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A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II
, 2000
"... Multi-objective evolutionary algorithms which use non-dominated 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) non-elitism approach, and (iii) the need for specifying a sharing param ..."
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Cited by 1815 (60 self)
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Multi-objective evolutionary algorithms which use non-dominated 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) 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(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 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. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems eciently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint non-linear problem, are compared with another constrained multi-objective optimizer and much better performance of NSGA-II is observed. Because of NSGA-II's low computational requirements, elitist approach, parameter-less niching approach, and simple constraint-handling strategy, NSGA-II should find increasing applications in the coming years.
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 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.
A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques
- Knowledge and Information Systems
, 1998
"... . This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search cap ..."
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Cited by 292 (22 self)
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. This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using genetic-based search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...
Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems
- Evolutionary Computation
, 1999
"... In this paper, we study the problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front. Identification of such features helps us develop difficult test problems for multi-objective optimization. Multi-objective test problems ..."
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Cited by 207 (11 self)
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In this paper, we study the problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front. Identification of such features helps us develop difficult test problems for multi-objective optimization. Multi-objective test problems are constructed from single-objective optimization problems, thereby allowing known difficult features of single-objective problems (such as multi-modality, isolation, or deception) to be directly transferred to the corresponding multi-objective 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 multi-objective optimization. Keywords Genetic algorithms, multi-objective optimization, niching, pareto-optimality, problem difficulties, test problems. 1 Introduction After a decade since the pioneering wor...
Multi-Objective Optimization Using Genetic Algorithms: A Tutorial
"... 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 ..."
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Cited by 114 (0 self)
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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.
PISA - A Platform and Programming Language Independent Interface for Search Algorithms
, 2003
"... This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hm-specific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules. ..."
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Cited by 107 (11 self)
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This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hm-specific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules.
Feature Selection in Unsupervised Learning via Evolutionary Search
- In Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
, 2000
"... Feature subset selection is an important problem in knowl- edge discovery, not only for the insight gained from deter- mining relevant modeling variables but also for the improved understandability, scalability, and possibly, accuracy of the resulting models. In this paper we consider the problem of ..."
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Cited by 79 (4 self)
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Feature subset selection is an important problem in knowl- edge discovery, not only for the insight gained from deter- mining relevant modeling variables but also for the improved understandability, scalability, and possibly, accuracy of the resulting models. In this paper we consider the problem of feature selection for unsupervised learning. A number of heuristic criteria can be used to estimate the quality of clusters built from a given featuresubset. Rather than combining such criteria, we use ELSA, an evolutionary lo- cal selection algorithm that maintains a diverse population of solutions that approximate the Pareto front in a multi- dimensional objectiv espace. Each evolved solution repre- sents a feature subset and a number of clusters; a standard K-means algorithm is applied to form the given n umber of clusters based on the selected features. Preliminary results on both real and synthetic data show promise in finding Pareto-optimal solutions through which we can identify the significant features and the correct number of clusters.
A Tutorial on Evolutionary Multiobjective Optimization
- In Metaheuristics for Multiobjective Optimisation
, 2003
"... Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. ..."
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Cited by 78 (0 self)
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Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1
Reducing Bloat and Promoting Diversity using Multi-Objective Methods
, 2001
"... Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We exp ..."
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Cited by 78 (5 self)
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Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We explore the potential of techniques from multi-objective optimization to aid GP by adding explicit objectives to avoid bloat and promote diversity. The even 3, 4, and 5-parity problems were solved efficiently compared to basic GP results from the literature. Even though only non-dominated individuals were selected and populations thus remained extremely small, appropriate diversity was maintained. The size of individuals visited during search consistently remained small, and solutions of what we believe to be the minimum size were found for the 3, 4, and 5-parity problems.
Statistical strategies for avoiding false discoveries in metabolomics and related experiments
, 2006
"... Many metabolomics, and other high-content or high-throughput, experiments are set up such that the primary aim is the discovery of biomarker metabolites that can discriminate, with a certain level of certainty, between nominally matched ‘case ’ and ‘control ’ samples. However, it is unfortunately ve ..."
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Cited by 61 (11 self)
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Many metabolomics, and other high-content or high-throughput, experiments are set up such that the primary aim is the discovery of biomarker metabolites that can discriminate, with a certain level of certainty, between nominally matched ‘case ’ and ‘control ’ samples. However, it is unfortunately very easy to find markers that are apparently persuasive but that are in fact entirely spurious, and there are well-known examples in the proteomics literature. The main types of danger are not entirely independent of each other, but include bias, inadequate sample size (especially relative to the number of metabolite variables and to the required statistical power to prove that a biomarker is discriminant), excessive false discovery rate due to multiple hypothesis testing, inappropriate choice of particular numerical methods, and overfitting (generally caused by the failure to perform adequate validation and cross-validation). Many studies fail to take these into account, and thereby fail to discover anything of true significance (despite their claims). We summarise these problems, and provide pointers to a substantial existing literature that should assist in the improved design and evaluation of metabolomics experiments, thereby allowing robust scientific conclusions to be drawn from the available data. We provide a list of some of the simpler checks that might improve one’s confidence that a candidate biomarker is not simply a statistical artefact, and suggest a series of preferred tests and visualisation tools that can assist readers and authors in assessing papers. These tools can be applied to individual metabolites by using multiple univariate tests performed in parallel across all metabolite peaks. They may also be applied to the validation of multivariate models. We stress in
