Evolutionary Multi-objective Ranking with Uncertainty and Noise

Hughes, E.J.

doi:10.1007/3-540-44719-9_23

Cited by 168 publications

(159 citation statements)

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“…(Horn and Nafpliotis 1993) were among the first to discuss uncertainty in the light of generating methods, although they did not propose a particular multiobjective optimizer for this purpose. Several 1 years later, Hughes (2001) and Teich (2001) independently proposed stochastic extensions of Pareto dominance and suggested similar ways to integrate probabilistic dominance in the fitness assignment procedure; both studies consider special types of probability distributions. In (Babbar, Lakshmikantha, and Goldberg 2003), another ranking method is proposed which is based on the average value per objective and the variance of the set of evaluations.…”

Section: Motivationmentioning

confidence: 99%

“…Therefore, we propose a general indicator-based model for uncertainty where every solution is associated with an arbitrary probability distribution over the objective space. Extending (Zitzler and Künzli 2004), different algorithms for this model and a particular quality indicator, namely the ǫ-indicator, are presented and investigated in comparison with the methods in (Hughes 2001) and (Deb and Gupta 2005). Moreover, this paper also considers the issue of analyzing and visualizing Pareto set approximations in the presence of uncertainty, which to our best knowledge has not been considered so far in the multiobjective literature.…”

Section: Motivationmentioning

confidence: 99%

“…• The second approach (P DR) is the fitness assignment method proposed by Hughes (2001) which is based on the probabilistic dominance relation between solutions:…”

Section: Algorithm Designmentioning

confidence: 99%

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Handling Uncertainty in Indicator-Based Multiobjective Optimization

Basseur

Zitzler

2006

IJCIR

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Real-world optimization problems are often subject to uncertainties caused by, e.g., missing information in the problem domain or stochastic models. These uncertainties can take different forms in terms of distribution, bounds, and central tendency. In the multiobjective context, some approaches have been proposed to take uncertainties into account within the optimization process. Most of them are based on a stochastic extension of Pareto dominance that is combined with standard, non-stochastic diversity preservation mechanisms. Furthermore, it is often assumed that the shape of the underlying probability distribution is known and that for each solution there is a 'true' objective value per dimension which is disturbed by noise.In this paper, we consider a slightly different scenario where the optimization goal is specified in terms of a quality indicator-a real-valued function that induces a total preorder on the set of Pareto set approximations. We propose a general indicator-model that can handle any type of distribution representing the uncertainty, allows different distributions for different solutions, and does not assume a 'true' objective vector per solution, but in general regards a solution to be inherently associated with an unknown probability distribution in the objective space. To this end, several variants of an evolutionary algorithm for a specific quality indicator, namely the ǫ-indicator, are suggested and empirically investigated. The comparison to existing techniques such as averaging or probabilistic dominance ranking indicates that the proposed approach is especially useful for high-dimensional objective spaces. Moreover, we introduce a general methodology to visualize and analyze Pareto set approximations in the presence of uncertainty which extends the concept of attainment functions. I. MotivationKnowledge about the set of Pareto-optimal solutions is useful in many applications involving multiple objectives. Therefore, considerable research, particularly in the context of evolutionary computation, has been devoted to generating methods, i.e., techniques that try to generate the entire Pareto set or approximations of it. One recent approach is based on quality indicators where a function I assigns each Pareto set approximation a real value reflecting its quality, cf. (Zitzler et al. 2003); the goal is to identify a Pareto set approximation that minimizes (or maximizes) I. As such, I induces a total order of the set of approximation sets in the objective space, in contrast to the classical aggregation functions like weighted sum that operate on single solutions only and gives rise to a total order of the corresponding objective vectors. Since evolutionary multiobjective optimization using quality indicators is a relatively new concept, it is an open question how to deal with uncertainties in this framework. Many real-world optimization problems are subject to uncertainties and therefore this aspect needs to be accounted for. Among the different types of uncertainty one can distin...

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Section: Motivationmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

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Handling Uncertainty in Indicator-Based Multiobjective Optimization

Basseur

Zitzler

2006

IJCIR

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“…Most of them assume particular noise distributions in advance; for example, normal distributions [1,[8][9][10]13], uniform distributions [14] and Poisson distributions [6,17]. Given a noise distribution, existing noise-aware dominance operators collect objective value samples from each individual [6,8,9,14,17], or each cluster of individuals [1], in order to determine dominance relationships among individuals.…”

Section: Related Workmentioning

confidence: 99%

A Non-parametric Statistical Dominance Operator for Noisy Multiobjective Optimization

Phan

Suzuki

2012

Lecture Notes in Computer Science

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Abstract. This paper describes and evaluates a new noise-aware dominance operator for evolutionary algorithms to solve the multiobjective optimization problems (MOPs) that contain noise in their objective functions. This operator is designed with the Mann-Whitney U -test, which is a non-parametric (i.e., distribution-free) statistical significance test. It takes objective value samples of given two individuals, performs a U -test on the two sample sets and determines which individual is statistically superior. Experimental results show that it operates reliably in noisy MOPs and outperforms existing noise-aware dominance operators particularly when many outliers exist under asymmetric noise distributions.

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“…Probability-based With the probability-based Pareto ranking scheme, the original Pareto ranking scheme is replaced by a probabilistic ranking process that takes noise into consideration (Hughes, 2001;Teich, 2001). In this ranking process, a solution s is assigned a rank representing the sum of probabilities that each of the solutions in the population dominates s (the lower the rank, the better the solution).…”

Section: Modified Pareto Ranking Schemementioning

confidence: 99%

Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling

Syberfeldt

John

et al. 2010

European Journal of Operational Research

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Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling. European Journal of Operational AbstractMany real-world optimisation problems approached by evolutionary algorithms are subject to noise. When noise is present, the evolutionary selection process may become unstable and the convergence of the optimisation adversely affected. In this paper, we present a new technique that efficiently deals with noise in multi-objective optimisation. This technique aims at preventing the propagation of inferior solutions in the evolutionary selection due to noisy objective values. This is done by using an iterative resampling procedure that reduces the noise until the likelihood of selecting the correct solution reaches a given confidence level. To achieve an efficient utilisation of resources, the number of samples used per solution varies based on the amount of noise in the present area of the search space. The proposed algorithm is evaluated on the ZDT benchmark problems and two complex real-world problems of manufacturing optimisation. The first realworld problem concerns the optimisation of engine component manufacturing in aviation industry, while the second real-world problem concerns the optimisation of a camshaft machining line in automotive industry. The results from the optimisations indicate that the proposed technique is successful in reducing noise, and it competes successfully with other noise handling techniques.

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Evolutionary Multi-objective Ranking with Uncertainty and Noise

Cited by 168 publications

References 3 publications

Handling Uncertainty in Indicator-Based Multiobjective Optimization

Handling Uncertainty in Indicator-Based Multiobjective Optimization

A Non-parametric Statistical Dominance Operator for Noisy Multiobjective Optimization

Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling

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