A Merit Function Approach for Evolution Strategies

TL;DR

This paper introduces a merit function framework for evolution strategies that ensures global convergence in constrained optimization, effectively handling relaxable and unrelaxable constraints with promising preliminary numerical results.

Contribution

It extends evolution strategies with a merit function approach to handle general constraints while guaranteeing global convergence properties.

Findings

Successful handling of relaxable constraints using merit functions.

Effective treatment of unrelaxable constraints via barrier or projection methods.

Preliminary numerical experiments show promising results on test problems.

Abstract

In this paper, we extend a class of globally convergent evolution strategies to handle general constrained optimization problems. The proposed framework handles relaxable constraints using a merit function approach combined with a specific restoration procedure. The unrelaxable constraints in our framework, when present, are treated either by using the extreme barrier function or through a projection approach. The introduced extension guaranties to the regarded class of evolution strategies global convergence properties for first order stationary constraints. Preliminary numerical experiments are carried out on a set of known test problems as well as on a multidisciplinary design optimization problem