Modeling the optimal flight route of unmanned aerial vehicle for conducting forest fire exploration

Abstract

Between 2018 and 2023, more than 3,600 forest fires were recorded across Kazakhstan, burning 561,000 hectares and causing losses exceeding 192.8 billion tenge. Fire-prone zones such as the Borovoe forest area of Akmola region illustrate a problem that field commanders routinely face: when several ignition sites are detected simultaneously, there is no established procedure for sequencing a fixed-wing UAV reconnaissance flight to cover all of them in minimum time. Without such a procedure, route selection defaults to the operator’s judgement, which carries a real risk of redundant traversals and delayed situation assessment. This article examines whether the Travelling Salesman Problem (TSP), a classical tool of discrete mathematics, can fill that procedural gap and serve as the computational core of a UAV mission planning module for the Commander of Forest Fire Extinguishing (CFE). We formulate the multi-site reconnaissance task as an asymmetric integer program with subtour-elimination constraints, derive the globally optimal Hamiltonian circuit for a four-node test case drawn from representative inter-site distances, and show that the resulting route (1→4→2→3→1, total 860 m) is up to 47.7% shorter than non-optimal alternatives. The model is platform-agnostic; however, it is discussed in the context of fixed-wing UAV characteristics relevant to Kazakhstan’s operational conditions. Findings provide a formal algorithmic foundation for embedding route optimization into existing software-information systems for forest fire monitoring and CFE decision support within the Ministry of Emergency Situations of the Republic of Kazakhstan.