The Hessian Estimation Evolution Strategy

We present a novel black box optimization algorithm called Hessian Estimation Evolution Strategy. The algorithm updates the covariance matrix of its sampling distribution by directly estimating the curvature of the objective function. This algorithm design is targeted at twice continuously differentiable problems. For this, we extend the cumulative step-size adaptation algorithm of the CMA-ES to mirrored sampling. We demonstrate that our approach to covariance matrix adaptation is efficient by evaluation it on the BBOB/COCO testbed. We also show that the algorithm is surprisingly robust when its core assumption of a twice continuously differentiable objective function is violated. The approach yields a new evolution strategy with competitive performance, and at the same time it also offers an interesting alternative to the usual covariance matrix update mechanism

Algorithm Portfolios for Noisy Optimization: Compare Solvers Early

International audienceNoisy optimization is the optimization of objective functions corrupted by noise. A portfolio of algorithms is a set of algorithms equipped with an algorithm selection tool for distributing the compu- tational power among them. We study portfolios of noisy optimization solvers, show that different settings lead to dramatically different perfor- mances, obtain mathematically proved adaptivity by an ad hoc selection algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag; i.e., recommend the current recommendation of the best solver, selected from a comparison based on their recommendations earlier in the run

Microstructure and local mechanical properties of pea starch / protein composites

Biopolymer composites based on pea starch-protein blends and pea flour are processed using extrusion at various levels of specific mechanical energy (SME). Their morphology was a continuous matrix phase of starch with embedded protein particles, as revealed by Confocal Laser Scanning Microscopy (CLSM). The motivation is to correlate the local Young's modulus (E) in starch and protein phases, as well as their interphase, through nanoindentation tests to macroscopic three-point bending testing results of starch-protein composites. The differences between E of starch and protein phases and interphase were significant and their values were found to vary in the ranges of 4.2–7, 3–6.9 and 4–6.9 GPa, respectively. The local E can be tuned by the protein content and composite morphology, the latter depending on the level of transformation of the biopolymers during extrusion (SME). Pea flour composites have larger modulus values, which can be attributed to the presence of fibres

On multiplicative noise models for stochastic search

Abstract. In this paper we investigate multiplicative noise models in the context of continuous optimization. We illustrate how some intrinsic properties of the noise model imply the failure of reasonable search algorithms for locating the optimum of the noiseless part of the objective function. Those findings are rigorously investigated on the (1 + 1)-ES for the minimization of the noisy sphere function. Assuming a lower bound on the support of the noise distribution, we prove that the (1 + 1)-ES diverges when the lower bound allows to sample negative fitness with positive probability and converges in the opposite case. We provide a discussion on the practical applications and non applications of those outcomes and explain the differences with previous results obtained in the limit of infinite search-space dimensionality.