A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization under Linear Constraints

TL;DR

This paper introduces lcCMSA-ES, a covariance matrix self-adaptation evolution strategy designed for constrained optimization problems, using a specialized mutation and projection repair to efficiently handle linear constraints.

Contribution

It presents a novel evolution strategy that self-adapts covariance matrices and effectively manages linear constraints through a projection-based repair mechanism.

Findings

Demonstrates effectiveness on various test problems

Shows significant improvement over existing methods

Maintains feasibility with linear constraints during optimization

Abstract

This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.