Task Representation in Optimization: Utilizing Image Modalities for Effective Comparison

This paper addresses the challenge of identifying similarities between different optimization tasks, which is crucial for enhancing transfer learning and automated optimization systems. Traditional rule-based methods often fail to capture the complexity of problems, while existing data-driven approaches lack comprehensive feature representation and generalization across domains. Moreover, there is a severe lack of training data when applying deep learning strategies. To overcome these limitations, we propose a novel model based on contrastive learning for optimization task similarity recognition. Our approach integrates information from the decision space, objective space, and derivative space, creating a unified representation framework inspired by image data formats. We employ a convolutional neural network to extract task features and utilize contrastive learning to measure task similarity. Experimental results demonstrate the model’s effectiveness in generalizing to new optimization tasks and its sensitivity to task differences. We conducted experiments on 40- and 60-dimensional problems, where sampling only 5 times the dimensionality of data points was sufficient for distinction. The proposed method not only provides a comprehensive representation of optimization tasks but also enhances the model’s generalization performance.