Author

# Kalyanmoy Deb

Other affiliations: Indian Institute of Technology Kanpur, ETH Zurich, Indian Institutes of Technology ...read more

Bio: Kalyanmoy Deb is an academic researcher from Michigan State University. The author has contributed to research in topics: Multi-objective optimization & Evolutionary algorithm. The author has an hindex of 112, co-authored 713 publications receiving 122802 citations. Previous affiliations of Kalyanmoy Deb include Indian Institute of Technology Kanpur & ETH Zurich.

##### Papers published on a yearly basis

##### Papers

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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

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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

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TL;DR: Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously are investigated and suggested to be extended to higher dimensional and more difficult multiobjective problems.

Abstract: In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.

6,411 citations

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18 Sep 2000

TL;DR: Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Paretimal front.

Abstract: Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II's low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come.

4,878 citations

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TL;DR: This paper provides a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions and shows that elitism is shown to be an important factor for improving evolutionary multiobjectives search.

Abstract: In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

4,867 citations

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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

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TL;DR: This historical survey compactly summarizes relevant work, much of it from the previous millennium, review deep supervised learning, unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.

14,635 citations

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01 Jan 1992TL;DR: This book discusses the evolution of architecture, primitive functions, terminals, sufficiency, and closure, and the role of representation and the lens effect in genetic programming.

Abstract: Background on genetic algorithms, LISP, and genetic programming hierarchical problem-solving introduction to automatically-defined functions - the two-boxes problem problems that straddle the breakeven point for computational effort Boolean parity functions determining the architecture of the program the lawnmower problem the bumblebee problem the increasing benefits of ADFs as problems are scaled up finding an impulse response function artificial ant on the San Mateo trail obstacle-avoiding robot the minesweeper problem automatic discovery of detectors for letter recognition flushes and four-of-a-kinds in a pinochle deck introduction to biochemistry and molecular biology prediction of transmembrane domains in proteins prediction of omega loops in proteins lookahead version of the transmembrane problem evolutionary selection of the architecture of the program evolution of primitives and sufficiency evolutionary selection of terminals evolution of closure simultaneous evolution of architecture, primitive functions, terminals, sufficiency, and closure the role of representation and the lens effect Appendices: list of special symbols list of special functions list of type fonts default parameters computer implementation annotated bibliography of genetic programming electronic mailing list and public repository

13,487 citations

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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