A Surrogate Piecewise Linear Loss Function for Contextual Stochastic Linear Programs in Transport

Qi Hong, Mo Jia, Xuecheng Tian (), Zhiyuan Liu and Shuaian Wang
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Qi Hong: School of Transportation, Southeast University, Nanjing 211189, China
Mo Jia: School of Transportation, Southeast University, Nanjing 211189, China
Xuecheng Tian: Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Zhiyuan Liu: Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing 211189, China
Shuaian Wang: Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Mathematics, 2025, vol. 13, issue 12, 1-17

Abstract: Accurate decision making under uncertainty for transport problems often requires predicting unknown parameters from contextual information. Traditional two-stage frameworks separate prediction and optimization, which can lead to suboptimal decisions, as minimizing prediction error does not necessarily minimize decision loss. To address this limitation, inspired by the smart predict-then-optimize framework, we introduce a novel tunable piecewise linear loss function (PLLF). Rather than directly incorporating decision loss into the learning objective based on specific problem, PLLF serves as a general feedback mechanism that guides the prediction model based on the structure and sensitivity of the downstream optimization task. This design enables the training process to prioritize predictions that are more decision-relevant. We further develop a heuristic parameter search strategy that adapts PLLF using validation data, enhancing its generalizability across different data settings. We test our method with a binary route selection task—the simplest setting to isolate and assess the impact of our modeling approach on decision quality. Experiments across multiple machine learning models demonstrate consistent improvements in decision quality, with neural networks showing the most significant gains—improving decision outcomes in 36 out of 45 cases. These results highlight the potential of our framework to enhance decision-making processes that rely on predictive insights in transportation systems, particularly in routing, scheduling, and resource allocation problems where uncertainty plays a critical role. Overall, our approach offers a practical and scalable solution for integrating prediction and optimization in real-world transport applications.

Keywords: piecewise linear loss function; optimization under uncertainty; machine learning; contextual stochastic optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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