Multidisciplinary Optimization in the Design of Future Space Launchers

Collange, Guillaume; Delattre, Nathalie; Hansen, Nikolaus; Quinquis, Isabelle; Schoenauer, Marc

doi:10.1002/9781118600153.ch12

Cited by 11 publications

(18 citation statements)

References 5 publications

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“…Recent research efforts have been devoted to overcome this difficulty. The use of adaptive penalty functions was investigated in [38], where the weight of each constraint in the penalty function was modified according to the number of iterations during which that constraint was violated. Another penalty function has been proposed in [41], where the constraint violation of all the solutions in the population is used to scale the relative violation of each solution.…”

Section: A Methods Based On Cma-esmentioning

confidence: 99%

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%

Memetic Viability Evolution for Constrained Optimization

Maesani

Iacca

Floreano

2016

IEEE Trans. Evol. Computat.

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“…Collange et al [3] introduce a constraint handling approach for CMA-ES that strives to ensure that within some given number of iterations the population contains at least one feasible candidate solution. Their approach relies on constraint function values and a user defined constraint value threshold.…”

Section: Related Workmentioning

confidence: 99%

A (1+1)-CMA-ES for constrained optimisation

Arnold

Hansen

2012

Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation

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102

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This paper introduces a novel constraint handling approach for covariance matrix adaptation evolution strategies (CMA-ES). The key idea is to approximate the directions of the local normal vectors of the constraint boundaries by accumulating steps that violate the respective constraints, and to then reduce variances of the mutation distribution in those directions. The resulting strategy is able to approach the boundary of the feasible region without being impeded in its ability to search in directions tangential to the boundaries. The approach is implemented in the (1 + 1)-CMA-ES and evaluated numerically on several test problems. The results compare very favourably with data for other constraint handling approaches applied to unimodal test problems that can be found in the literature.

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“…1: Left: Two Pareto sets for n = 2 represented in R 2 with Q 1 and Q 2 randomly sampled and different. Right: Pareto set for n = 10 with matrices given in (7) represented as the function of the parameter t given in (3). The coordinates are ordered, the first one is on top and last one below.…”

Section: Convexity Of the Pareto Frontmentioning

confidence: 99%

On Bi-objective Convex-Quadratic Problems

Touré

Auger

Brockhoff

et al. 2019

Lecture Notes in Computer Science

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In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional. We then propose a novel set of convex-quadratic test problems, describe their theoretical properties and the algorithm abilities required by those test problems. This includes in particular testing the sensitivity with respect to separability, ill-conditioned problems, rotational invariance, and whether the Pareto set is aligned with the coordinate axis.

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Multidisciplinary Optimization in the Design of Future Space Launchers

Cited by 11 publications

References 5 publications

Memetic Viability Evolution for Constrained Optimization

Memetic Viability Evolution for Constrained Optimization

A (1+1)-CMA-ES for constrained optimisation

On Bi-objective Convex-Quadratic Problems

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