Accelerated Random Search for Black-Box Constraint Satisfaction and Optimization

Abstract

The Constrained Accelerated Random Search (CARS) algorithm is a stochastic search method that converges with probability 1 to the global minimum of a constrained black-box optimization problem under certain conditions. CARS randomly selects its sample point from a box centered at the current best solution and adjusts the size of this box depending on whether the point yields an improvement in constraint violation or feasible objective function value. For computationally expensive problems, the CARS- RBF algorithm that uses Radial Basis Function (RBF) surrogates was proposed. Numerical experiments showed the effectiveness of CARS and CARS-RBF compared to alternatives on many test problems. However, both algorithms require a feasible starting point. This paper extends CARS and CARS-RBF to handle constrained black-box optimization problems when a feasible starting point is not available. The extended algorithms begin by minimizing a measure of constraint violation to find a feasible solution and then they search for the global minimum until the computational budget is reached. The algorithms were tested on 19 benchmark problems and on a 12-D engineering optimization problem with 68 black-box constraints where none of the initial points are guaranteed to be feasible. CARS outperformed Constrained Pure Random Search (CPRS) and the ISRES and jDE evolutionary algorithms on the test problems, and CARS-RBF is generally an improvement over CARS. Furthermore, CARS-RBF outperformed other methods including RBF -assisted CPRS and the COBYLA trust region method and it compared favorably with constrained EGO.