Algorithm Runtime Prediction: Methods & Evaluation (1211.0906v2)

Abstract: Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance features. Such models have important applications to algorithm analysis, portfolio-based algorithm selection, and the automatic configuration of parameterized algorithms. Over the past decade, a wide variety of techniques have been studied for building such models. Here, we describe extensions and improvements of existing models, new families of models, and -- perhaps most importantly -- a much more thorough treatment of algorithm parameters as model inputs. We also comprehensively describe new and existing features for predicting algorithm runtime for propositional satisfiability (SAT), travelling salesperson (TSP) and mixed integer programming (MIP) problems. We evaluate these innovations through the largest empirical analysis of its kind, comparing to a wide range of runtime modelling techniques from the literature. Our experiments consider 11 algorithms and 35 instance distributions; they also span a very wide range of SAT, MIP, and TSP instances, with the least structured having been generated uniformly at random and the most structured having emerged from real industrial applications. Overall, we demonstrate that our new models yield substantially better runtime predictions than previous approaches in terms of their generalization to new problem instances, to new algorithms from a parameterized space, and to both simultaneously.

• The paper presents novel machine learning approaches, including random forests and Gaussian processes, achieving runtime prediction correlations above 0.9.
• It rigorously compares diverse models across SAT, TSP, and MIP datasets to showcase enhanced scalability and predictive accuracy.
• The research lays the groundwork for automated algorithm configuration and improved performance modeling in complex computational tasks.

Analyzing Algorithm Runtime Prediction Techniques

The paper under examination presents a thorough investigation into the utilization of machine learning methodologies for predicting algorithm runtimes on previously unseen inputs. This research addresses a challenge of considerable importance for both theoretical exploration and practical application: estimating the execution time of algorithms based on problem-specific instance features. The paper spans a variety of problem domains, including propositional satisfiability (SAT), the traveling salesperson problem (TSP), and mixed integer programming (MIP), and evaluates these techniques across extensive empirical datasets.

Overview of Methodologies

Within the framework of this paper, several approaches for algorithm runtime prediction are detailed and assessed. These encompass both existing methods and novel advancements. A range of models is employed, notably random forests and approximate Gaussian processes, alongside more classical approaches such as ridge regression and neural networks. Each technique is rigorously evaluated on extensive data, spanning empirical performance models and response surface models, to ascertain their predictive capability, scalability, and generalization performance across different algorithm configurations and problem instances.

Among the notable innovations, the paper introduces sophisticated techniques address model inputs comprehensively, particularly the modeling of runtime variations due to a large number of algorithm parameters. New features are incorporated specifically for SAT, MIP, and TSP problems, enhancing the predictive power of the models substantially.

Strong Results and Implications

A pivotal element of this paper is its empirical evaluation—the largest of its kind for such predictive models. The experiments demonstrate that the proposed models, particularly those leveraging random forests, consistently outperform existing techniques. The models' proficiency in predicting algorithm performance is underscored by strong numerical results, yielding correlation coefficients between predicted and actual runtimes exceeding 0.9 across several datasets. These results are compelling, showcasing the potential for robust generalization to new problem instances, configurations, and even new instances and configurations simultaneously.

This research trajectory has substantial implications. Practically, it offers enhanced tools for areas like automated algorithm configuration, portfolio-based algorithm selection, and the design of more efficient computational benchmarks. Theoretically, it advances understanding of algorithm performance variations, linking empirical findings to potential strategies for improvement in algorithm design.

Speculative Future Directions

The paper's findings inspire several avenues for future research. The application of these predictive models could be expanded to additional, complex problem landscapes beyond SAT, MIP, and TSP, potentially integrating even more nuanced instance-specific features. Moreover, exploring hybrid models that merge the strengths of different machine learning techniques might unlock further performance gains. Additionally, while the paper already considers some aspects of handling censored data, further integrating advanced survival analysis techniques could refine predictive accuracy in extreme scenarios.

In conclusion, this paper contributes valuable insights into the prediction of algorithm runtimes, demonstrating both the depth and breadth of current capabilities and setting a foundation for future developments in machine learning-guided algorithm analysis. The research not only bridges gaps between theory and application but also pushes the boundaries of what empirical performance models can achieve in predicting computational effort effectively.