Computation of robust Pareto points

Dellnitz, Michael; Witting, Katrin

doi:10.1504/ijcsm.2009.027876

Cited by 22 publications

(13 citation statements)

References 17 publications

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“…A more detailed explanation of the variational approach can be found in [152], the path-following method has been published in [35], and the dissertation [151] gives a comprehensive overview of all topics covered in this section. The examples of the application of the numerical path-following method have been published in [23] (ICs) and [145] (RailCab) and the RailCab example of the variational method in [86].…”

Section: Further Readingmentioning

confidence: 99%

Methods of Improving the Dependability of Self-optimizing Systems

Dorociak

Gausemeier

2014

Lecture Notes in Mechanical Engineering

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Abstract. Various methods have been developed in the Collaborative ResearchCenter 614 which can be used to improve the dependability of self-optimizing systems. These methods are presented in this chapter. They are sorted into two categories with regard to the development process of self-optimizing systems. On one hand, there are methods which can be applied during the Conceptual Design Phase. On the other hand, there are methods that are applicable during Design and Development.There are domain-spanning methods as well as methods that have been specifically developed for particular domains, e.g., software engineering or control engineering. The methods address different attributes of dependability, such as reliability, availability or safety.Each section is prefaced with a short overview of the classification of the described method regarding the corresponding domain(s), as well as its dependability attributes, to provide the reader with a brief outline of the methods' areas of application. Information about independently applicable methods or existing relationships and interactions with other methods or third-party literature is also provided.The development process for self-optimizing mechatronic systems which was introduced in Chap. 2 consists of two main phases: Conceptual Design and Design and Development. The main result of the Conceptual Design is the Principle Solution, which includes all information required for the concrete development during the second phase. Conceptual Design PhaseEven as early as during the specification of the Principle Solution, the dependability of self-optimizing mechatronic systems can be evaluated and improved by employing appropriate methods. The result is an improved Principle Solution, as such methods take the whole system into account before splitting it up into domain-specific tasks for the following development phase.

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Section: Further Readingmentioning

confidence: 99%

Methods of Improving the Dependability of Self-optimizing Systems

Dorociak

Gausemeier

2014

Lecture Notes in Mechanical Engineering

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“…In [5] the same problem as studied in this work (ParMOP), is addressed. In that work, a numerical approach for the computation of points that stay substationary under the variation of an external parameter λ ∈ R within a given interval has been developed.…”

Section: State Of the Art Of Robustness Concepts For Multiobjective Omentioning

confidence: 99%

“…In contrast to this, in this paper a new robustness formulation is developed which is based on the minimization of the path length over the entire interval [λ start , λ end ]. Thus, the main difference to [5] is that the path is generated in a different way. To obtain this 'global' path the classical calculus of variations is used.…”

Section: State Of the Art Of Robustness Concepts For Multiobjective Omentioning

confidence: 99%

“…In Sect. 3, Example 1 a path generated by the approach described in [5] is compared to a path computed by the new approach presented in this paper. A deeper discussion about the differences and similarities between the two approaches can be found in [25].…”

Section: State Of the Art Of Robustness Concepts For Multiobjective Omentioning

confidence: 99%

“…But, as the Kuhn-Tucker constraints of the variational problem (25) depend on λ explicitly, the minimization of energy instead of length does in general not lead to the same optimal solution Fig. 1 Visualization of the λ-robust solution path (black), the λ-dependent Pareto set (on the left), the projection onto the x 1 -x 2 -plane (in the middle), and comparison of the robustness concept described in [5] with the variational approach for a given, fixed starting point (on the right) Example 1 Consider the parametric multiobjective optimization problem min x F :…”

Section: Since For a Matrix A It Holds Ker(a) ⊥ Image(a T )mentioning

confidence: 99%

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A variational approach to define robustness for parametric multiobjective optimization problems

2012

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In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter λ ∈ R, so-called parametric multiobjective optimization problems. The solution of such a problem is given by the λ-dependent Pareto set. In this work we give a new definition that allows to characterize λ-robust Pareto points, meaning points which hardly vary under the variation of the parameter λ. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe λ-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.

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Multiobjective optimization for interwoven systems

Klamroth

Mostaghim

Naujoks

et al. 2017

J. Multi-Crit. Decis. Anal.

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In practical situations, complex systems are often composed of subsystems or subproblems with single or multiple objectives. These subsystems focus on different aspects of the overall system, but they often have strong interactions with each other and they are usually not sequentially ordered or obviously decomposable. Thus, the individual solutions of subproblems do not generally induce a solution for the overall system. Here, we strive to identify "re-composition architectures" of such "interwoven" systems. Our intention is to connect the subsystems adequately, analyze the resulting performance, model/solve the overall system, and improve the overall solution instead of just solving each subsystem separately. We review recent developments in this field and discuss modeling and solution paradigms in a general and unified framework using the example of an interwoven system consisting of two interacting subsystems. KEYWORDSinterwoven systems, multiobjective optimization, systems of systems 1 As discussed in the next section, models and methods for dealing with multiobjective complex systems have been proposed in the literature, especially in the area of engineering optimization. However, they lack rigorous mathematical analyses and optimality proofs.

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Computation of robust Pareto points

Cited by 22 publications

References 17 publications

Methods of Improving the Dependability of Self-optimizing Systems

Methods of Improving the Dependability of Self-optimizing Systems

A variational approach to define robustness for parametric multiobjective optimization problems

Multiobjective optimization for interwoven systems

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