Long-span suspension bridges are becoming prevalent globally with the rapid progress in design methodologies and construction technologies. Although with apparent progress, the balance between excessive displacement and inner forces, under dynamic loads, is still a main concern because of increased flexibility and low structural damping. Therefore, effective controllers should be employed to control the seismic responses to ensure their normal operation. In this chapter, the combination of the analytic hierarchy process (AHP) and first-order optimization method are formulated to optimize seismic response control effect of the Runyang suspension bridge (RSB) under earthquakes, considering traveling wave effect. The compositive optimal parameters of dampers are achieved on the basis of 3-dimensional nonlinear seismic response analyses for the RSB and parameters sensitivity analyses. Results show that the dampers with rational parameters can reduce the seismic responses of the bridge significantly, and the application of the AHP and first-order optimization method can lead to accurate optimization effects.
TopFoundations Of Optimization Theory
Optimization theory is widely used in civil engineering to combat various issues such as sensor placement for structural health monitoring (Heo, Wang, & Satpathi, 1997; Meo & Zumpano, 2005), finite element model updating (Wang, Li, & Miao, 2005), cable force optimization of the cable-stayed bridges (Zhang & Xiao, 2005), bridge design (Ming, Hu, & Huang, 2007), acoustic design (Duhring, Jensen, & Sigmund, 2008), structural damage identification (Andrzej, Przemyslaw, & Jan, 2008), et cetera. Generally, the constrained optimization problem can be expressed as:Minimize 
(1) subjected to:
(i=1,2,3,…,N)
(j=1,2,3,…,m1)
(k=1,2,3,…, m2)
(l=1,2,3,…, m3)where xi is the design variable; gj, hk, and wl represent the state variables; N is the number of design variables and m1+m2+m3 is the number of state variables. The bar above/below variables represents the lower/upper bound.