A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem
TL;DR: This paper contains a complete and updated review of the literature for multiobjective flowshop problems, which are among the most studied environments in the scheduling research area, and identifies the best-performing methods from the literature.
Abstract: This paper contains a complete and updated review of the literature for multiobjective flowshop problems, which are among the most studied environments in the scheduling research area. No previous comprehensive reviews exist in the literature. Papers about lexicographical, goal programming, objective weighting, and Pareto approaches have been reviewed. Exact, heuristic, and metaheuristic methods have been surveyed. Furthermore, a complete computational evaluation is also carried out. A total of 23 different algorithms including both flowshop-specific methods as well as general multiobjective optimization approaches have been tested under three different two-criteria combinations with a comprehensive benchmark. All methods have been studied under recent state-of-the-art quality measures. Parametric and nonparametric statistical testing is profusely employed to support the observed performance of the compared methods. As a result, we have identified the best-performing methods from the literature, which along with the review, constitutes a reference work for further research.
Citations
More filters
Journal Article•
TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.
Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON
13,333 citations
TL;DR: A literature review on exact, heuristic and metaheuristic methods that have been proposed for the solution of the hybrid flow shop problem is presented.
647 citations
Additional excerpts
...[122]....
[...]
TL;DR: The DPFSP is characterized and six different alternative mixed integer linear programming (MILP) models that are carefully and statistically analyzed for performance are proposed.
353 citations
TL;DR: This paper develops a chromosome that can describe a feasible schedule such that meta-heuristics can be applied and innovatively adopts an improved nondominated sorting genetic algorithm to solve the optimization problem for the first time.
Abstract: With the interaction of discrete-event and continuous processes, it is challenging to schedule crude oil operations in a refinery. This paper studies the optimization problem of finding a detailed schedule to realize a given refining schedule. This is a multiobjective optimization problem with a combinatorial nature. Since the original problem cannot be directly solved by using heuristics and meta-heuristics, the problem is transformed into an assignment problem of charging tanks and distillers. Based on such a transformation, by analyzing the properties of the problem, this paper develops a chromosome that can describe a feasible schedule such that meta-heuristics can be applied. Then, it innovatively adopts an improved nondominated sorting genetic algorithm to solve the problem for the first time. An industrial case study is used to test the proposed solution method. The results show that the method makes a significant performance improvement and is applicable to real-life refinery scheduling problems.
229 citations
Cites background from "A Review and Evaluation of Multiobj..."
...As pointed out in [18], NSGA-II may not be the best multiobjective algorithm for scheduling....
[...]
TL;DR: A brief literature review of the contributions to MOFSP is provided and areas of opportunity for future research are identified.
Abstract: The flow shop scheduling problem is finding a sequence given n jobs with same order at m machines according to certain performance measure(s). 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, many real-world scheduling problems are multi-objective by nature. Over the years there have been several approaches used to deal with the multi-objective flow shop scheduling problems (MOFSP). Hence, in this study, we provide a brief literature review of the contributions to MOFSP and identify areas of opportunity for future research.
191 citations
References
More filters
TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.
37,111 citations
"A Review and Evaluation of Multiobj..." refers background in this paper
...In Deb (2002) an evolution of the NSGA was presented....
[...]
Journal Article•
TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.
Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON
13,333 citations
"A Review and Evaluation of Multiobj..." refers methods in this paper
...The MOGA algorithm of Murata et al. (1996) was designed to tackle the multi objective flowshop problem....
[...]
Book•
01 Jan 2001
TL;DR: This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
Abstract: From the Publisher:
Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run. · Comprehensive coverage of this growing area of research · Carefully introduces each algorithm with examples and in-depth discussion · Includes many applications to real-world problems, including engineering design and scheduling · Includes discussion of advanced topics and future research · Features exercises and solutions, enabling use as a course text or for self-study · Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.
12,134 citations
Book•
01 Jan 1971
TL;DR: Probability Theory. Statistical Inference. Contingency Tables. Appendix Tables. Answers to Odd-Numbered Exercises and Answers to Answers to Answer Questions as discussed by the authors.
Abstract: Probability Theory. Statistical Inference. Some Tests Based on the Binomial Distribution. Contingency Tables. Some Methods Based on Ranks. Statistics of the Kolmogorov-Smirnov Type. References. Appendix Tables. Answers to Odd-Numbered Exercises. Index.
10,382 citations
TL;DR: The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface.
Abstract: Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0/1 knapsack problem.
7,512 citations