In this paper, we investigate a non-elitist Evolution Strategy designed to handle black-box constraints by an adaptive Augmented Lagrangian penalty approach, AL-(µ/µ w , λ)-CMA-ES, on problems with up to 28 constraints. Based on stability and performance observations, we propose an improved default parameter setting. We exhibit failure cases of the Augmented Lagrangian technique and show how surrogate modeling of the constraints can overcome some difficulties. Several variants of AL-CMA-ES are compared on a set of nonlinear constrained problems from the literature. Simple adaptive penalty techniques serve as a baseline for comparison.
CCS CONCEPTS• Computing methodologies → Randomized search; • Mathematics of computing → Bio-inspired optimization.
In this paper, we propose a comparative benchmark of MO-CMA-ES, COMO-CMA-ES (recently introduced in [12]) and NSGA-II, using the COCO framework for performance assessment and the Bi-objective test suite bbob-biobj. For a xed number of points p, COMO-CMA-ES approximates an optimal p-distribution of the Hypervolume Indicator. While not designed to perform on archivebased assessment, i.e. with respect to all points evaluated so far by the algorithm, COMO-CMA-ES behaves well on the COCO platform. e experiments are done in a true Black-Blox spirit by using a minimal se ing relative to the information shared by the 55 problems of the bbob-biobj Testbed.
In this paper, we benchmark several versions of a population-based evolution strategy with covariance matrix adaptation, handling constraints with an Augmented Lagrangian fitness function. The versions only differ in the strategy to adapt the penalty parameter of the fitness function. We compare the resulting algorithms, AL-CMA-ES, with random search and Powell's derivative-free COBYLA on the recently released bbob-constrained test suite for constrained continuous optimization in dimensions ranging from 2 to 40. The experimental results allow identifying classes of problems where one algorithm is more advantageous to use. They also reveal features of the merit function used for performance assessment and in particular situations where even on simple problems the targets can be hard to meet for algorithms based on Lagrange multipliers.
CCS CONCEPTS• Computing methodologies → Continuous space search.
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