Opt2Vec - a continuous optimization problem representation based on the algorithm's behavior: A case study on problem classification

• Published in: Information sciences Vol. 680; p. 121134
• Main Authors: Korošec, Peter, Eftimov, Tome
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2024
• Subjects: Anytime problem identification; Autoencoder; Continuous optimization; Dynamic problem characterization; Problem representation; Problem representation; Anytime problem identification; Dynamic problem characterization; Continuous optimization; Autoencoder
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2024.121134

Characterization of the optimization problem is a crucial task in many recent optimization research topics (e.g., explainable algorithm performance assessment, and automated algorithm selection and configuration). The state-of-the-art approaches use exploratory landscape analysis to represent the optimization problem, where for each one, a set of features is extracted using a set of candidate solutions sampled by a sampling strategy over the whole decision space. This paper proposes a novel representation of continuous optimization problems by encoding the information found in the interaction between an algorithm and an optimization problem. The new problem representation is learned using the information from the states/positions in the optimization run trajectory (i.e., the candidate solutions visited by the algorithm). With the novel representation, the problem can be characterized dynamically during the optimization run, instead of using a set of candidate solutions from the whole decision space that have never been observed by the algorithm. The novel optimization problem representation is called Opt2Vec and uses an autoencoder type of neural network to encode the information found in the interaction between an optimization algorithm and optimization problem into an embedded subspace. The Opt2Vec representation efficiency is shown by enabling different optimization problems to be successfully identified using only the information obtained from the optimization run trajectory. •Representation learning is applied on each individual population of optimization process trajectory.•The Opt2Vec representations are captured through the algorithm's behavior (its populations).•The Opt2Vec representations are suitable for dynamic problem characterization.•The Opt2Vec representations are invariant to simple transformations (shifting/scaling).•The Opt2Vec representations are scalable over different problem dimensions.