Positioning of new mobile tower using Circle Packing Problem

Yogesh Kumar, Kusum Deep

Abstract: The Circle Packing Problem determines a circle of the largest area that can fit into the vacant space when \(\varvec{n}\) arbitrary-sized non-overlapping given circles are placed inside a given container. One of its numerous applications is to determine the optimal positioning of mobile towers in a city. This constrained nonlinear optimization problem is solved using four variants of the Real Coded Genetic Algorithm. These four variants are created by the combination of two well-known real-coded crossover operators: Arithmetic Crossover and Hybrid Crossover, and two well-known real-coded mutation operators: Uniform Mutation and Discrete Uniform Mutation. The performance of these algorithms is evaluated using the mean, standard deviation, best, worst of the objective function values and Friedman’s mean ranking test is applied when 30 runs of each variants are carried out. On the basis of the computational analysis, the performance of the variant of RCGA having Arithmetic Crossover-Uniform Mutation (AX-UM) outperforms all other RCGAs considered in this study in terms of faster convergence and better accuracy of the solution. In a practical demonstration, this methodology is implemented to a case study in Roorkee City in Uttarakhand of Northen India. Currently, there are 14 existing mobile towers in Roorkee city. However, there are certain regions in which internet connectivity is unsatisfactory. Therefore, based on the recommendation of this study, AX-UM is recommended to install three new mobile towers.