Generating set search using simplex gradients for bound-constrained black-box optimization

The optimization problems arising in modern engineering practice are increasingly simulation-based, characterized by extreme types of nonsmoothness, the inaccessibility of derivatives, and high computational expense. While generating set searches (GSS) generally offer a satisfying level of robustness and convergence to stationary points, the convergence rates may be slow. In order to accelerate the solution process without sacrificing robustness, we introduce (simplex) gradient-informed generating set search (GIGS) methods for solving bound-constrained minimization problems. These algorithms use simplex gradients, acquired over several iterations, as a guidance for adapting the search stencil to the local topography of the objective function. GIGS is shown to inherit first-order convergence properties of GSS and to possess a natural tendency for avoiding saddle points. Numerical experiments are performed on an academic set of smooth, nonsmooth and noisy test problems, as well as a realistic engineering case study. The results demonstrate that including simplex gradient information enables computational cost savings over non-adaptive GSS methods.

Jaar van publicatie:2021

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:1

CSS-citation score:2

Authors from:Government, Higher Education

Toegankelijkheid:Open