The Optimal Logical Structure of the Ad Hoc Network Based on the Nonlinear Programming Method

Currently it is still the most important and basic work that how to construct an optimal Ad Hoc network. In this paper, for a typical problem of constructing optimal Ad Hoc network according to the requirement that any two adjacent circles of the communication nodes intersect and their public area are at least k% of the area of a circle, we use the nonlinear programming method of the optimization theory to research it. Firstly, we draw the basic covering graphics constructed by two circles of a given radius r, and build the corresponding nonlinear programming model for making the total area of two circles to reach maximum as the objective function and making the public area no less than k% of the area of a circle as the constraints. The model adequately characterizes the optimal geometric properties of the basic covering graphics. Then we also construct the similar but more complex model for the basic covering graphics when adding a new circle. The new model can better reflect the optimal combination and growth among the circles. Solved the models through LINGO software, we obtain the data rules of the optimal basic covering graphics changes with the value of k. Next, for a given rectangular region of the Ad Hoc network, we take two typical values of k, including 5.76689, and 18.16901, and design an optimal covering method according to the data rules, and conclude the algorithm of calculating the minimum total numbers of the circles of the communication nodes. This paper is very helpful to research on the optimal topological structure and routing algorithm or protocol of the Ad Hoc network.