On the Design of Constraint Covariance Matrix Self-Adaptation Evolution Strategies Including a Cardinality Constraint

Beyer, Hans-Georg; Finck, Steffen

doi:10.1109/tevc.2011.2169967

Cited by 26 publications

(11 citation statements)

References 17 publications

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“…Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [36] is considered nowadays the state-of-the-art in unconstrained single-objective optimization. In the presence of constraints, however, the step-size control used by CMA-ES to refine the search does not work properly [42], an effect known also in standard ES. Recent research efforts have been devoted to overcome this difficulty.…”

Section: A Methods Based On Cma-esmentioning

confidence: 99%

“…Among the most effective algorithms for single objective optimization, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [36] has gained considerable attention in the last decade due to its ability of solving highly non-separable, ill-conditioned, and multi-modal functions. Although some attempts of extending CMA-ES to constrained optimization problems have been made [37]- [41], CMA-ES is not yet competitive on these types of problems: the self-adaptation of the algorithm's parameters is not suitable in constrained landscapes [42]. Moreover, due to the use of a single search distribution in CMA-ES, it is difficult to explore disconnected feasible areas unless restarts occur.…”

Section: Introductionmentioning

confidence: 99%

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Memetic Viability Evolution for Constrained Optimization

Maesani

Iacca

Floreano

2016

IEEE Trans. Evol. Computat.

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The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while Covariance Matrix Adaptation Evolution Strategy is one of the most efficient algorithms for unconstrained optimization problems, it cannot be readily applied to constrained ones. Here, we used concepts from Memetic Computing, i.e. the harmonious combination of multiple units of algorithmic information, and Viability Evolution, an alternative abstraction of artificial evolution, to devise a novel approach for solving optimization problems with inequality constraints. Viability Evolution emphasizes elimination of solutions not satisfying viability criteria, defined as boundaries on objectives and constraints. These boundaries are adapted during the search to drive a population of local search units, based on Covariance Matrix Adaptation Evolution Strategy, towards feasible regions. These units can be recombined by means of Differential Evolution operators. Of crucial importance for the performance of our method, an adaptive scheduler toggles between exploitation and exploration by selecting to advance one of the local search units and/or recombine them. The proposed algorithm can outperform several state-of-the-art methods on a diverse set of benchmark and engineering problems, both for quality of solutions and computational resources needed.

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Section: A Methods Based On Cma-esmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Memetic Viability Evolution for Constrained Optimization

Maesani

Iacca

Floreano

2016

IEEE Trans. Evol. Computat.

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“…Beyer and Sendhoff [25] introduced a covariance matrix self-adaptation evolution strategy (CMSA-ES algorithm) as a simple and efficient variant of so-called covariance matrix adaptation (CMA) strategies [21], [22]. Beyer and Finck [26] introduced a CMSA-ES for solving a mixed linear/nonlinear constrained optimization problem arising in portfolio optimization.…”

Section: Bare Bones Pso With Scale Matrixmentioning

confidence: 99%

Bare Bones Particle Swarm Optimization With Scale Matrix Adaptation

Campos

Krohling

Enriquez

2014

IEEE Trans. Cybern.

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Bare bones particle swarm optimization (BBPSO) is a swarm algorithm that has shown potential for solving single-objective unconstrained optimization problems over continuous search spaces. However, it suffers of the premature convergence problem that means it may get trapped into a local optimum when solving multimodal problems. In order to address this drawback and improve the performance of the BBPSO, we propose a variant of this algorithm, named by us as BBPSO with scale matrix adaptation (SMA), SMA-BBPSO for short reference. In the SMA-BBPSO, the position of a particle is selected from a multivariate t-distribution with a rule for adaptation of its scale matrix. We use the multivariate t-distribution in its hierarchical form, as a scale mixtures of normal distributions. The t -distribution has heavier tails than those of the normal distribution, which increases the ability of the particles to escape from a local optimum. In addition, our approach includes the normal distribution as a particular case. As a consequence, the t -distribution can be applied during the optimization process by maintaining the proper balance between exploration and exploitation. We also propose a simple update rule to adapt the scale matrix associated with a particle. Our strategy consists of adapting the scale matrix of a particle such that the best position found by any particle in its neighborhood is sampled with maximum likelihood in the next iteration. A theoretical analysis was developed to explain how the SMA-BBPSO works, and an empirical study was carried out to evaluate the performance of the proposed algorithm. The experimental results show the suitability of the proposed approach in terms of effectiveness to find good solutions for all benchmark problems investigated. Nonparametric statistical tests indicate that SMA-BBPSO shows a statistically significant improvement compared with other swarm algorithms.

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“…The work has been recently extended to non-linear constraints, learning models using support vector machines [20]. Another recently proposed variant of CMA-ES [21] makes use of repair mechanisms, but the algorithm is very specific to the problem being solved (financial portfolio optimization).…”

Section: Related Workmentioning

confidence: 99%

Viability Principles for Constrained Optimization Using a (1+1)-CMA-ES

Maesani

Floreano

2014

Parallel Problem Solving From Nature – PPSN XIII

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Abstract. Viability Evolution is an abstraction of artificial evolution which operates by eliminating candidate solutions that do not satisfy viability criteria. Viability criteria are defined as boundaries on the values of objectives and constraints of the problem being solved. By adapting these boundaries it is possible to drive the search towards desired regions of solution space, discovering optimal solutions or those satisfying a set of constraints. Although in previous work we demonstrated the feasibility of the approach by implementing it on a simple genetic algorithm, the method was clearly not competitive with the current evolutionary computation state-of-the-art. In this work, we test Viability Evolution principles on a modified (1+1)-CMA-ES for constrained optimization. The resulting method shows competitive performance when tested on eight unimodal problems.

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On the Design of Constraint Covariance Matrix Self-Adaptation Evolution Strategies Including a Cardinality Constraint

Cited by 26 publications

References 17 publications

Memetic Viability Evolution for Constrained Optimization

Memetic Viability Evolution for Constrained Optimization

Bare Bones Particle Swarm Optimization With Scale Matrix Adaptation

Viability Principles for Constrained Optimization Using a (1+1)-CMA-ES

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