Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

Abstract

Recent metamodel-based global optimization algorithms are very promising for box-constrained expensive optimization problems. However, few of them can tackle constrained optimization problems. This article presents an improved constrained optimization algorithm, called eDIRECT-C, for expensive constrained optimization problems. In the eDIRECT-C algorithm, we present a novel DIRECT-type constraint-handling technique that separately handles feasible and infeasible cells. This technique has no user-defined parameter and is beneficial for exploring the undetected feasible regions and boundary of feasible regions. We also employ an adaptive metamodeling strategy to build appropriate metamodel types for objective and constraints respectively. This strategy yields more accurate predictions and therefore significantly speeds up the convergence. To assess the performance of eDIRECT-C, we compare it with some state-of-the-art metamodel-based constrained optimization algorithms and the original DIRECT algorithm on 13 benchmark problems and 4 engineering examples. The comparative results imply that the proposed algorithm is very promising for constrained problems in terms of the convergence speed, quality of final solutions and success rate.

Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

“…4.2.2 in this paper). Liu et al (2016) proposed a two-phase method that uses a constraint-handling technique based on the DIRECT algorithm and that uses an adaptive metamodeling strategy for the objective and constraints. Gramacy et al (2016) developed an hybrid approach that uses Kriging with the expected improvement (EI) criterion combined with the augmented Lagrangian framework for constrained optimization.…”

A Population-Based Stochastic Coordinate Descent Method

“…is the score of the point x ki [6]. The normalized distanceD(x ki ), from x ki to the center point of the k subpopulation, and the normalized objective function valuef (x ki ) at x ki are defined bŷ…”

The DIRECT algorithm: 25 years Later

“…In their eDIRECT algorithm, Liu et al [37] add nonlinear constraints by modifying how the regions (Voronoi cells) are selected for sampling and subdivision. If no feasible point has been found, they select regions using the lower-right convex hull in a diagram of normalized constraint violations versus region size.…”

“…For example, in a recent comparison of derivative-free algorithms on a large set of test problems with up to 300 variables, a variation of DIRECT (glcCluster) was among the top performers [57]. Another promising variation, called eDIRECT-C [36,37], was recently successfully applied to optimizing a quantum simulator with respect to 15 parameters [31].…”