Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Solution Development and Software Implementation of the Object Placement Problem on a Plane Subject to Constraints YA.V. KRAVCHENKO, N.A. MAMEDOVA, M.A. AFANASEV The paper presents a universal approach to solving the problem of completing a partial placement of objects on a plane subject to heterogeneous constraints. A generalization of the classical N-Queens problem is used as the basic model. The key element is the formalization of constraints through attack sets, which describe conflict zones for objects of various types, enabling a unifi ed description of rules for different object types. Based on this model, an algorithm employing the Backtracking method has been developed and implemented in C++ as a modular software system. The correctness and effi ciency of the approach were confi rmed through a computational experiment on the N-Queens problem, establishing the boundaries of its practical applicability. The adaptation of the method to an applied problem–optimizing a parking lot layout considering existing infrastructure–is demonstrated. The obtained results highlight the potential of the proposed method as a foundational tool for decision support systems in logistics, spatial planning, and design. Keywords: combinatorial optimization, placement problem, N-Queens problem, placement completion problem, partial placement, attack set, backtracking algorithm, formal model, software implementation, spatial planning. DOI: 10.25791/pribor.4.2026.1667 Pp. 38-50.