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Journal Article

MOPED: A multi-objective parzen-based estimation of distribution algorithm for continuous problems

TL;DR: In this article, an evolutionary multi-objective optimization tool based on an estimation of distribution algorithm is proposed, which uses the ranking method of non-dominated sorting genetic algorithm-II and the Parzen estimator to approximate the probability density of solutions lying on the Pareto front.
Abstract: An evolutionary multi-objective optimization tool based on an estimation of distribution algorithm is proposed. The algorithm uses the ranking method of non-dominated sorting genetic algorithm-II and the Parzen estimator to approximate the probability density of solutions lying on the Pareto front. The proposed algorithm has been applied to different types of test case problems and results show good performance of the overall optimization procedure in terms of the number of function evaluations. An alternative spreading technique that uses the Parzen estimator in the objective function space is proposed as well. When this technique is used, achieved results appear to be qualitatively equivalent to those previously obtained by adopting the crowding distance described in non-dominated sorting genetic algorithm-II.
Citations
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Proceedings ArticleDOI
Aimin Zhou1, Yaochu Jin2, Qingfu Zhang1, Bernhard Sendhoff2, Edward Tsang1 
24 Jan 2006
TL;DR: The proposed hybrid method is verified on widely used test problems and simulation results show that the method is effective in achieving Pareto-optimal solutions compared to two state-of-the-art evolutionary multi-objective algorithms.
Abstract: In our previous work conducted by Aimin Zhou et. al., (2005), it has been shown that the performance of multi-objective evolutionary algorithms can be greatly enhanced if the regularity in the distribution of Pareto-optimal solutions is used. This paper suggests a new hybrid multi-objective evolutionary algorithm by introducing a convergence based criterion to determine when the model-based method and when the genetics-based method should be used to generate offspring in each generation. The basic idea is that the genetics-based method, i.e., crossover and mutation, should be used when the population is far away from the Pareto front and no obvious regularity in population distribution can be observed. When the population moves towards the Pareto front, the distribution of the individuals will show increasing regularity and in this case, the model-based method should be used to generate offspring. The proposed hybrid method is verified on widely used test problems and our simulation results show that the method is effective in achieving Pareto-optimal solutions compared to two state-of-the-art evolutionary multi-objective algorithms: NSGA-II and SPEA2, and our pervious method in Aimin Zhou et. al., (2005).

281 citations

Journal ArticleDOI
TL;DR: This paper proposes a new model-based method for representing and searching nondominated solutions that is able to alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated.
Abstract: To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.

248 citations

BookDOI
01 Jan 2012
TL;DR: This work proposes customized model ensembles on demand, inspired by Lazy Learning, which finds the most relevant models from a DB of models, using their meta-information, and creates an ensemble, which produces an output that is a weighted interpolation or extrapolation of the outputs of the models ensemble.
Abstract: In the not so distant future, we expect analytic models to become a commodity. We envision having access to a large number of data-driven models, obtained by a combination of crowdsourcing, crowdservicing, cloud-based evolutionary algorithms, outsourcing, in-house development, and legacy models. In this new context, the critical question will be model ensemble selection and fusion, rather than model generation. We address this issue by proposing customized model ensembles on demand, inspired by Lazy Learning. In our approach, referred to as Lazy Meta-Learning, for a given query we find the most relevant models from a DB of models, using their meta-information. After retrieving the relevant models, we select a subset of models with highly uncorrelated errors. With these models we create an ensemble and use their meta-information for dynamic bias compensation and relevance weighting. The output is a weighted interpolation or extrapolation of the outputs of the models ensemble. Furthermore, the confidence interval around the output is reduced as we increase the number of uncorrelated models in the ensemble. We have successfully tested this approach in a power plant management application.

171 citations

Journal ArticleDOI
TL;DR: A taxonomy and a comprehensive review of applications of MOEAs in aeronautical and aerospace design problems are presented and some potential paths for future research are provided, which are considered promising within this area.
Abstract: Nowadays, the solution of multiobjective optimization problems in aeronautical and aerospace engineering has become a standard practice. These two fields offer highly complex search spaces with different sources of difficulty, which are amenable to the use of alternative search techniques such as metaheuristics, since they require little domain information to operate. From the several metaheuristics available, multiobjective evolutionary algorithms (MOEAs) have become particularly popular, mainly because of their availability, ease of use, and flexibility. This paper presents a taxonomy and a comprehensive review of applications of MOEAs in aeronautical and aerospace design problems. The review includes both the characteristics of the specific MOEA adopted in each case, as well as the features of the problems being solved with them. The advantages and disadvantages of each type of approach are also briefly addressed. We also provide a set of general guidelines for using and designing MOEAs for aeronautical and aerospace engineering problems. In the final part of the paper, we provide some potential paths for future research, which we consider promising within this area.

142 citations

Journal ArticleDOI
TL;DR: This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems and gives a survey of Probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compares different methods for probabilism modeling in these algorithms.
Abstract: Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

100 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Abstract: : Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and of determining the mode of a probability function are discussed. Only estimates which are consistent and asymptotically normal are constructed. (Author)

10,114 citations

Journal ArticleDOI
TL;DR: The problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front are studied to enable researchers to test their algorithms for specific aspects of multi- objective optimization.
Abstract: 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 multi-objective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multi-objective optimization.

1,439 citations

01 Jun 1994
TL;DR: This paper presents an empirical analysis of where the proposed technique will outperform genetic algorithms, and describes a class of problems in which a genetic algorithm may be able to perform better.
Abstract: Genetic algorithms (GAs) are biologically motivated adaptive systems which have been used, with varying degrees of success, for function optimization. In this study, an abstraction of the basic genetic algorithm, the Equilibrium Genetic Algorithm (EGA), and the GA in turn, are reconsidered within the framework of competitive learning. This new perspective reveals a number of different possibilities for performance improvements. This paper explores population-based incremental learning (PBIL), a method of combining the mechanisms of a generational genetic algorithm with simple competitive learning. The combination of these two methods reveals a tool which is far simpler than a GA, and which out-performs a GA on large set of optimization problems in terms of both speed and accuracy. This paper presents an empirical analysis of where the proposed technique will outperform genetic algorithms, and describes a class of problems in which a genetic algorithm may be able to perform better. Extensions to this algorithm are discussed and analyzed. PBIL and extensions are compared with a standard GA on twelve problems, including standard numerical optimization functions, traditional GA test suite problems, and NP-Complete problems.

1,264 citations

Proceedings Article
13 Jul 1999
TL;DR: Preliminary experiments show that the BOA outperforms the simple genetic algorithm even on decomposable functions with tight building blocks as a problem size grows.
Abstract: In this paper, an algorithm based on the concepts of genetic algorithms that uses an estimation of a probability distribution of promising solutions in order to generate new candidate solutions is proposed. To estimate the distribution, techniques for modeling multivariate data by Bayesian networks are used. The proposed algorithm identifies, reproduces and mixes building blocks up to a specified order. It is independent of the ordering of the variables in the strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm. However, prior information is not essential. Preliminary experiments show that the BOA outperforms the simple genetic algorithm even on decomposable functions with tight building blocks as a problem size grows.

1,073 citations