Abstract <p>The efficiency of metal heat treatment production processes is measured according to various characteristics, including productivity, energy consumption, and quality of the end product. Each of them can be enhanced through optimization by the relevant integral criterion. The quality of the end product made from a high-iron alloy depends, after heat treatment, on metal loss to scale, which is inevitably formed during high-intensity heating in an induction installation. For this reason, to reduce the percentage of rejects, it is necessary to find an optimal operating mode of the inductor, which will minimize this loss. This paper is devoted to the optimization of static induction heating of steel cylindrical workpieces before subsequent plastic deformation operations. A 2D numerical mathematical model of the induction heating process, developed in Altair FLUX, is considered as a controlled object with distributed parameters. Control problems with respect to time-optimal, minimum energy consumption, and minimum metal scale loss criteria are formulated. A solution to the formulated control problems after their parametrization and reduction to semi-infinite optimization can be found using the alternance method of parametric optimization of objects with distributed parameters. A system of transcendental equations is written based on the alternance method as an example for the minimum scale formation problem. These equations are closed to all unknown parameters of the heating process. The system is solved using an automated procedure developed in the MATLAB software package. An analysis of numerical results shows that solving this one-criterion optimal control problem reduces the amount of scale significantly increasing heating time compared to time-optimal and minimum energy consumption problems. That is why it is planned to solve a multi-criteria optimization problem taking into account several typical goal functions simultaneously at the next stage of research.</p>