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The paper addresses an optimization problem of hydraulic conditions of heat supply systems. The research shows that when the main methods of operation control, including the control of the number of connected pumps at pumping stations, are used this problem is reduced to a mixed discrete-continuous programming problem which involves a nonlinear objective function, nonlinear equality constraints and simple inequalities. The paper presents the basic principles of the methods for calculation of feasible and optimal conditions on the basis of continuous variables as a constituent of the suggested technique for solving the general problem. Consideration is given to four possible strategies to fraction and cut the variants while searching for solutions on the basis of discrete variables. The results of computational experiments illustrating the comparative efficiency of different strategies are presented.Keywords Discrete-continuous optimization · Strategies for problem solving on the basis of continuous and integer-valued variables · Hydraulic conditions · Heat supply systems

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