Measuring algorithm footprints in instance space

This paper proposes a new methodology to determine the relative performance of optimization algorithms across various classes of instances. Rather than reporting performance based on a chosen test set of benchmark instances, we aim to develop metrics for an algorithm´s performance generalized across a diverse set of instances. Instances are summarized by a set of features that correlate with difficulty, and we propose methods for visualizing instances and algorithm performance in this high-dimensional feature space. The footprint of an algorithm is where good performance can be expected, and we propose new metrics to measure the relative size of an algorithm´s footprint in instance space. The methodology is demonstrated using the Traveling Salesman Problem as a case study.