RESEARCH PAPER A genetic algorithm-based multi-objective optimization for hybrid fiber reinforced polymeric deck and cable system of cable-stayed bridges Hongwei Cai 1,2 & Amjad J. Aref 2 Received: 2 February 2014 /Revised: 8 May 2015 /Accepted: 8 May 2015 # Springer-Verlag Berlin Heidelberg 2015 Abstract As the length of main span of cable-stayed bridge increases, several technical challenges become more prevalent with traditional materials. Such technical challenges include: large axial stresses in main girders, cable sagging effect, and aerodynamic instability, consequently limiting the prospects of extending the span length of future cable-stayed bridges with traditional materials. In order to remedy these issues, we propose fiber reinforced polymeric (FRP) composites for the deck and cable system of cable-stayed bridges in combi- nation with traditional materials. To use FRP composites most effectively, we developed a genetic algorithm (GA)-based op- timization procedure to solve for the distribution of Glass FRP and concrete in the hybrid deck system, and the distribution of carbon FRP and steel in the hybrid cable system. This pro- posed optimization-based procedure aimed at developing two systems: (1) optimized hybrid Glass FRP-concrete deck sys- tem (OHDS), and (2) optimized Carbon FRP-steel cable sys- tem (OHCS), which can maximize static and aerodynamic performances concurrently. As an example, we utilized an existing long-span composite cable-stayed bridge and imple- mented these two systems. For a typical long span cable- stayed bridge, the results of this benchmark example provide insights about the typical composition of OHDS and OHCS and suggest that these two systems can concurrently improve the static and aerodynamic performances by 33 and 12 %, respectively. Keywords Cable-stayed bridge . Glass fiber reinforced polymer-concrete deck system . Carbon fiber reinforced polymer-steelcable system . Geneticalgorithm . Criticalflutter velocity 1 Introduction Since the concept of cable-stayed bridges was first proposed in the 17th century, modern cable-stayed bridges have entered the era of 1000-m main span length. However, as the span length of cable-stayed bridge increases, there exist several technical challenges pertaining to axial stresses in main girders, cable stiffness, cable strength, and aerodynamic sta- bility. In particular, the following four issues are of key significance: i. As the span length increases, dead loads and cable tensions increase. The axial compressions from stay cables applied on main girders will increase accordingly. ii. As the span length and cable length increase, cables sag more and thus nonlinear cable behavior becomes more evident, which will lead to the deterioration of the cable stiffness. iii. Cables need to hold large tensions to keep taut, reduce sagging effect, and carry the ever-increasing dead loads as the span length increases. However, traditional mate- rial can’t provide comparable strength without increasing the cross-sectional area significantly, which will increase the self-weight of cables and result in cable sagging issue in return. iv. For long-span cable-stayed bridges, the critical aerody- namic issue is the flutter instability (Wang 2003). The main factors influencing flutter instability on bridge char- acteristics are: (i) geometry of the bridge deck; (ii) * Hongwei Cai caihongwei023658@gmail.com 1 Parsons Brinckerhoff, 2777 N. Stemmons Freeway, Dallas, TX, USA 2 Department of Civil, Structural and Environmental Engineering, University at Buffalo-the State University of New York, Buffalo, NY 14260, USA Struct Multidisc Optim DOI 10.1007/s00158-015-1266-4