Generating Instances with Performance Differences for More Than Just Two Algorithms

TL;DR

This paper introduces methods to evolve problem instances that exhibit significant performance differences across multiple algorithms simultaneously, aiding in understanding algorithm strengths and weaknesses.

Contribution

It proposes fitness functions for evolving instances with large performance gaps among more than two algorithms, extending prior work focused on two algorithms.

Findings

Strategies show promise in evolving multi-algorithm performance differences

Success depends on the algorithms' performance complementarity

Proof-of-principle demonstrated on multi-component Traveling Thief Problem

Abstract

In recent years, Evolutionary Algorithms (EAs) have frequently been adopted to evolve instances for optimization problems that pose difficulties for one algorithm while being rather easy for a competitor and vice versa. Typically, this is achieved by either minimizing or maximizing the performance difference or ratio which serves as the fitness function. Repeating this process is useful to gain insights into strengths/weaknesses of certain algorithms or to build a set of instances with strong performance differences as a foundation for automatic per-instance algorithm selection or configuration. We contribute to this branch of research by proposing fitness-functions to evolve instances that show large performance differences for more than just two algorithms simultaneously. As a proof-of-principle, we evolve instances of the multi-component Traveling Thief Problem~(TTP) for three incomplete TTP-solvers. Our results point out that our strategies are promising, but unsurprisingly their success strongly relies on the algorithms' performance complementarity.