Multilevel Optimization Algorithms Based on Metamodel- and Fitness Inheritance-Assisted Evolutionary Algorithms

Giannakoglou, Kyriakos C.; Kampolis, Ioannis C.

doi:10.1007/978-3-642-10701-6_3

Cited by 11 publications

(5 citation statements)

References 67 publications

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“…Problem approximation is used with function approximation in [151] to decrease the computational complexity of the problem in question and the numbers of function evaluations. Moreover, the use of multilevel approaches [43,68] which depend on the problem to be solved needs more attention from both researchers and practitioners. In these approaches, either different solvers were used to solve governing equations (e.g.…”

Section: Promising Elements In the Literaturementioning

confidence: 99%

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A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

et al. 2017

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Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008-2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation based algorithms. We also compare these algorithms based on different criteria such as metamodelling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive mmultiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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Section: Promising Elements In the Literaturementioning

confidence: 99%

“…Navier-Stokes equations) or different problems were solved at different levels. For more details about multilevel approaches, see [43].…”

Section: Promising Elements In the Literaturementioning

confidence: 99%

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

et al. 2017

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“…Extending fitness inheritance to multiobjective optimization involves several issues, mainly related to its apparent limitation for dealing with non-convex Pareto fronts [45]. However, some researchers have managed to successfully adapt fitness inheritance to MOEAs [55,128,135,169], reporting important savings on the total number of objective function evaluations performed.…”

Section: Dealing With Expensive Objective Functionsmentioning

confidence: 99%

Evolutionary multiobjective optimization: open research areas and some challenges lying ahead

Coello¹,

Brambila²,

Gamboa³

et al. 2019

Complex Intell. Syst.

126

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Evolutionary multiobjective optimization has been a research area since the mid-1980s, and has experienced a very significant activity in the last 20 years. However, and in spite of the maturity of this field, there are still several important challenges lying ahead. This paper provides a short description of some of them, with a particular focus on open research areas, rather than on specific research topics or problems. The main aim of this paper is to motivate researchers and students to develop research in these areas, as this will contribute to maintaining this discipline active during the next few years.

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“…A closely-related idea, utilized in a different application and treated by Artificial Immune Systems, was presented in [47]. Finally, a metamodel-assisted framework for expensive aerodynamics simulationbased optimization problems, either single-or multi-objective, was devised in [17]. This comprehensive framework proposed an EA in possibly three multi-level modes -one of which was multi-level parameterization.…”

Section: Introductionmentioning

confidence: 99%

Multi-Level Evolution Strategies for High-Resolution Black-Box Control

Shir¹,

Xi²,

Rabitz³

2020

Preprint

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This paper introduces a multi-level (m-lev) mechanism into Evolution Strategies (ESs) in order to address a class of global optimization problems that could benefit from fine discretization of their decision variables. Such problems arise in engineering and scientific applications, which possess a multi-resolution control nature, and thus may be formulated either by means of low-resolution variants (providing coarser approximations with presumably lower accuracy for the general problem) or by high-resolution controls. A particular scientific application concerns practical Quantum Control (QC) problems, whose targeted optimal controls may be discretized to increasingly higher resolution, which in turn carries the potential to obtain better control yields. However, state-of-the-art derivative-free optimization heuristics for high-resolution formulations nominally call for an impractically large number of objective function calls. Therefore, an effective algorithmic treatment for such problems is needed. We introduce a framework with an automated scheme to facilitate guided-search over increasingly finer levels of control resolution for the optimization problem, whose on-the-fly learned parameters require careful adaptation. We instantiate the proposed m-lev self-adaptive ES framework by two specific strategies, namely the classical elitist single-child (1+1)-ES and the non-elitist multi-child derandomized (µW , λ)-sep-CMA-ES. We first show that the approach is suitable by simulation-based optimization of QC systems which were heretofore viewed as too complex to address. We also present a laboratory proof-of-concept for the proposed approach on a basic experimental QC system objective.

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Multilevel Optimization Algorithms Based on Metamodel- and Fitness Inheritance-Assisted Evolutionary Algorithms

Cited by 11 publications

References 67 publications

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

Evolutionary multiobjective optimization: open research areas and some challenges lying ahead

Multi-Level Evolution Strategies for High-Resolution Black-Box Control

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