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The aim of the paper is to popularize the Razna National Park’s tourist attractions. The opportunity to choose the shortest route to visit all the most interesting potential sightseeing objects is offered. The authors continue their research on the theoretical and practical aspects of searching for the shortest route. Theoretical research has been carried out and mathematically the shortest route has been calculated for various sightseeing objects of the Razna National Park. The paper also provides mapping of these objects and an analysis of the locations of the sightseeing objects at different levels. The main goal of the paper is to show the possibilities of applying mathematical models in solving practical tasks – to determine the shortest route between the sightseeing objects. This research describes an optimization method called Simulated Annealing. The Simulated Annealing method is widely used for various combinatorial optimization tasks. Simulated Annealing is a stochastic optimization method that can be used to minimize the specified cost function given a combinatorial system with multiple degrees of freedom. In this paper, the application of the Travelling Salesman Problem is demonstrated, and an experiment aimed to find the shortest route between the Razna National Park sightseeing objects is performed. Common research methods are used in this research: the descriptive research method, the statistical method, mathematical modelling.

Information about the merger of schools or their optimization periodically appears in the society. It is believed that the ideal school network is not yet ready. The paper provides the analysis of the educational institutions locations by their availability. A theoretical research has been conducted and mathematically the shortest path has been calculated between different educational institutions. The paper also provides mapping of these educational institutions and location analysis of educational institutions at different levels. The main goal of the paper is to show the possibilities of applying the mathematical models in solving practical tasks – to determine the shortest path between the educational institutions. This study describes an optimization method called Simulated Annealing. The Simulated Annealing method is widely used in various combinatorial optimization tasks. Simulated Annealing is a stochastic optimization method that can be used to minimize the specified cost function given a combinatorial system with multiple degrees of freedom. In this paper the application of Travelling Salesman Problem, is demonstrated and an experiment aimed to find the shortest route between educational institutions of Rezekne Municipality is performed. It gives possibilities to analyse and search optimal school' s network in the Rezekne Municipality. Common research methods are used in this research: descriptive research method, statistical method, mathematical modelling

This study describes an optimization method called Simulated Annealing. The Simulated Annealing method is widely used in various combinatorial optimization tasks. Simulated Annealing is a stochastic optimization method that can be used to minimize the specified cost function given a combinatorial system with multiple degrees of freedom. In this study the application of the Simulated Annealing method to a well - known task of combinatorial analysis, Travelling Salesman Problem, is demonstrated and an experiment aimed to find the shortest tour distances between educational institutions of Rēzekne Municipality is performed. It gives possibilities to analyze and search optimal schools' network in Rēzekne Municipality.