Analysis of the (1,λ)-σ-Self-Adaptation Evolution Strategy with repair by projection applied to a conically constrained problem

Spettel, Patrick; Beyer, Hans-Georg

doi:10.1016/j.tcs.2018.10.036

Cited by 3 publications

(12 citation statements)

References 13 publications

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“…is introduced, which returnsx of the problem (4). Appendix A in the supplementary material of Spettel and Beyer (2018b) shows a geometrical approach for deriving a closed-form solution to the projection optimization problem (4). Given an infeasible individual x, it readŝ…”

Section: Problem and Algorithmmentioning

confidence: 99%

“…Similar to the analysis in Section IV of Spettel and Beyer (2018b), fluctuation terms are neglected and deterministic evolution equations under asymptotic assumptions are derived. This allows predicting the mean value dynamics of the ES.…”

Section: Derivation Of a Mean Value Iterative System For Modeling Thementioning

confidence: 99%

“…(it is referred to Appendix B in the supplementary material of Spettel and Beyer (2018b) for the detailed derivation). The results that build the basis for the following CSA analysis are briefly recapped here.…”

Section: Derivation Of Mean Value Difference Equations For X and Rmentioning

confidence: 99%

“…2 infeas ] have already been derived in Appendix D in the supplementary material of Spettel and Beyer (2018b). The used Taylor approximation in Equation (D.157) of that work allows using the square of Equation (D.165) for the feasible case yielding…”

Section: Derivation Of a Mean Value Difference Equation For Smentioning

confidence: 99%

“…Spettel and Beyer (2018a) have considered the same problem and have analyzed a (1, λ)-σ-Self-Adaptation ES (σSA-ES). It has been extended to the multi-recombinative (µ/µ I , λ) variant (Spettel and Beyer, 2018b). The contribution of this paper is the analysis considering CSA instead of σSA for the mutation strength control mechanism.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the (μ/μI,λ)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

Spettel

Beyer

2020

Evolutionary Computation

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Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Non-linear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs.

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Section: Problem and Algorithmmentioning

confidence: 99%

Section: Derivation Of a Mean Value Iterative System For Modeling Thementioning

confidence: 99%

Section: Derivation Of Mean Value Difference Equations For X and Rmentioning

confidence: 99%

Section: Derivation Of a Mean Value Difference Equation For Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of the (μ/μI,λ)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

Spettel

Beyer

2020

Evolutionary Computation

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Analysis of the (μ/μI,λ)-σ-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem

Spettel

Beyer

2019

IEEE Trans. Evol. Computat.

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EDA++: Estimation of Distribution Algorithms With Feasibility Conserving Mechanisms for Constrained Continuous Optimization

Shirazi

Ceberio

Lozano

2022

IEEE Trans. Evol. Computat.

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Handling non-linear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and non-linear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this paper, we adopt the framework of Estimation of Distribution Algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with non-linear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint handling methods. Conducted experiments confirm the speed, robustness and efficiency of the proposed algorithm in tackling various problems with linear and non-linear constraints.

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Analysis of the (1,λ)-σ-Self-Adaptation Evolution Strategy with repair by projection applied to a conically constrained problem

Cited by 3 publications

References 13 publications

Analysis of the (μ/μI,λ)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

Analysis of the (μ/μI,λ)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

Analysis of the (μ/μI,λ)-σ-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem

EDA++: Estimation of Distribution Algorithms With Feasibility Conserving Mechanisms for Constrained Continuous Optimization

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