A method for optimizing multiple responses in solenoids utilized in a magnetic nozzle assembly for an electric plasma thruster is presented. The primary goal is to minimize power usage while maintaining a sufficiently high magnetic flux density at the coil axis. This is especially critical during testing in a vacuum chamber, where heat dissipation is a challenge, especially for small components and intricate assemblies. This paper presents a method for quickly calculating the magnetic field along the solenoid axis that provides accurate estimates, independent of coil size. Additionally, we present general and concrete results for the employed magnetic nozzle design to illustrate the applied optimization method. The paper details a methodology for optimizing multiple parameters of a solenoid, including its radius, length, current, number of turns, and wire diameter. The aim is to minimize, maximize, or meet specific targets for magnetic flux density, power, or mass. Additional studies could utilize a suitable metric to optimize the homogeneity of the magnetic field of multiple coils. The coils designed using the algorithm have a radius of 17.5mm, a length of 21mm, consist of 300 turns with a wire diameter of 1mm, and operate at a direct current of about 5 A. The potential maximum magnetic field is 40mT with a power consumption of around 30 W.