March 2024 On the fair comparison of optimization algorithms in different machines
Etor Arza, Josu Ceberio, Ekhiñe Irurozki, Aritz Pérez
Author Affiliations +
Ann. Appl. Stat. 18(1): 42-62 (March 2024). DOI: 10.1214/23-AOAS1778


An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud.

In this paper we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.

Funding Statement

This work was funded in part by the Spanish Ministry of Science, Innovation and Universities through PID2019-1064536A-I00 and the BCAM Severo Ochoa excellence accreditation SEV-2017-0718, by Basque Government through consolidated groups 2019–2021 IT1244-19, ELKARTEK program and BERC 2018–2021 program, and by the Spanish Ministry of Economy and Competitiveness through the project TIN2017-82626-R.


Download Citation

Etor Arza. Josu Ceberio. Ekhiñe Irurozki. Aritz Pérez. "On the fair comparison of optimization algorithms in different machines." Ann. Appl. Stat. 18 (1) 42 - 62, March 2024.


Received: 1 December 2022; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1778

Keywords: algorithms , benchmarking , optimization , statistical tests

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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