The External Penalty Function Method for Optimization Design of Reinforced Concrete Underground Penstock

The external penalty function methods transform the basic optimization problem into alternative formulations such that numerical solutions are sought by solving a sequence of unconstrained minimization problem. This paper uses the external penalty function method to solve constrained optimal control problems for optimization design of underground reinforced concrete penstock. Through establishing the cost of construction of underground penstock as objective function and strength, stability and deformation as constrain conditions, hence we have solved the minimum cost constrained optimal control problems and gained the minimum cost. Due to the optimized design, the rate of reinforcement rebar decreased 15%.