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

Spettel, Patrick; Beyer, Hans-Georg; Hellwig, Michael

doi:10.1109/tevc.2018.2871944

Cited by 32 publications

(8 citation statements)

References 31 publications

(62 reference statements)

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“…However, many purpose-built algorithms for linear optimization [57,58] show poor performance in this environment. The Klee-Minty problem was already used to compare a specially designed CMSA-ES variant for linear optimization with open source interior point LP solvers in [59].…”

Section: Resultsmentioning

confidence: 99%

Benchmarking evolutionary algorithms for single objective real-valued constrained optimization – A critical review

Hellwig

Beyer

2019

Swarm and Evolutionary Computation

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Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.

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Section: Resultsmentioning

confidence: 99%

Benchmarking evolutionary algorithms for single objective real-valued constrained optimization – A critical review

Hellwig

Beyer

2019

Swarm and Evolutionary Computation

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“…Thus, additional information on each constraint can be gathered to help search faster. Spettel et al (2019) devised a special mutation operator that did not violate any linear constraints and repaired the non-negativity constraints by projection.…”

Section: Accelerating Convergence Speedmentioning

confidence: 99%

A survey on evolutionary computation for complex continuous optimization

et al. 2021

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Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

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“…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%

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.

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

Cited by 32 publications

References 31 publications

Benchmarking evolutionary algorithms for single objective real-valued constrained optimization – A critical review

Benchmarking evolutionary algorithms for single objective real-valued constrained optimization – A critical review

A survey on evolutionary computation for complex continuous optimization

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

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