A Fast Incremental BSP Tree Archive for Non-dominated Points

TL;DR

This paper introduces a fast, incremental BSP tree algorithm for maintaining non-dominated points in multi-objective optimization, outperforming brute-force methods especially with three or more objectives.

Contribution

It presents a novel efficient algorithm using binary space partitioning for updating non-dominated sets in multi-objective optimization with multiple objectives.

Findings

Superiority over brute-force baseline

Efficient scaling to many objectives

Effective for three or more objectives

Abstract

Maintaining an archive of all non-dominated points is a standard task in multi-objective optimization. Sometimes it is sufficient to store all evaluated points and to obtain the non-dominated subset in a post-processing step. Alternatively the non-dominated set can be updated on the fly. While keeping track of many non-dominated points efficiently is easy for two objectives, we propose an efficient algorithm based on a binary space partitioning (BSP) tree for the general case of three or more objectives. Our analysis and our empirical results demonstrate the superiority of the method over the brute-force baseline method, as well as graceful scaling to large numbers of objectives.