Optimization methods for local building plans of the area

It is shown that the problem of maximizing living space with restrictions on the cost of construction and the land plot area is reduced to the problem of integer programming with two restrictions. To solve it, you can apply standard known methods and algorithms. Consider, however, another approach based on the method of networks of admissible solutions, proposed by Burkov V.N. The idea of the method is following. We consider the first the constraints of the problem and construct a network of all admissible solutions for this restriction. On the basis of the introduced notion of a problem vertex, a theorem is proved that the proposed method for constructing a network of all admissible solutions will contain all solutions satisfying the constraints of the original problem, and the length of the maximal path in such a network will determine the upper bound for the original problem. It is shown that if the path of maximum length does not contain problem vertices, then the corresponding solution is optimal. The algorithm is generalized to the case of accounting for construction risks.