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220
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 1815 (60 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.
A Fast Elitist NonDominated Sorting Genetic Algorithm for MultiObjective Optimization: NSGAII
, 2000
"... Multiobjective evolutionary algorithms which use nondominated 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) nonelitism approach, and (iii) the need for specifying a sharing ..."
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Cited by 662 (15 self)
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Multiobjective evolutionary algorithms which use nondominated 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) 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 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 NSGAII is able to find much better spread of solutions in all problems compared to PAESanother elitist multiobjective EA which pays special attention towards creating a diverse Paretooptimal front. Because of NSGAII's low computational requirements, elitist approach, and parameterless sharing approach, NSGAII should find increasing applications in the years to come.
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
, 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 ..."
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Cited by 628 (41 self)
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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 Paretooptimal 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.
An Efficient Constraint Handling Method for Genetic Algorithms
 Computer Methods in Applied Mechanics and Engineering
, 1998
"... Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods hav ..."
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Cited by 246 (19 self)
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Many realworld search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's populationbased approach and ability to make pairwise comparison in tournament selection operator are explo...
Tackling realcoded genetic algorithms: operators and tools for the behavioural analysis
 Arti Intelligence Reviews
, 1998
"... Abstract. Genetic algorithms play a significant role, as search techniques for handling complex spaces, in many fields such as artificial intelligence, engineering, robotic, etc. Genetic algorithms are based on the underlying genetic process in biological organisms and on the natural evolution prin ..."
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Cited by 198 (27 self)
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Abstract. Genetic algorithms play a significant role, as search techniques for handling complex spaces, in many fields such as artificial intelligence, engineering, robotic, etc. Genetic algorithms are based on the underlying genetic process in biological organisms and on the natural evolution principles of populations. These algorithms process a population of chromosomes, which represent search space solutions, with three operations: selection, crossover and mutation. Under its initial formulation, the search space solutions are coded using the binary alphabet. However, the good properties related with these algorithms do not stem from the use of this alphabet; other coding types have been considered for the representation issue, such as real coding, which would seem particularly natural when tackling optimization problems of parameters with variables in continuous domains. In this paper we review the features of realcoded genetic algorithms. Different models of genetic operators and some mechanisms available for studying the behaviour of this type of genetic algorithms are revised and compared. Key words: genetic algorithms, real coding, continuous search spaces Abbreviations: GAs – genetic algorithms; BCGA – binarycoded genetic algorithm; RCGA – realcoded genetic algorithm
Indicatorbased selection in multiobjective search
 in Proc. 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII
, 2004
"... Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection ..."
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Cited by 172 (12 self)
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Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection process. To this end, we propose a general indicatorbased evolutionary algorithm (IBEA) that can be combined with arbitrary indicators. In contrast to existing algorithms, IBEA can be adapted to the preferences of the user and moreover does not require any additional diversity preservation mechanism such as fitness sharing to be used. It is shown on several continuous and discrete benchmark problems that IBEA can substantially improve on the results generated by two popular algorithms, namely NSGAII and SPEA2, with respect to different performance measures. 1
Combining convergence and diversity in evolutionary multiobjective optimization
 Evolutionary Computation
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms c ..."
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Cited by 159 (15 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Paretooptimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Paretooptimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Paretooptimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept ofdominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modi�cations to the baseline algorithm are also suggested. The concept ofdominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
A Computationally Efficient Evolutionary Algorithm for RealParameter Optimization
, 2002
"... Due to an increasing interest in solving realworld optimization problems using evolutionary algorithms (EAs), researchers have developed a number of realparameter genetic algorithms (GAs) in the recent past. In such studies, the main research effort is spent on developing an efficient recombina ..."
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Cited by 91 (11 self)
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Due to an increasing interest in solving realworld optimization problems using evolutionary algorithms (EAs), researchers have developed a number of realparameter genetic algorithms (GAs) in the recent past. In such studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an ospring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parentcentric recombination operator (PCX) and a steadystate, elitepreserving, scalable, and computationally fast populationalteration model (we called the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonlyused test problems and is compared with a number of evolutionary and classical optimization algorithms including other realparameter GAs with UNDX and SPX operators, the correlated selfadaptive evolution strategy, the dierential evolution technique and the quasiNewton method. The proposed approach is found to be consistently and reliably performing better than all other methods used in the study. A scaleup study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling realparameter optimization problems.
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.