Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks

We propose a two-stage stochastic second-order cone programming formulation of the semidefinite stochastic location-aided routing (SLAR) model, described in Ariyawansa and Zhu (Q. J. Oper. Res. 4(3), 239-253, 2006). The aim is to provide a sender node S with an algorithm for optimally determining a region that is expected to contain a destination node D (the expected zone). The movements of the destination node are represented by ellipsoid scenarios, randomly generated by uniform and normal distributions in a neighborhood of the starting position of the destination node. By using a second-order cone model, we are able to solve problems with a much larger number of scenarios (20250) than it is possible with the semidefinite model (500). The use of a larger number of scenarios allows for the computation of a new expected zone, that may be very effective in practical applications, and for obtaining stability results for the optimal first-stage solutions and the optimal cost function values.