Combining Cross Entropy and MADS methods for inequality constrained global optimization

TL;DR

This paper introduces a novel hybrid optimization approach combining MADS and Cross-Entropy methods, enhancing global search capabilities for inequality constrained problems while maintaining convergence properties.

Contribution

The paper presents a new method that integrates CE sampling into MADS, improving exploration and escape from local minima in constrained optimization.

Findings

Enhanced ability to reach feasible regions

Improved escape from local minima

Numerical results show significant performance gains

Abstract

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for non smooth constrained optimization. The CE method is used as a Search step by the MADS algorithm. The result of this combination retains the convergence properties of MADS and allows an efficient exploration in order to move away from local minima. The CE method samples trial points according to a multivariate normal distribution whose mean and standard deviation are calculated from the best points found so far. Numerical experiments show an important improvement of this method to reach the feasible region and to escape local minima.