The need to optimize the deployment and maintenance costs for service delivery in wireless networks is an essential task for each service provider. The goal of this paper was to optimize the number of service centres (gNodeB) to cover selected customer locations based on the given requirements. This optimization need is especially emerging in emerging 5G and beyond cellular systems that are characterized by a large number of simultaneously connected devices, which is typically difficult to handle by the existing wireless systems. Currently, the network infrastructure planning tools used in the industry include Atoll Radio Planning Tool, RadioPlanner and others. These tools do not provide an automatic selection of a deployment position for specific gNodeB nodes in a given area with defined requirements. To design a network with those tools, a great deal of manual tasks that could be reduced by more sophisticated solutions are required. For that reason, our goal here and our main contribution of this paper were the development of new mathematical models that fit the currently emerging scenarios of wireless network deployment and maintenance. Next, we also provide the design and implementation of a verification methodology for these models through provided simulations. For the performance evaluation of the models, we utilize test datasets and discuss a case study scenario from a selected district in Central Europe.

The assignment problem is a problem that takes many forms in optimization and graph theory, and by changing some of the constraints or interpreting them differently and adding other constraints, it can be converted to routing, distribution, and scheduling problems. Showing such correlations is one of the aims of this paper. For some of the derived problems having exponential time complexity, the question arises of their solvability for larger instances. Instead of the traditional approach based on the use of approximate or stochastic heuristic methods, we focus here on the direct use of mixed integer programming models in the GAMS environment, which is now capable of solving instances much larger than in the past and does not require complex parameter settings or statistical evaluation of the results as in the case of stochastic heuristics because the computational core of software tools, nested in GAMS, is deterministic in nature. The source codes presented may be an aid because this tool is not yet as well known as the MATLAB Optimisation Toolbox. Benchmarks of the permutation flow shop scheduling problem with the informally derived MIP model and the traveling salesman problem are used to present the limits of the software’s applicability.

The amount of internet traffic generated during mass public events is significantly growing in a way that requires methods to increase the overall performance of the wireless network service. Recently, legacy methods in form of mobile cell sites, frequently called cells on wheels, were used. However, modern technologies are allowing the use of unmanned aerial vehicles (UAV) as a platform for network service extension instead of ground-based techniques. This results in the development of flying base stations (FBS) where the number of deployed FBSs depends on the demanded network capacity and specific user requirements. Large-scale events, such as outdoor music festivals or sporting competitions, requiring deployment of more than one FBS need a method to optimally distribute these aerial vehicles to achieve high capacity and minimize the cost. In this paper, we present a mathematical model for FBS deployment in large-scale scenarios. The model is based on a location set covering problem and the goal is to minimize the number of FBSs by finding their optimal locations. It is restricted by users’ throughput requirements and FBSs’ available throughput, also, all users that require connectivity must be served. Two meta-heuristic algorithms (cuckoo search and differential evolution) were implemented and verified on a real example of a music festival scenario. The results show that both algorithms are capable of finding a solution. The major difference is in the performance where differential evolution solves the problem six to eight times faster, thus it is more suitable for repetitive calculation. The obtained results can be used in commercial scenarios similar to the one used in this paper where providing sufficient connectivity is crucial for good user experience. The designed algorithms will serve for the network infrastructure design and for assessing the costs and feasibility of the use-case.

The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.