St Petersburg University mathematician develops a method for modelling the optimal trajectory for road construction

Artem Sharlay, Research Engineer in the Department of Mathematical Modelling of Control Systems at St Petersburg University, has proposed a formalised approach to addressing this task, grounded in mathematical modelling techniques.

One of the most pressing practical challenges in designing roads, waterways, pipelines, and other transportation networks is determining the shortest path with the lowest construction cost. Moreover, solutions to these challenges are needed across a wide range of fields, including robotics and space exploration.

The challenges frequently encountered in the engineering design process have long been a major focus of study for research engineers. To efficiently find the shortest path, methods such as the Dijkstra’s algorithm, RRT (Rapidly-exploring Random Tree) and its variants, along with other similar approaches, are typically employed.

The goal of Artem Sharlay’s PhD thesis research was to mathematically model the cost of constructing a road that connects a starting point, where construction materials are sourced, to a final point. This approach reduces the challenge of finding the road trajectory with the optimal construction cost to a problem in the calculus of variations. The primary factors considered are the cost of delivering the road construction materials and the cost of laying them, both of which significantly influence the overall expenditure for the entire road.

The study titled "Search for the optimal road alignment on the terrain in terms of construction cost" was conducted as part of a dissertation for the Candidate of Physics and Mathematics degree at St Petersburg University.

The findings from the dissertation research have clear relevance for advancing theoretical studies. Additionally, Artem Sharlay proposed a software implementation of the constructed algorithms using the MATLAB mathematical package, which has practical implications not only for road construction but also for a broader range of applications.

The research can be further extended by refining the model and incorporating constraints into the mathematical problem. For instance, addressing scenarios where natural obstacles and impediments, such as swamps, ponds, or rivers, are present on the terrain is of significant practical interest. Like the problem examined in Artem Sharlay’s study, this would involve deriving necessary conditions and developing methods for their solution.

Given the vast territory of our country and the active development of transportation infrastructure, the dissertation topic is of high practical relevance. It offers the potential to significantly reduce road construction costs.

"Artem Sharlay has developed a method for mathematicallly modelling a road trajectory that connects two points with optimal construction cost. He proposed finding the equation of the desired curve as a function that minimises the integral cost functional. This functional includes two components: the first represents the cost of delivering road construction materials, and the second represents the cost of the construction work itself," said Professor Majid Elkhan oglu Abbasov, Acting Head of the Department of Mathematical Modelling of Control Systems at St Petersburg University and the research supervisor of the dissertation. "Throughout his research work, Artem Sharlay proved himself to be a determined, independent, and energetic researcher."

The mathematical model and methods developed in the reviewed research pave the way for creating a modern software product. This tool could greatly facilitate the construction of railways, motorways, pipelines, and other transportation infrastructure with minimal material expenditure.

When asked whether defending the dissertation under St Petersburg University’s own terms is challenging, Artem Sharlay responded: "I have attended dissertation defences at St Petersburg University before; and in my opinion, defending under the University’s own terms is better. Specifically, you do not need an abstract, although an English translation is required. The Dissertation Council, established for each specific defence, has fewer members now. This creates a more favourable environment for the candidate, while the quality of the public defence is not compromised because the requirements for council members are much higher than before. Before and after the defence, all paperwork is handled by the Dissertation Department; you only need to submit the necessary documents on time. I am very glad that everything worked out for me!"