A two-stage meta-heuristic optimization model is introduced to find the optimal shape of double-arch concrete dams. The main aim is that computational merits of the continuous ant colony optimization (ACOR) and the particle swarm optimization (PSO) be integrated. This proposed method called ACOR–PSO can accelerate the capability of exploitation and convergence of PSO. To achieve this, a preliminary optimization is accomplished using ACOR in the first stage of ACOR–PSO. In the second phase ACOR–PSO, PSO is utilized by using the optimal initial swarm of the first phase results. The weighted least squares support vector machine (WLS-SVM) is considered as the most reliable method for predicting the dynamic responses of dams. To testify the robustness and efficiency of the proposed ACOR–PSO, first, the well-known benchmark functions in literatures are optimized using the proposed ACOR–PSO, and provides comparisons with ACOR and PSO. Then, a real world double-arch dam is presented to demonstrate the effectiveness and practicality of the ACOR–PSO. The numerical results reveal that ACOR–PSO not only converges to better solutions but also provides faster convergence rate in comparison with ACOR and PSO. 
Hybridizing two-stage meta-heuristic optimization model with weighted least squares support vector machine for optimal shape of double-arch dams