Results 1 - 10 of 1,815

A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II

by Kalyanmoy Deb, Samir Agrawal, Amrit Pratap, T Meyarivan , 2000
"... Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) -4 computational complexity (where is the number of objectives and is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing ..."
Abstract - Cited by 662 (15 self) - Add to MetaCart
Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) -4 computational complexity (where is the number of objectives and 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 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) solutions. Simulation results on five difficult test problems show that the proposed NSGA-II is able to find much better spread of solutions in all problems compared to PAES---another elitist multi-objective EA which pays 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.

Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

by Eckart Zitzler, Lothar Thiele, Kalyanmoy Deb , 2000
"... 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 conver ..."
Abstract - Cited by 628 (41 self) - Add to MetaCart
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.

Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art

by David A. Van Veldhuizen, Gary B. Lamont , 2000
"... Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
Abstract - Cited by 440 (7 self) - Add to MetaCart
Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...
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Adaptive service composition in flexible processes

by Danilo Ardagna, Barbara Pernici - IEEE TRANS. SOFTWARE ENG , 2007
"... In advanced service oriented systems, complex applications, described as abstract business processes, can be executed by invoking a number of available Web services. End users can specify different preferences and constraints and service selection can be performed dynamically identifying the best s ..."
Abstract - Cited by 141 (5 self) - Add to MetaCart
In advanced service oriented systems, complex applications, described as abstract business processes, can be executed by invoking a number of available Web services. End users can specify different preferences and constraints and service selection can be performed dynamically identifying the best set of services available at runtime. In this paper, we introduce a new modeling approach to the Web service selection problem that is particularly effective for large processes and when QoS constraints are severe. In the model, the Web service selection problem is formalized as a mixed integer linear programming problem, loops peeling is adopted in the optimization, and constraints posed by stateful Web services are considered. Moreover, negotiation techniques are exploited to identify a feasible solution of the problem, if one does not exist. Experimental results compare our method with other solutions proposed in the literature and demonstrate the effectiveness of our approach toward the identification of an optimal solution to the QoS constrained Web service selection problem.
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private communication

by Chen, J. Kimball, Quô C Anh Ngô, S. S. Dragomir
"... Integral inequality. In this paper, an integral inequality is studied. An answer to an open problem proposed by Feng Qi and Yin Chen and John Kimball is given. Many thanks to Professor Feng Qi for his comments. The authors also want to give their deep gratitude to the anonymous referee for his/her v ..."
Abstract - Cited by 124 (8 self) - Add to MetaCart
Integral inequality. In this paper, an integral inequality is studied. An answer to an open problem proposed by Feng Qi and Yin Chen and John Kimball is given. Many thanks to Professor Feng Qi for his comments. The authors also want to give their deep gratitude to the anonymous referee for his/her valuable comments and suggestions on the proof of Theorem 2.2 which made the article more readable. Special thanks goes to the research assistant for the quick responsibility. Notes on an Open Problem Quô ´ c Anh Ngô and Pham Huy Tung vol. 8, iss. 2, art. 41, 2007 Title Page
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Multi-Objective Optimization Using Genetic Algorithms: A Tutorial

by Abdullah Konak, David W. Coit, Alice E. Smith
"... abstract – Multi-objective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many real-life problems, objectives under consid ..."
Abstract - Cited by 114 (0 self) - Add to MetaCart
abstract – Multi-objective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many real-life problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms developed specifically for these problems with multiple objectives. They differ from traditional genetic algorithms by using specialized fitness functions, introducing methods to promote solution diversity, and other approaches. 1.
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Covariance Matrix Adaptation for Multi-objective Optimization

by Christian Igel, Nikolaus Hansen, Stefan Roth - Evolutionary Computation
"... The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most pow-erful evolutionary algorithms for real-valued single-objective optimization. In this pa-per, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist C ..."
Abstract - Cited by 113 (13 self) - Add to MetaCart
The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most pow-erful evolutionary algorithms for real-valued single-objective optimization. In this pa-per, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist CMA-ES using plus-selection and step size con-trol based on a success rule. This algorithm is compared to the standard CMA-ES. The elitist CMA-ES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in sub-optimal local minima. In the new multi-objective CMA-ES (MO-CMA-ES) a population of individuals that adapt their search strategy as in the elitist CMA-ES is maintained. These are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume as second sorting criterion. Both the elitist single-objective CMA-ES and the MO-CMA-ES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMA-ES. The bene-fits of the new MO-CMA-ES in comparison to the well-known NSGA-II and to NSDE, a multi-objective differential evolution algorithm, are experimentally shown.
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Balance between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling

by Hisao Ishibuchi, Tadashi Yoshida, Tadahiko Murata - IEEE Trans. on Evolutionary Computation , 2002
"... This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative ..."
Abstract - Cited by 100 (14 self) - Add to MetaCart
This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative effect is the increase in the computation time per generation. Thus the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: SPEA and NSGA-II. Finally, we demonstrate that local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.

An EMO Algorithm Using the Hypervolume Measure as Selection Criterion

by Michael Emmerich, Nicola Beume, Boris Naujoks - 2005 Int’l Conference, March 2005 , 2005
"... The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is self-evident. A steady-state EMOA will be devised, that combines concepts of non-dominated sor ..."
Abstract - Cited by 67 (10 self) - Add to MetaCart
The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is self-evident. A steady-state EMOA will be devised, that combines concepts of non-dominated sorting with a selection operator based on the hypervolume measure. The algorithm computes a well distributed set of solutions with bounded size thereby focussing on interesting regions of the Pareto front(s). By means of standard benchmark problems the algorithm will be compared to other well established EMOA. The results show that our new algorithm achieves good convergence to the Pareto front and outperforms standard methods in the hypervolume covered.

Multiobjective optimization problems with complicated pareto sets

by Hui Li, Qingfu Zhang, Senior Member - MOEA/D and NSGA-II,” Trans. Evolutionary Computation , 2009
"... Abstract—Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper in-troduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shap ..."
Abstract - Cited by 66 (11 self) - Add to MetaCart
Abstract—Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper in-troduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also pro-poses a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based mul-tiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes. Index Terms—Aggregation, decomposition, differential evolu-tion, evolutionary algorithms, multiobjective optimization, Pareto optimality, test problems. I.
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