Pareto Explorer: a global/local exploration tool for many-objective optimization problems

Schütze, Oliver; Cuate, Oliver; Martín, Adanay; Peitz, Sebastian; Dellnitz, Michael

doi:10.1080/0305215x.2019.1617286

Cited by 32 publications

(33 citation statements)

References 35 publications

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“…The optimizer produces feasible points and the decision maker provides preference information. 38,39 In this work, we investigate a hybrid approach. First, we compute an approximation to the efficient set of the family of uMOCP in an offline fashion.…”

Section: The Methodsmentioning

confidence: 99%

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Explicit multiobjective model predictive control for nonlinear systems under uncertainty

Castellanos

Ober‐Blöbaum

Peitz

2020

Intl J Robust & Nonlinear

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In real-world problems, uncertainties (eg, errors in the measurement, precision errors, among others) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where in the case of uncertainties, optimal solutions can degrade in quality or they can even become unfeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multiobjective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control. For such problems, not much has been reported in terms of uncertainties. To address this problem class, we design an offline/online framework to compute an approximation of efficient control strategies. In order to reduce the numerical cost of the offline phase-which grows exponentially with the parameter dimension-we exploit symmetries in the control problems. Furthermore, in order to ensure optimality of the solutions, we include an additional online optimization step, which is considerably cheaper than the original multiobjective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multiobjective framework allows for online adaptations of the desired objective. Our results show that the method is capable of designing driving strategies that deal better with uncertainties in the initial conditions, which translates into potentially safer and faster driving strategies.

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Section: The Methodsmentioning

confidence: 99%

“…▪ Next, we investigate the limit behavior of the sequence A i of archives. To guarantee convergence, we have to assume the following (see also Shütze et al 39,43 ):…”

Section: Algorithm 2 Generic Stochastic Search Algorithmmentioning

confidence: 99%

Explicit multiobjective model predictive control for nonlinear systems under uncertainty

Castellanos

Ober‐Blöbaum

Peitz

2020

Intl J Robust & Nonlinear

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“…Both methods are well known for problems related to multi-modality, solution equivalence, and low resolution. It is known that the Pareto approach can provide detailed insight into details of feasible solutions and support the decision of choosing the final one [2,6,10,12,15]. Herein, we analyze the other approach in which solutions from Pareto front are taken into consideration all at once.…”

Section: Methodsmentioning

confidence: 99%

“…Additionally, classic joint inversion suffers from the necessity of weighting and scaling target functions from incomparable methods. One of the possible strategies of solving this problem is the Pareto approach [2,4,6,10,12,15], however, it does not provide one sure answer about the final model, but rather kind of set of equally feasible solutions. What is worse, the same set of parameters can produce a few different models what raises the problem of equivalence.…”

Section: Introductionmentioning

confidence: 99%

Pareto Joint Inversion of 2D magnetometric and gravity data- synthetic study

et al. 2019

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Pareto joint inversion for two or more data sets is an attractive and promising tool which eliminates target functions weighing and scaling, providing a set of acceptable solutions composing a Pareto front. In former author’s study MARIA (Modular Approach Robust Inversion Algorithm) was created as a flexible software based on global optimization engine (PSO) to obtain model parameters in process of Pareto joint inversion of two geophysical data sets. 2D magnetotelluric and gravity data were used for preliminary tests, but the software is ready to handle data from more than two geophysical methods. In this contribution, the authors’ magnetometric forward solver was implemented and integrated with MARIA. The gravity and magnetometry forward solver was verified on synthetic models. The tests were performed for different models of a dyke and showed, that even when the starting model is a homogeneous area without anomaly, it is possible to recover the shape of a small detail of the real model. Results showed that the group analysis of models on the Pareto front gives more information than the single best model. The final stage of interpretation is the raster map of Pareto front solutions analysis.

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“…Hence, it is rather unclear if these solutions are indeed the "ideal" solutions according to the given problem. The Pareto Explorer (PE [30]) is a global/local exploration tool for the numerical treatment of MaOPs: in a first step, one (or several) optimal solutions are computed and presented to the decision-maker. These could be the results of any of the above mentioned scalarization methods, or any other (preferably global) multi-objective solver.…”

Section: Introductionmentioning

confidence: 99%

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Cuate

Schütze

2020

Mathematics

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Optimization problems where several objectives have to be considered concurrently arise in many applications. Since decision-making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known as many objective optimization problems (MaOPs). For such problems, it is not possible any more to compute finite size approximations that suitably represent the entire solution set. If no users preferences are at hand, so-called knee points are promising candidates since they represent at least locally the best trade-off solutions among the considered objective values. In this paper, we extend the global/local exploration tool Pareto Explorer (PE) for the detection of such solutions. More precisely, starting from an initial solution, the goal of the modified PE is to compute a path of evenly spread solutions from this point along the Pareto front leading to a knee of the MaOP. The knee solution, as well as all other points from this path, are of potential interest for the underlying decision-making process. The benefit of the approach is demonstrated in several examples.

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Pareto Explorer: a global/local exploration tool for many-objective optimization problems

Cited by 32 publications

References 35 publications

Explicit multiobjective model predictive control for nonlinear systems under uncertainty

Explicit multiobjective model predictive control for nonlinear systems under uncertainty

Pareto Joint Inversion of 2D magnetometric and gravity data- synthetic study

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

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