A Homotopy Method for Large-Scale Multi-Objective Optimization

TL;DR

This paper introduces a homotopy method for large-scale multi-objective optimization that efficiently produces uniformly distributed Pareto fronts, significantly improving solution evenness and computational efficiency over existing methods.

Contribution

The paper presents a novel homotopy-based algorithm that enhances solution uniformity and computational efficiency in multi-objective optimization, especially for simulation-based engineering problems.

Findings

Achieves an order of magnitude improvement in solution evenness over existing methods.

Maintains high solution quality even in complex test cases.

Reduces computational expense compared to traditional geometric methods.

Abstract

A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering optimization problems where economy of function evaluations, smoothness of result, and time-to-solution are critical. The presented algorithm achieves an order of magnitude improvement over other geometrically motivated methods, like Normal Boundary Intersection and Normal Constraint, with respect to solution evenness for similar computational expense. Furthermore, the resulting uniformity of solutions extends even to more difficult problems, such as those appearing in common Evolutionary Algorithm test cases.