Improving Automated Algorithm Selection by Advancing Fitness Landscape Analysis (2312.03105v1)

Abstract: Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully exists a plethora of different algorithms that can find solutions more reliably than ever before. Yet, choosing an appropriate algorithm for any given problem is challenging in itself. The field of automated algorithm selection provides various approaches to tackle this latest problem. This is done by delegating the selection of a suitable algorithm for a given problem to a complex computer model. This computer model is generated through the use of Artificial Intelligence. Many of these computer models rely on some sort of information about the problem to make a reasonable selection. Various methods exist to provide this informative input to the computer model in the form of numerical data. In this cumulative dissertation, I propose several improvements to the different variants of informative inputs. This in turn enhances and refines the current state-of-the-art of automated algorithm selection. Specifically, I identify and address current issues with the existing body of work to strengthen the foundation that future work builds upon. Furthermore, the rise of deep learning offers ample opportunities for automated algorithm selection. In several joint works, my colleagues and I developed and evaluated several different methods that replace the existing methods to extract an informative input. Lastly, automated algorithm selection approaches have been restricted to certain types of problems. I propose a method to extend the generation of informative inputs to other problem types and provide an outlook on further promising research directions.

• The paper introduces a normalization process for ELA metrics to eliminate bias from scaling or shifting in the fitness landscape.
• It leverages open-source tools like pflacco and neural network-based benchmark generation to extend ELA to complex, mixed-variable problems.
• Enhanced ELA features significantly improve automated algorithm selection, outperforming traditional solvers in optimized problem tackling.

Exploratory Landscape Analysis for Improved Algorithm Selection

Understanding the Fitness Landscape

Exploratory Landscape Analysis (ELA) is a critical technique for understanding the "terrain" of optimization problems. Much like a map can tell us about the geography of an area, ELA provides valuable insights into the structure of a problem's solution space, which is often referred to as its fitness landscape. A well-characterized fitness landscape can help in selecting the most effective algorithm for solving a particular optimization problem.

Advancements in Fitness Landscape Analysis

A comprehensive analysis of optimization techniques revealed that some practices might benefit from refinement. For example, researchers have identified certain metrics, derived from ELA, that were previously not considered invariant — their values would unfairly change just based on how a problem was scaled or shifted, not on the features of the landscape itself. Addressing this, researchers have suggested applying a normalization process to the data before calculating the ELA metrics, ensuring a bias-free analysis.

Additionally, the open-source software landscape in this domain has expanded with the introduction of pflacco, a Python package that implements a wide array of ELA features originally available in the R package flacco. This software makes it easier for researchers to apply ELA techniques to their problems and could lead to more standardized practices across the field.

Researchers have also explored the automation of benchmark problem generation. They have developed a neural network-based method to generate new optimization problems that mimic certain characteristics of real-world or other benchmark problems. This could help in creating more diverse and challenging test cases for optimization algorithms.

Expanding to Complex Problem Domains

ELA has typically been focused on continuous and combinatorial problem domains. However, many real-world problems are neither purely continuous nor purely combinatorial. To extend ELA's benefits to mixed search spaces, which might include any combination of continuous, integer, and categorical variables, researchers have adapted ELA features to be applicable to these more complex problems. By doing so, they open up a new frontier in fitness landscape analysis, providing tools to understand and optimize across a broader array of problems that more closely resemble real-world conditions.

Automated Algorithm Selection on the Horizon

With advances in handling various problem domains, researchers have been able to execute more effective automated algorithm selection (AAS). Through extensive machine learning analysis, including feature selection and classification techniques, AAS models have demonstrated significant improvements over more naive approaches such as merely using the best-known solver. Notably, these advanced AAS models can outperform the solver best by effectively narrowing down the right algorithm selection for a given problem. This underscores the value of ELA features in AAS and the potential to significantly expedite the optimization process.

Future Directions

As the research community continues to embrace and adapt ELA, there are opportunities to enhance these approaches and address their limitations. Suggestions include developing more efficient sampling strategies, creating a better understanding of feature costs, and possibly integrating ELA feature computation directly into optimization procedures. Moreover, new methodologies will incorporate deep learning for feature-free approachs that operate directly on the problem's data, potentially offering new ways to select and configure algorithms without the need for explicit landscape features.

As ELA branches out to mixed-variable problems, this could lead to broader applications, potentially making their way into commercial optimization software and bringing sophisticated algorithm selection strategies to a range of industries and applications. The journey of ELA from research to practice promises to be impactful, offering smarter, more adaptable approaches to solving complex optimization challenges.