###### Abstract  
Seismic mitigation of transportation systems has become a worldwide challenge, because identifying an optimal retrofit strategy entails significant computational efforts, especially for large-scale networks with numerous candidate strategies and time-consuming risk assessment processes. An efficient joint importance-based methodology is proposed in this paper to address the challenge. The proposed method selects the component set (_e.g._, bridges) that is most decisive to the network seismic risk based on only one set of stochastic samples but takes into account the uncertainty of multiple damage states and the interactive effect between different components. The reliability and stability of the proposed method are verified on a hypothetical transportation network under different conditions. transportation network; seismic risk; risk mitigation; decision making; network functionality +
Footnote †: journal: Applied Sciences  
**Citation:** [PERSON]; [PERSON]; [PERSON]. **Technical Joint Importance-Based Retrofit Strategy for Seismic Risk Mitigation of Transportation Networks. To address the above challenges, many researches proposed importance-ranking methods as an alternative to the above optimization models. Traditional ranking methods are mainly based on the structural attributes of individual components [29; 30; 31], and some recent studies have proposed Multi-Criteria Decision-Making (MCDM) methods to integrate the technical and socioeconomic attributes [32; 33; 34; 35]. These methods do not consider the roles of components in the transportation network from a system prospect. Some other researches have prioritized the components according to their spatial importance in network topology (e.g., betweenness centrality [36; 37; 38]). However, such measures do not correlate well with the functionality of transportation networks. In literature, the importance of a component in the transportation network is most commonly assessed according to the impact of removing that component from the network [39; 40; 41]. Although all the above methods greatly reduce the computational effort, there could be a gap between their results and the real optimal solution because none of them takes into account the uncertainties in the damage states of network components. Several recent studies have proposed to evaluate the importance of components using conditional probability between component failure and system failure [42; 43; 44; 45]. These methods consider both the vulnerability of a component and its impact on system reliability, which improves the identification of retrofit importance. However, there are still some defects. The post-earthquake condition of a component is usually assumed to be binary (i.e., functional or non-functional), and the effects of multiple potential damage states are rarely considered. More importantly, all the above ranking methods are designed for individual components, and the retrofitted components are selected one by one according to their importance value. However, the set of top-ranked components cannot ensure the largest mitigation benefit since the retrofit benefit from different components are not independent [14]. This paper formulates the general seismic retrofit problem for risk mitigation of transportation networks under multiple uncertainties. To efficiently solve the problem, a probabilistic joint importance-based method is introduced to select the component set with the highest retrofit priority instead of the time-consuming optimization process. This approach transforms the complex SO problem into a feature subset-selection problem associated with the network seismic risk, and the joint importance of component sets can be obtained based on only a limited number of stochastic samples. The proposed method is applied to the seismic mitigation problem of emergency response on a hypothetical transportation network.