An Active-Set Evolution Strategy for Optimization with Known Constraints

Arnold, Dirk V.

doi:10.1007/978-3-319-45823-6_18

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…We experimentally confirm the affine invariance of ARCH and resampling technique 4 on the problems defined above. Moreover, we compare the behaviors of the CMA-ES with these constraint handling techniques with those of the CMA-ES on the unconstrained Figure 5 shows typical single runs of the CMA-ES (1st row) on unconstrained problems, and the CMA-ES with resampling (2nd row), AP-BCH (3rd row) and ARCH (4th row), respectively, on f sph and f ell with Box in n = 20.…”

Section: Resultssupporting

confidence: 53%

“…where A and b are as defined in (4). We define an initial mean vector and initial covariance matrix as m (0) and C (0) , respectively, on this coordinate system.…”

Section: Test Problemmentioning

confidence: 99%

“…A (1 + 1)-ES with a stochastic active-set method (Active-Set ES) [4,5] is a CHT for explicit constraints that it reduces the search space dimension by forcing active constraints to be equality constraints. Linear Constraint Covariance Matrix Self-Adaptation Evolution Strategy (lcCMSA-ES) [29] is a CHT for a variant of CMA-ES, namely CMSA-ES [11], on explictly and linearly constrained optimization.…”

Section: Other Strategiesmentioning

confidence: 99%

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Adaptive ranking based constraint handling for explicitly constrained black-box optimization

Sakamoto

Akimoto

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.

show abstract

Section: Resultssupporting

confidence: 53%

“…where A and b are as defined in (4). We define an initial mean vector and initial covariance matrix as m (0) and C (0) , respectively, on this coordinate system.…”

Section: Test Problemmentioning

confidence: 99%

Section: Other Strategiesmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive ranking based constraint handling for explicitly constrained black-box optimization

Sakamoto

Akimoto

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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“…Three variants of DE that showed promising results in benchmarks are tested, namely "Selfadaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization" (conSaDE) [20], "Differential Evolution with Ensemble of Constraint Handling Techniques" (ECHT-DE) [21], and "Constrained Optimization by the ε Constrained Differential Evolution with an Archive and Gradient-Based Mutation" (εDEag) [22]. Further, an Active-Set ES [33], an ES with augmented Lagrangian constraint handling [34] and a method based on surrogate modeling with adaptive parameter control [45] (SACOBRA) are benchmarked and compared to the approach presented in this work.…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

“…There exists an extension of this idea to a (µ, λ)-CMA-ES motivated by an application in the area of rocket design [32]. In [33] an Active-Set ES that is able to handle constraints is described. Further, an ES with augmented Lagrangian constraint handling is presented in [34].…”

Section: Introductionmentioning

confidence: 99%

A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization Under Linear Constraints

Spettel

Beyer

Hellwig

2019

IEEE Trans. Evol. Computat.

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This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.

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Multi-fidelity Optimization Approach Under Prior and Posterior Constraints and Its Application to Compliance Minimization

Akimoto

Sakamoto

Ohtani

2020

Parallel Problem Solving From Nature – PPSN XVI

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An Active-Set Evolution Strategy for Optimization with Known Constraints

Cited by 8 publications

References 11 publications

Adaptive ranking based constraint handling for explicitly constrained black-box optimization

Adaptive ranking based constraint handling for explicitly constrained black-box optimization

A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization Under Linear Constraints

Multi-fidelity Optimization Approach Under Prior and Posterior Constraints and Its Application to Compliance Minimization

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