The problem of synthesis of boundary control for damping transverse oscillations of a string is investigated. The feedback is carried out by the use of integral measurements of the amplitude of the oscillatory process in the vicinity of measurement points The measurements are performed by measuring devices (sensors) moving along the string. The values of amplitude measurements at the current and past time moments in the vicinity of the measuring points are used to determine the boundary control. The paper presents a formulation of the problem of boundary control synthesis, in which both the velocity of the motion of the measuring devices and the parameters of the feedback are optimized. The paper considers the case of linear feedback, which determines the dependencies between integral measurements of the string amplitude in the vicinity of the measurement points, on the one hand, and the boundary control and the velocity of motion of the measuring devices, on the other hand. To determine the values of the optimized parameters involved in these dependencies, formulas are obtained that allow the use of efficient numerical methods of first-order optimization. The results of numerical experiments for solving test problems are presented.