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A Fast and Elitist MultiObjective Genetic Algorithm: NSGAII
, 2000
"... Multiobjective evolutionary algorithms which use nondominated sorting and sharing have been mainly criticized for their (i) O(MN computational complexity (where M is the number of objectives and N is the population size), (ii) nonelitism approach, and (iii) the need for specifying a sharing param ..."
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Cited by 1707 (58 self)
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Multiobjective evolutionary algorithms which use nondominated sorting and sharing have been mainly criticized for their (i) O(MN computational complexity (where M is the number of objectives and N is the population size), (ii) nonelitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a nondominated sorting based multiobjective evolutionary algorithm (we called it the Nondominated Sorting GAII or NSGAII) which alleviates all the above three difficulties. Specifically, a fast nondominated sorting approach with O(MN ) 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 a number of difficult test problems show that the proposed NSGAII, in most problems, is able to find much better spread of solutions and better convergence near the true Paretooptimal front compared to PAES and SPEA  two other elitist multiobjective EAs which pay special attention towards creating a diverse Paretooptimal front. Moreover, we modify the definition of dominance in order to solve constrained multiobjective problems eciently. Simulation results of the constrained NSGAII on a number of test problems, including a fiveobjective, sevenconstraint nonlinear problem, are compared with another constrained multiobjective optimizer and much better performance of NSGAII is observed. Because of NSGAII's low computational requirements, elitist approach, parameterless niching approach, and simple constrainthandling strategy, NSGAII should find increasing applications in the coming years.
Multiobjective Evolutionary Algorithms: Analyzing the StateoftheArt
, 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 mideighties in an attempt to stochastically solve problems of this generic class. During the past decade, ..."
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Cited by 424 (7 self)
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Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mideighties 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...
A ParameterLess Genetic Algorithm
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1999
"... From the user's point of view, setting the parameters of a genetic algorithm (GA) is far from a trivial task. Moreover, the user is typically not interested in population sizes, crossover probabilities, selection rates, and other GA technicalities. He is just interested in solving a probl ..."
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Cited by 279 (34 self)
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From the user's point of view, setting the parameters of a genetic algorithm (GA) is far from a trivial task. Moreover, the user is typically not interested in population sizes, crossover probabilities, selection rates, and other GA technicalities. He is just interested in solving a problem, and what he would really like to do, is to handin the problem to a blackbox algorithm, and simply press a start button. This paper explores the development of a GA that fulfills this requirement. It has no parameters whatsoever. The development of the algorithm takes into account several aspects of the theory of GAs, including previous research work on population sizing, the schema theorem, building block mixing, and genetic drift.
MultiObjective Genetic Algorithms: Problem Difficulties and Construction of Test Problems
 Evolutionary Computation
, 1999
"... In this paper, we study the problem features that may cause a multiobjective genetic algorithm (GA) difficulty in converging to the true Paretooptimal front. Identification of such features helps us develop difficult test problems for multiobjective optimization. Multiobjective test problems ..."
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Cited by 199 (11 self)
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In this paper, we study the problem features that may cause a multiobjective genetic algorithm (GA) difficulty in converging to the true Paretooptimal front. Identification of such features helps us develop difficult test problems for multiobjective optimization. Multiobjective test problems are constructed from singleobjective optimization problems, thereby allowing known difficult features of singleobjective problems (such as multimodality, isolation, or deception) to be directly transferred to the corresponding multiobjective problem. In addition, test problems having features specific to multiobjective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multiobjective optimization. Keywords Genetic algorithms, multiobjective optimization, niching, paretooptimality, problem difficulties, test problems. 1 Introduction After a decade since the pioneering wor...
Bayesian Optimization Algorithm: From Single Level to Hierarchy
, 2002
"... There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decompositi ..."
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Cited by 101 (19 self)
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There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decomposition as opposed to decomposition on only a single level. Third, design a class of difficult hierarchical problems that can be used to test the algorithms that attempt to exploit hierarchical decomposition. Fourth, test the developed algorithms on the designed class of problems and several realworld applications. The dissertation proposes the Bayesian optimization algorithm (BOA), which uses Bayesian networks to model the promising solutions found so far and sample new candidate solutions. BOA is theoretically and empirically shown to be capable of both learning a proper decomposition of the problem and exploiting the learned decomposition to ensure robust and scalable search for the optimum across a wide range of problems. The dissertation then identifies important features that must be incorporated into the basic BOA to solve problems that are not decomposable on a single level, but that can still be solved by decomposition over multiple levels of difficulty. Hierarchical
Linkage Problem, Distribution Estimation, and Bayesian Networks
, 2000
"... This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. Th ..."
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Cited by 99 (21 self)
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This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. TheBOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.
SelfAdaptive Genetic Algorithms with Simulated Binary Crossover
 COMPLEX SYSTEMS
, 1999
"... Selfadaptation is an essential feature of natural evolution. However, in the context of function optimization, selfadaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the selfa ..."
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Cited by 84 (12 self)
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Selfadaptation is an essential feature of natural evolution. However, in the context of function optimization, selfadaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the selfadaptive feature of realparameter genetic algorithms (GAs) using simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of selfadaptive ESs and realparameter GAs with SBX operator is also discussed. Thereafter, the selfadaptive behavior of realparameter GAs is demonstrated on a number of test problems commonlyused in the ES literature. The remarkable similarity in the working principle of realparameter GAs and selfadaptive ESs shown in this study suggests the need of emphasizing further studies on selfadaptive GAs.
Domino Convergence, Drift, and the TemporalSalience Structure of Problems
, 1998
"... The convergence speed of building blocks depends on their marginal fitness contribution or on the salience structure of the problem. We use a sequential parameterization approach to build models of the differential convergence behavior, and derive time complexities for the boundary case which is obt ..."
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Cited by 57 (19 self)
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The convergence speed of building blocks depends on their marginal fitness contribution or on the salience structure of the problem. We use a sequential parameterization approach to build models of the differential convergence behavior, and derive time complexities for the boundary case which is obtained with an exponentially scaled problem (BinInt). We show that this domino convergence time complexity is linear in the number of building blocks (O(l)) for selection algorithms with constant selection intensity (such as tournament selection and ( ; ) or truncation selection), and exponential (O(2 l )) for proportionate selection. These complexities should be compared with the convergence speed for uniformly salient problems which are respectively (O( p l)) and (O(l ln l)). In addition we relate this facetwise model to a genetic drift model, and identify where and when the stochastic uctuations due to drift overwhelms the domino convergence, resulting in drift stall. The combined mo...
An Incremental Genetic Algorithm Approach to Multiprocessor Scheduling
 IEEE Transactions on Parallel and Distributed Systems
, 2004
"... Abstract—We have developed a genetic algorithm (GA) approach to the problem of task scheduling for multiprocessor systems. Our approach requires minimal problem specific information and no problem specific operators or repair mechanisms. Key features of our system include a flexible, adaptive proble ..."
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Cited by 49 (0 self)
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Abstract—We have developed a genetic algorithm (GA) approach to the problem of task scheduling for multiprocessor systems. Our approach requires minimal problem specific information and no problem specific operators or repair mechanisms. Key features of our system include a flexible, adaptive problem representation and an incremental fitness function. Comparison with traditional scheduling methods indicates that the GA is competitive in terms of solution quality if it has sufficient resources to perform its search. Studies in a nonstationary environment show the GA is able to automatically adapt to changing targets. Index Terms—Genetic algorithm, task scheduling, parallel processing. 1
The Race, the Hurdle, and the Sweet Spot: Lessons from Genetic Algorithms for the Automation of Design Innovation and Creativity
, 1998
"... this article, I will argue rather strongly that computational innovationat least certain important facets of the processes of innovationhas been achieved, and that computational creativity is plausibly within our sights. Specifically, I will argue that modern research in genetic algorithmss ..."
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Cited by 47 (17 self)
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this article, I will argue rather strongly that computational innovationat least certain important facets of the processes of innovationhas been achieved, and that computational creativity is plausibly within our sights. Specifically, I will argue that modern research in genetic algorithmssearch