A Novel Ranking Scheme for the Performance Analysis of Stochastic Optimization Algorithms using the Principles of Severity

TL;DR

This paper introduces a new ranking scheme for stochastic optimization algorithms based on a football league analogy, utilizing severity principles and bootstrapping to evaluate performance without distributional assumptions.

Contribution

The paper presents a novel ranking method that considers performance magnitude and relevance, using a league-based comparison and severity principles, improving over classical hypothesis testing.

Findings

The proposed ranking scheme is comparable to classical methods in results.

It provides additional benefits such as considering performance magnitude.

The method does not rely on distributional assumptions.

Abstract

Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes the task of the performance analysis of the algorithms extremely important. In this paper, we provide a novel ranking scheme to rank the algorithms over multiple single-objective optimization problems. The results of the algorithms are compared using a robust bootstrapping-based hypothesis testing procedure that is based on the principles of severity. Analogous to the football league scoring scheme, we propose pairwise comparison of algorithms as in league competition. Each algorithm accumulates points and a performance metric of how good or bad it performed against other algorithms analogous to goal differences metric in football league scoring system. The goal differences performance metric can not only be used as a tie-breaker but also be used to obtain a quantitative performance of each algorithm. The key novelty of the proposed ranking scheme is that it takes into account the performance of each algorithm considering the magnitude of the achieved performance improvement along with its practical relevance and does not have any distributional assumptions. The proposed ranking scheme is compared to classical hypothesis testing and the analysis of the results shows that the results are comparable and our proposed ranking showcases many additional benefits.