Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

Abstract

This paper develops a new surrogate-assisted evolutionary programming (EP) algorithm for computationally expensive constrained black-box optimization. The proposed algorithm, TRICEPS (Trust Regions In Constrained Evolutionary Programming using Surrogates) builds surrogates for the black-box objective function and inequality constraint functions in every generation of the EP and uses a trustregion-like approach to refine the best solution at the end of each generation. Each parent produces a large number of trial offspring in each generation, and then the surrogates are used to identify promising trial offspring, which become the actual offspring where the objective and constraint functions are evaluated. After the function evaluations at these offspring, TRICEPS finds a minimizer of the surrogate of the objective function within a trust region centered at the current best solution and subject to surrogate inequality constraints with a small margin and with a distance requirement from previously evaluated points. The trust region is either expanded or reduced depending on whether the subproblem solution turned out to be feasible and whether the ratio of the actual improvement to the predicted improvement exceeds or falls below certain thresholds. TRICEPS is implemented using a cubic radial basis function (RBF) model with a linear polynomial tail and is compared to an RBF-assisted EP called CEP-RBF (Regis 2014b) and to other alternatives on 18 benchmark problems and on an automotive application with 124 decision variables and 68 black-box inequality constraints. Performance and data profiles show that TRICEPS is a substantial improvement over CEP-RBF and it is much better than the other alternatives on the test problems used. Keywords IntroductionIn many real-world engineering optimization problems, the values of the objective and constraint functions are outputs of computationally expensive simulations. These types of optimization problems are found in the automotive and aerospace industries (e.g., Jones 2008;Ong et al. 2003) and in various parameter estimation problems (e.g., Mugunthan et al. 2005;Tolson and Shoemaker 2007). A reasonable strategy for solving these problems is to use surrogate-based or surrogate-assisted optimization methods, including surrogate-assisted evolutionary algorithms (EAs) Jin (2011), where the algorithm uses surrogate models to approximate the black-box objective and constraint functions. For instance, Regis (2014b) successfully developed a surrogate-assisted Evolutionary Programming (EP) algorithm and applied it to a large-scale automotive optimization application with 124 decision variables and 68 black-box inequality constraints given a severely limited computational budget of only 1,000 simulations, where one simulation yields the objective function value and each of the constraint function values at a given input vector. The purpose of this paper is two-fold: (1) To develop a new surrogate-assisted EP for constrained black-box optimization that improves on the algorithm ...

Global and Local Surrogate-Assisted Differential Evolution for Expensive Constrained Optimization Problems With Inequality Constraints

“…Subsequently, the location information is utilized to determine whether or not the local search should be applied to an individual. Regis [51] designed a trust region-like approach to improve the best solution at the end of each generation.…”

Parallel surrogate-assisted global optimization with expensive functions – a survey

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Multi-objective constrained black-box optimization using radial basis function surrogates

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