Mixed-Integer Constrained Grey-Box Optimization based on Dynamic Surrogate Models and Approximated Interval Analysis

Mohamad Nachawati, Alexander Brodsky

2021

Abstract

In this paper an algorithmic framework, called GreyOpt, is proposed for the heuristic global optimization of simulations over general constrained mixed-integer sets, where simulations are expressed as a grey-box, i.e. computations using a mix of (1) closed-form analytical expressions, and (2) evaluations of numerical black- box functions that may be non-differentiable and computationally expensive. GreyOpt leverages the partially analytical structure of such problems to dynamically construct differentiable surrogate problems for multiple regions of the search space. These surrogate problems are then used in conjunction with a derivative-based method to locally improve sample points in each region. GreyOpt extends Moore interval arithmetic for approximating the intervals of grey-box objective and constraint functions by fitting quadric surfaces that attempt to roughly underestimate and overestimate embedded black-box functions. This serves as the foundation of a recursive partitioning technique that GreyOpt uses to refine the best points found in each region. An experimental study of GreyOpt’s performance is conducted on a set of grey-box optimization problems derived from MINLPLib, where the ratio of black-box function evaluations to analytical expressions is small. The results of the study show that GreyOpt significantly outperforms three derivative-free optimization algorithms on these problems.

Paper Citation

in Harvard Style

Nachawati M. and Brodsky A. (2021). Mixed-Integer Constrained Grey-Box Optimization based on Dynamic Surrogate Models and Approximated Interval Analysis.In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-485-5, pages 99-112. DOI: 10.5220/0010350100990112

in Bibtex Style

@conference{icores21,
author={Mohamad Nachawati and Alexander Brodsky},
title={Mixed-Integer Constrained Grey-Box Optimization based on Dynamic Surrogate Models and Approximated Interval Analysis},
booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2021},
pages={99-112},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010350100990112},
isbn={978-989-758-485-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - Mixed-Integer Constrained Grey-Box Optimization based on Dynamic Surrogate Models and Approximated Interval Analysis
SN - 978-989-758-485-5
AU - Nachawati M.
AU - Brodsky A.
PY - 2021
SP - 99
EP - 112
DO - 10.5220/0010350100990112