Purpose. The synthesis of active screening system of magnetic field, generated by several high voltage overhead transmission lines, with the help of single compensation cables is presented. Methodology. The initial parameters for the synthesis of active screening system parameters are the location of the high voltage overhead transmission lines with respect to the protected transmission line space, geometry and number of cables, operating currents, as well as the size of the protected space and normative value of magnetic flux density, which should be achieved as a result of screening. The objective of the synthesis of the active screening system is to determine their number, configuration, spatial arrangement, wiring diagrams and compensation cables currents, setting algorithm of the control systems as well as the resulting value of the induction magnetic field at the points of the protected space. Synthesis of active screening system is reduced to the problem of multi objective nonlinear programming with constraints in which calculation of the objective functions and constraints are carried out on the basis of the Maxwell equations solutions in the quasi-stationary approximation. The problem is solved by a stochastic multi swarm multi agent particles optimization, which can significantly reduce the time to solve it. Results. Active screening system synthesis results for reduction of a magnetic field generated by several high voltage overhead transmission lines are presented. The possibility of a significant reduction in the level of source magnetic flux density within a given. Originality. For the first time the synthesis of the active screening systems of magnetic field generated by the several high voltage overhead transmission lines within a given region of space is carried out. Practical value. Practical recommendations on reasonable choice of the number and spatial arrangement of compensating cables of active screening systems of the magnetic field generated by the several high voltage overhead transmission lines is given.