and meta-heuristic methods and hybrid procedures are proven much more useful than other methods in large and complex situations. Finally, future research trends and challenges in this field are proposed and analyzed. Our survey shows that algorithms developed for MFSP continues to attract significant research interest from both theoretical and practical perspectives.

Non-Conventional Optimization Methods Hybridation For Solving Flow-Shop Multiobjective Pharmaceutical Industries Problem

This paper deals with an hybridation of two non-conventional optimization methods, genetic algorithms and a new based particle swarm, is proposed for optimization of multiobjective flow-shop scheduling problem in pharmaceutical industries. The comparison of results obtained by this hybridation and those obtained by the separate use of each one of the two methods shows the efficiency of the proposed approach.

Genetic algorithm integrated with artificial chromosomes for multi-objective flowshop scheduling problems

Recently, a wealthy of research works has been dedicated to the design of effective and efficient genetic algorithms in dealing with multi-objective scheduling problems. In this paper, an artificial chromosome generating mechanism is designed to reserve patterns of genes in elite chromosomes and to find possible better solutions. The artificial chromosome generating mechanism is embedded in simple genetic algorithm (SGA) and the non-dominated sorting genetic algorithm (NSGA-II) to solve single-objective and multi-objective flowshop-scheduling problems, respectively. The single-objective problems are to minimize the makespan while the multi-objective scheduling problems are to minimize the makespan and the maximum tardiness. Extensive numerical studies are conducted and the results indicate that artificial chromosomes embedded with SGA and NSGAII are able to further speed up the convergence of the genetic algorithm and improve the solution quality. This promising result may be of interests to industrial practitioners and academic researchers in the field of evolutionary algorithm or machine scheduling.

Ant colony optimization for multi-objective flow shop scheduling problem

Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared.

A new multiobjective genetic algorithm with heterogeneous population for solving flowshop scheduling problems

The present paper discusses the application of a new genetic algorithm (GA) featuring heterogeneous population to solve multiobjective flowshop scheduling problems. Many GAs have been developed to solve multiobjective scheduling problems, but they used a non-heterogeneous population approach, which could lead to premature convergence and local Pareto-optimum solutions. Our experiments with a 20-job and 20-machine benchmark problem given in Taillard (1993) show that the heterogeneous multiobjective genetic algorithm (hMGA) developed in this research outperforms NSGA-II (Deb 2001) one of the widely used algorithms with non-heterogeneous population. Moreover, in this paper we also present the comparison of hMGA with another meta-heuristic method, i.e. multi-objective simulated annealing (MOSA), proposed by Varadharajan and Rajendran (2005). This research concludes that hMGA developed in this work is promising as it can produce a new set of Pareto-optimum solutions that have not been found by MOSA before.

A Hybrid Quantum-Inspired Genetic Algorithm for Multiobjective Flow Shop Scheduling

This paper proposes a hybrid quantum-inspired genetic algorithm (HQGA) for the multiobjective flow shop scheduling problem (FSSP), which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. On the one hand, a quantum-inspired GA (QGA) based on Q-bit representation is applied for exploration in the discrete 0-1 hyperspace by using the updating operator of quantum gate and genetic operators of Q-bit. Moreover, random-key representation is used to convert the Q-bit representation to job permutation for evaluating the objective values of the schedule solution. On the other hand, permutation-based GA (PGA) is applied for both performing exploration in permutation-based scheduling space and stressing exploitation for good schedule solutions. To evaluate solutions in multiobjective sense, a randomly weighted linear-sum function is used in QGA, and a nondominated sorting technique including classification of Pareto fronts and fitness assignment is applied in PGA with regard to both proximity and diversity of solutions. To maintain the diversity of the population, two trimming techniques for population are proposed. The proposed HQGA is tested based on some multiobjective FSSPs. Simulation results and comparisons based on several performance metrics demonstrate the effectiveness of the proposed HQGA.

Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems

According to previous research of Chang et al. [Chang, P. C., Chen, S. H., & Lin, K. L. (2005b). Two phase sub-population genetic algorithm for parallel machine scheduling problem. Expert Systems with Applications, 29(3), 705-712], the sub-population genetic algorithm (SPGA) is effective in solving multiobjective scheduling problems. Based on the pioneer efforts, this research proposes a mining gene structure technique integrated with the SPGA. The mining problem of elite chromosomes is formulated as a linear assignment problem and a greedy heuristic using threshold to eliminate redundant information. As a result, artificial chromosomes are created according to this gene mining procedure and these artificial chromosomes will be reintroduced into the evolution process to improve the efficiency and solution quality of the procedure. In addition, to further increase the quality of the artificial chromosome, a dynamic threshold procedure is developed and the flowshop scheduling problems are applied as a benchmark problem for testing the developed algorithm. Extensive tests in the flow-shop scheduling problem show that the proposed approach can improve the performance of SPGA significantly.

Genetic local search for multi-objective flowshop scheduling problems

This paper addresses flowshop scheduling problems with multiple performance criteria in such a way as to provide the decision maker with approximate Pareto optimal solutions. Genetic algorithms have attracted the attention of researchers in the nineties as a promising technique for solving multi-objective combinatorial optimization problems. We propose a genetic local search algorithm with features such as preservation of dispersion in the population, elitism, and use of a parallel multi-objective local search so as intensify the search in distinct regions. The concept of Pareto dominance is used to assign fitness to the solutions and in the local search procedure. The algorithm is applied to the flowshop scheduling problem for the following two pairs of objectives: (i) makespan and maximum tardiness; (ii) makespan and total tardiness. For instances involving two machines, the algorithm is compared with Branch-and-Bound algorithms proposed in the literature. For such instances and larger ones, involving up to 80 jobs and 20 machines, the performance of the algorithm is compared with two multi-objective genetic local search algorithms proposed in the literature. Computational results show that the proposed algorithm yields a reasonable approximation of the Pareto optimal set.

A partial enumeration heuristic for multi-objective flowshop scheduling problems

This paper addresses the flowshop scheduling problem with multiple performance objectives in such a way as to provide the decision maker with approximate Pareto optimal solutions. It is well known that the partial enumeration constructive heuristic NEH and its adaptations perform well for single objectives such as makespan, total tardiness and flowtime. In this paper, we develop a similar heuristic using the concept of Pareto dominance when comparing partial and complete schedules. The heuristic is tested on problems involving combinations of the above criteria. For the two-machine case, and the pairs of objectives: (i) makespan and maximum tardiness, (ii) makespan and total tardiness, the heuristic is compared with branch-and-bound algorithms proposed in the literature. For two and more than two machines, and the criteria combinations considered in this article, the heuristic performance is tested against constructive heuristics reported in the literature. By means of an illustrative example, it is shown that a genetic algorithm from the literature performs better when starting from heuristic solutions rather than random solutions.

A multi-objective genetic local search algorithm and its application to flowshop scheduling

We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems.