Doctoral dissertation
Problem landscape and search trajectory features for automated algorithm selection in continuous single-objective optimization
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Abstract
Black-box single-objective optimization (SOO) plays a critical role in solving diverse problems
across engineering, machine learning, and scientific computation. Despite extensive
research in this area, no single optimization algorithm performs best across all problem
instances. This challenge has led to increased interest in automated algorithm selection
(AS), which aims to match problem instances with the most effective algorithms based on
descriptive problem landscape features.
This dissertation investigates three key limitations in existing AS methodologies for
continuous SOO. First, it addresses the limitations of traditional landscape features, such
as those from Exploratory Landscape Analysis (ELA), by exploring alternative representations
learned through deep learning and topological data analysis. Second, it highlights
the variability and inconsistencies in AS evaluation protocols—particularly the influence of
different benchmarking strategies on model performance and interpretability. Third, it introduces
trajectory-based features that capture dynamic interactions between optimization
algorithms and problem landscapes, offering a complementary perspective beyond static
landscape descriptors.
Contrary to expectations, empirical findings reveal that the newly proposed features,
while capturing novel aspects of problem complexity, do not consistently outperform ELA
features in AS tasks. Moreover, models built on both traditional and novel feature sets
demonstrate limited generalizability, particularly when evaluated under more challenging
benchmark settings or across diverse problem domains. These results underscore the
persistent difficulty of building robust AS models and highlight the need for improved
benchmarking standards and more expressive, generalizable feature representations.
Through the systematic evaluation of feature types and AS protocols, this dissertation
contributes a comprehensive analysis of the current limitations and future potential of
algorithm selection in continuous SOO.