## 1 Introduction  
With continuous economic development, urban traffic congestion is increasingly becoming a serious problem. Overpasses play an important role in solving the urban traffic problem. As the connecting structure of the main bridge and ramps in urban overpasses, an irregularly-shaped bridge, as shown in Figure 1a, can solve the conflict of bridge and ground transportation effectively to improve the driving efficiency and keep it in harmony with the environment [1]. However, an irregularly-shaped bridge usually adopts the thin-walled box girder, which suffers salient restrained torsion and shear lag effects [2]. The main bridge and ramp are contacted and restricted with each other at the croft of the irregularly-shaped bridge, which results in a complicated strained condition and varying degrees of damage. In recent years, the collapse of irregular-shaped bridges have happened several times in China, as illustrated in Figure 1b [3]. The optimal design of such structures can be extremely useful to improve this situation. [PERSON] et al. [4; 5] had studied the dynamic behaviors of a pedestrian bridge before retrofitting, and after, using experimental and numerical methods. The dynamic interaction between pedestrians and the bridge and the damping factor were investigated. Due to the change of mass and stiffness of the footbridge caused by retrofitting using glass fiber-reinforced polymers (GFRPs), the dynamic behavior was indeed modified. Dynamic interaction still existed, and the modal damping factors for the main modes of bending vibration almost doubled after retrofitting. Therefore, the dynamic interaction problem highlights the need to perform specific dynamic analysis during the design phase of light and slender bridges to avoid resonance. For the design of irregularly-shaped bridges, many parameters affect its mechanical properties. One of the key aspects of an optimization study is the sensitivity analysis of influence parameters. How to determine the major influence parameters of the design indices and find the optimal parameter levels for an irregularly-shaped bridge are becoming the focus of attention and demand for engineers. The thin-walled box girder adopted in irregularly-shaped bridges usually suffers from the influence of torsion, distortion, warping, and shear lag, which causes a severely uneven stress distribution [6; 7]. Many researchers have studied the calculation principles and analysis methods for the thin-walled box girder [8; 9; 10; 11; 12]. However, the mechanical property of an irregularly-shaped bridge is different from the conventional straight and curved thin-walled box girder bridge. The traditional analytical method is unsuitable to solve this problem. Finite element analysis (FEA) is a widely used numerical calculation method, which provides an effective way to analyze the static and dynamic properties of structures [13; 14; 15; 16; 17]. Through numerical simulation, the influence of design parameters on mechanical properties of irregularly-shaped bridges and curved bridges have been studied and demonstrated [1; 18]. However, the investigation on multi-indices optimization for the mechanical properties of irregularly-shaped bridges is relatively scarce [19; 20]. Due to numerous parameters affecting the strained condition of irregularly-shaped bridges, the influence of a single parameter is not able to reflect the effect of parameters in combination. Moreover, the comprehensive combination tests of influence parameters need repeated and complicated numerical modeling and analysis, which is difficult to be achieved due to the large degree of testing and calculation. The classical optimization procedures, such as back propagation neural networks (BPNN), support vector machines (SVM), and genetic algorithms (GA), need significant amounts of numerical simulation with different parameter combinations, which also makes the optimization design more complex. Even for a simple problem, the objective functions are calculated based on a large number of training samples.