An open-source solver for finding global solutions to constrained derivative-free optimization problems

TL;DR

This paper introduces GSDO, an open-source heuristic solver for constrained derivative-free optimization that uses surrogate models to efficiently find global solutions, demonstrating competitive performance against existing solvers.

Contribution

The paper presents GSDO, a novel surrogate-based heuristic solver for constrained DFO problems, capable of handling various constraint types and outperforming some existing methods.

Findings

GSDO performs competitively with state-of-the-art solvers.

The surrogate approach improves global optimization efficiency.

GSDO effectively handles different types of constraints.

Abstract

In this work, we propose a heuristic based open source solver for finding global solution to constrained derivative-free optimization (DFO) problems. Our solver named Global optimization using Surrogates for Derivative-free Optimization (GSDO) relies on surrogate approximation to the original problem. In the proposed algorithm, an initial feasible point is first generated. This point is subsequently used to generate well spaced feasible points for formulating better radial basis function based surrogate approximations to original objective and constraint functions. Finally, these surrogates are used to solve the derivative-free global optimization problems. The proposed solver is capable of handling quantifiable and nonquantifiable as well as relaxable and unrelaxable constraints. We compared the performance of proposed solver with state of the art solvers like Nonlinear Optimization by Mesh Adaptive Direct Search (NOMAD), differential evolution (DE) and Simplicial Homology Global Optimization (SHGO) on standard test problems. The numerical results clearly demonstrate that the performance of our method is competitive with respect to other solvers.