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

Peitz, Sebastian; Dellnitz, Michael

doi:10.20944/preprints201805.0221.v2

Cited by 9 publications

(7 citation statements)

References 128 publications

(163 reference statements)

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“…the set of the best compromises, which is also called the Pareto set). Many methods have been developed for multicriteria optimal control, and they are usually classified in three categories [ 136 ]: scalarization techniques, continuation methods and set-oriented approaches. Here we use the -constraint scalarization method, which transforms the original multiobjective problem into a finite set of single-objective optimal control problems.…”

Section: Methodsmentioning

confidence: 99%

Using optimal control to understand complex metabolic pathways

Tsiantis

Banga

2020

BMC Bioinformatics

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Background Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria. Results Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

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Section: Methodsmentioning

confidence: 99%

Using optimal control to understand complex metabolic pathways

Tsiantis

Banga

2020

BMC Bioinformatics

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“…Alternatively, one can compute a crude approximation of the entire front 7,8,38 or compute Pareto optimal controller parameters offline 9,10 . An extensive survey of feedback control with multiple objectives can be found in Reference 4. Before describing our method for addressing the real‐time requirements in Section 4, we will first discuss the importance of symmetries in the next section since these will play a crucial role for the cost of the offline phase.…”

Section: Multiobjective Optimization and Model Predictive Controlmentioning

confidence: 99%

“…Regardless of the solution method (cf Reference 1 for an introduction to deterministic and Reference 2 for evolutionary methods), the computation of the entire Pareto set is infeasible in the real‐time context, that is, in a model predictive control (MPC) framework 3 . There exist several approaches to circumvent this dilemma, see Reference 4 for a survey. One is a priori scalarization, where the conflicting objectives are synthesized into a scalar objective using, for example, weighted sums 5 or reference point techniques 6 .…”

Section: Introductionmentioning

confidence: 99%

Explicit multiobjective model predictive control for nonlinear systems with symmetries

Ober‐Blöbaum

Peitz

2020

Intl J Robust & Nonlinear

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Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, solving model-based optimal control problems in a very short amount of time can be challenging. For linear-quadratic problems, Bemporad et al have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and-more importantly-problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multiparametric programming approach is no longer valid in the nonlinear situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving. K E Y W O R D S (explicit) model predictive control, motion primitives, multiobjective optimal control, multiobjective optimization, symmetries This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…As this requires the solution of MOPs in real‐time, special measures need to be taken in the case of multiple criteria. Possible approaches are the weighting of objectives 1 or reference point tracking , 2 see also Peitz and Dellnitz 3 for an overview. An alternative approach is explicit MPC , 4 where instead of solving an optimization problem online, the optimal input is selected from a library of optimal inputs which is computed in an offline phase.…”

Section: Introductionmentioning

confidence: 99%

“…Then a small part of length t c ≤ t p is applied to the real system, and the problem has to be solved again on a shifted time horizon, that is, for t 0 = t 0 + t c and t e = t e + t p . Several extensions to multiple objectives have been presented 3 . Well‐known approaches are the weighted sum method 1 or reference point tracking 2 …”

Section: Introductionmentioning

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

Cited by 9 publications

References 128 publications

Using optimal control to understand complex metabolic pathways

Using optimal control to understand complex metabolic pathways

Explicit multiobjective model predictive control for nonlinear systems with symmetries

Explicit multiobjective model predictive control for nonlinear systems under uncertainty

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