Exploring the pre-disaster evacuation network design problem under five traffic equilibrium models

• Develop five evacuation network design models considering four types of equilibriums. • The superiority of each model is compared, and it is also demonstrated that equilibrium cannot be ignored in evacuation network design. • Design five heuristic algorithms to solve models, and analyze the algorithm design features and the performance. • The evacuation network design structure is continuous, and the reliability of the models and algorithms is verified using two test networks and analysis of 40 random instances. This paper explores modeling approaches for the pre-disaster Evacuation Network Design Problem (ENDP) considering different flow equilibrium conditions. We combine this problem with the modeling idea of Continuous Network Design Problem (CNDP), which we call Continuous Evacuation Network Design Problem (CENDP) in this paper. We develop five CENDP models, which are under the consideration of User Equilibrium (UE), Stochastic User Equilibrium (SUE), Boundedly Rational User Equilibrium (BRUE), and Non-equilibrium (NONE), among which we develop two types of models based on BRUE. The modeling is mainly to consider the single objective of optimizing the total evacuation time, and then to provide reasonable road expansion solutions under certain budget constraints and different equilibrium conditions. Our main motivation for developing models is to introduce various types of equilibrium conditions into models and design algorithms to solve these problems while mining for key insights. We design the corresponding five heuristic algorithms to solve models and verify the applicability of the models and algorithms by two test networks (Nguyen-Dupuis network and Sioux-Falls network). We demonstrate whether evacuation flow equilibrium need or not need to be considered in the CENDP, the applicability of different equilibrium conditions, and the correlation between the total evacuation time, the network investment cost, and the network congestion degree. Additionally, we conduct model and algorithm tests on 40 instance networks, dividing them into medium-sized networks (20 instances) and large-sized networks (20 instances). Not only do we further validate the insights obtained from the test networks, but we also expand upon them. Specifically, the main findings of this study are as follows: (1) We demonstrate that considering evacuation flow equilibrium in CENDP is essential to reduce total evacuation time, construction costs, and mitigate congestion. (2) While increased investment in road construction can meet evacuation time requirements, it is crucial to make informed decisions, as investment alone does not directly reduce total evacuation time and congestion. (3) Optimizing road evacuation time is more effective than merely increasing road capacity for reducing total evacuation time and mitigating congestion. (4) From the perspectives of total evacuation time, investment cost, and network congestion degree, the CENDP model considering user equilibrium performs better in medium-sized networks, while the CENDP model considering stochastic user equilibrium performs better in large-sized networks. Conversely, the CENDP model that does not consider flow equilibrium performs the worst across all above three metrics. Based on this, we also provide recommendations on which model to choose for different metrics. In summary, this study not only reveals the importance of different flow equilibrium conditions in evacuation network design but also provides valuable strategic recommendations for practical applications to optimize evacuation effectiveness and resource allocation.