Fast instance-specific algorithm configuration with graph neural network

TL;DR

This work tackles the problem of speeding up instance-specific algorithm configuration (ISAC) for combinatorial optimization by replacing expensive runtime feature extraction with a graph neural network (GNN) classifier. Building on ISAC, it trains a GNN to map graph representations of unseen instances to precomputed classes, enabling rapid selection of cluster-specific solver parameters and reducing the overhead of $T_{tot}=TTS+T_{tune}$. The approach combines heavy offline steps—feature extraction, dimensionality reduction, clustering, and SMBO-based tuning—with a lightweight online classification that delivers sub-second inference for $T_{tune}$. Experiments with the Digital Annealer on diverse BQP-like problems show the classifier achieves around 85% accuracy and yields notable reductions in time-to-solution and overall runtime for many instances, approaching the performance of per-problem tuning while substantially lowering preprocessing costs.

Abstract

Combinatorial optimization (CO) problems are pivotal across various industrial applications, where the speed of solving these problems is crucial. Improving the performance of CO solvers across diverse input instances requires fine-tuning solver parameters for each instance. However, this tuning process is time-consuming, and the time required increases with the number of instances. To address this, a method called instance-specific algorithm configuration (ISAC) has been devised. This approach involves two main steps: training and execution. During the training step, features are extracted from various instances and then grouped into clusters. For each cluster, parameters are fine-tuned. This cluster-specific tuning process results in a set of generalized parameters for instances belonging to each class. In the execution step, features are extracted from an unknown instance to determine its cluster, and the corresponding pre-tuned parameters are applied. Generally, the running time of a solver is evaluated by the time to solution ($TTS$). However, methods like ISAC require preprocessing. Therefore, the total execution time is $T_{tot}=TTS+T_{tune}$, where $T_{tune}$ represents the tuning time. While the goal is to minimize $T_{tot}$, it is important to note that extracting features in the ISAC method requires a certain amount of computational time. The extracting features include summary statistics of the solver execution logs, which takes several 10 seconds. This research presents a method to significantly reduce the time of the ISAC execution step by streamlining feature extraction and class determination with a graph neural network. Experimental results show that $T_{tune}$ in the execution step, which take several 10 seconds in the original ISAC manner, could be reduced to sub-seconds.

Figures (13)

• Figure 1: Overview of the instance-specific algorithm configuration framework.
• Figure 2: Overview of the proposed methodology framework.
• Figure 3:
• Figure 4:
• Figure 5: