In this paper, we focus on interconnected trajectory optimization of two sets of solenoid actuated butterfly valves dynamically coupled in series. The system undergoes different approach angles of a pipe contraction as a typical profile of the so-called "Smart Valves" network containing tens of actuated valves. A high fidelity interconnected mathematical modeling process is derived to reveal the expected complexity of such a multiphysics system dealing with electromagnetics, fluid mechanics, and nonlinear dynamic effects. A coupled operational optimization scheme is formulated in order to seek the most efficient trajectories of the interconnected valves minimizing the energy consumed enforcing stability and physical constraints. We examine various global optimizationmethods including Particle Swarm, Simulated Annealing, Genetic, and Gradient based algorithms to avoid being trapped in several possible local minima. The effect of the approach angles of the pipeline contraction on the amount of energy saved is discussed in detail. The results indicate that a substantial amount of energy can be saved by an intelligent operation that uses flow torques to augment the closing efforts.