A Globalized Robust Optimization Approach of Dynamic Network Design Problem With Demand Uncertainty

Zhao, Fangwei; Sun, Hua; Zhao, Fangxia; Zhang, Hong; Li, Tongfei · 2019 · OpenAlex-citations

DOI: 10.1109/access.2019.2933540

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the dynamic network design problem (NDP) under demand uncertainty, specifically focusing on the limitations of traditional robust optimization models. Traditional set-based robust optimization assumes uncertain parameters remain within a defined uncertainty set; however, real-world data may occasionally fall outside this "normal range," potentially leading to infeasible solutions. To address this, the authors propose a globalized robust optimization (GRO) approach that allows for controlled constraint violations when demand exceeds the defined bounds, thereby balancing robustness with flexibility. The study also incorporates a non-holding back cell transmission model (CTM) to accurately describe dynamic traffic flows without the artificial accumulation of vehicles often seen in standard CTM formulations. The methodology formulates the problem as a single-level system-optimal NDP using linear programming. The deterministic baseline model minimizes total travel time and unmet demand penalties, subject to flow conservation, capacity constraints, and budget limits. To handle uncertainty, the authors assume the normal range of uncertain demand follows a box set. They derive the globalized robust counterpart (GRC) of the model, introducing global sensitivity parameters that control the degree of constraint violation relative to the distance of the uncertain demand from the normal range. A key technical contribution is the transformation of this GRC into a tractable linear programming model by employing affine decision rules, ensuring the problem remains solvable in polynomial time despite the uncertainty. The study validates the proposed model through numerical experiments comparing the GRO solution against standard robust optimization and adjustable robust optimization (ARO) models. The results demonstrate that the GRO approach offers superior solution quality by providing a balance between conservatism and feasibility. Unlike standard robust models, which can be overly conservative, or models that fail when data exceeds the uncertainty set, the GRO framework maintains feasibility while controlling performance deterioration. The numerical analysis confirms that the linear programming formulation is computationally efficient and effective in managing demand fluctuations. The significance of this work lies in its practical applicability to traffic management and planning under uncertainty. By providing a computationally tractable model that accounts for rare but possible demand outliers, the GRO approach offers a more realistic tool for network designers. The findings suggest that this framework can be extended to other dynamic traffic problems, such as signal optimization and autonomous intersection control, where uncertainty and dynamic flow propagation are critical factors. The paper concludes that globalized robust optimization provides valuable insights for creating resilient transportation networks that can withstand demand variability without sacrificing computational efficiency.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• mental model of traffic