A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization

Basseur, Matthieu; Zitzler, Eckart

doi:10.1007/11732242_71

Cited by 33 publications

(20 citation statements)

References 9 publications

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“…Definition 3) was first introduced in order to handle uncertain objective values. Uncertainty has also been considered in the context of multiobjective evolutionary computation, see, e.g., [59][60][61]. Alternative methods such as probabilistic [62,63], deterministic [64] or set-oriented approaches [65,66] have also been proposed.…”

Section: Solution Methodsmentioning

confidence: 99%

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A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

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Abstract:Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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Section: Solution Methodsmentioning

confidence: 99%

“…Here, inexactness is introduced due to uncertainties in pricing. -dominance can be used for the development of algorithms for MOPs with uncertainties [59,[61][62][63]65,67,68], for accelerating expensive MOPs [60,66,73] as well as for increasing the number of compromise solutions for the decision maker [63][64][65]69].…”

Section: Inaccuracies and -Dominancementioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

View full text Add to dashboard Cite

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“…These approaches all build on the work of [13], [14] for the calculation of dominance probabilities. In [7] each solution is modelled as having a probability distribution over objective space, which is estimated by drawing samples at locations and used to estimate the expected indicator function to drive the search process. In [23] the probability of dominance is calculated based on [14] (which assumes the noise is independent on each dimension and Gaussian in nature) and integrated into an estimation of distribution/particle swarm optimisation hybrid algorithm.…”

Section: Noise-tolerant Moeasmentioning

confidence: 99%

“…However, in many problems there is additional uncertainty in the veracity of the results obtained from the system model. Clear examples arise in "embodied" optimisation [1], [2], [3], where measurement error or stochastic elements in a physical system leads to different results for repeated evaluations at the same parameter values [4], [5] or when the objectives are derived from Monte Carlo simulations or data-driven systems [6], [7].…”

Section: Introductionmentioning

confidence: 99%

“…However, it was not until the early 2000s that a significant number of multi-objective optimisers began to be developed specifically to tackle uncertain optimisation [12], [13], [14], [5], [6], [15], [7], [16], [17], [18], [19], [20], [21], [22], [23]. Typically uncertainty is modelled as noise added to the function evaluations, although recent work has begun looking at the situation where the objective functions themselves are uncertain [24].…”

Section: Introductionmentioning

confidence: 99%

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The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems

Fieldsend

Everson

2015

IEEE Trans. Evol. Computat.

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Abstract-As methods for evolutionary multi-objective optimisation (EMO) mature and are applied to a greater number of real world problems, there has been gathering interest in the effect of uncertainty and noise on multi-objective optimisation. Specifically, how algorithms are affected by it, how to mitigate its effects, and whether some optimisers are better suited to dealing with it than others. Here we address the problem of uncertain evaluation, where the uncertainty can be modelled as additive noise in objective space. We develop a novel algorithm, the rolling tide evolutionary algorithm (RTEA), which progressively improves the accuracy of its estimated Pareto set, whilst simultaneously driving the front towards the true Pareto front. It can cope with noise whose characteristics change as a function of location (both design and objective), or which alter during the course of an optimisation. Four state-of-the-art noisetolerant EMO algorithms, as well as four widely used standard EMO algorithms, are compared to RTEA on 70 instances of ten continuous space test problems from the CEC'09 multiobjective optimisation test suite. Different instances of these problems are generated by modifying them to exhibit different types and intensities of noise. RTEA is seen to provide competitive performance across both the range of test problems used, and noise types.

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Robust Multi‐Objective Genetic Algorithm (RMOGA) with Online Approximation under Interval Uncertainty

Butt

Almansoori

et al. 2013

Multi‐Objective Optimization in Chemical Engineering

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A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization

Cited by 33 publications

References 9 publications

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems

Robust Multi‐Objective Genetic Algorithm (RMOGA) with Online Approximation under Interval Uncertainty

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