When to be Discrete: Analyzing Algorithm Performance on Discretized Continuous Problems

arXiv (Cornell University)

Abstract

The domain of an optimization problem is seen as one of its most important characteristics. In particular, the distinction between continuous and discrete optimization is rather impactful. Based on this, the optimizing algorithm, analyzing method, and more are specified. However, in practice, no problem is ever truly continuous. Whether this is caused by computing limits or more tangible properties of the problem, most variables have a finite resolution. In this work, we use the notion of the resolution of continuous variables to discretize problems from the continuous domain. We explore how the resolution impacts the performance of continuous optimization algorithms. Through a mapping to integer space, we are able to compare these continuous optimizers to discrete algorithms on the exact same problems. We show that the standard $(μ_W, λ)$-CMA-ES fails when discretization is added to the problem.

Authors 6

1. André Thomaser

   BMW (Germany) · BMW Group (Germany)

   Affiliation as printed

   BMW Group Munich , Germany

2. Jacob de Nobel
3. Diederick Vermetten Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   LIACS , Leiden University Leiden , The Netherlands

4. Furong Ye Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   LIACS , Leiden University Leiden , The Netherlands

5. Thomas Bäck
6. Anna V. Kononova Aachen

   Leiden University · University of Applied Sciences Leiden

   Affiliation as printed

   LIACS , Leiden University Leiden , The Netherlands