Ultrasound elastography is an imaging technology which can detect differences in tissue stiffness based on tissue deformation. For successful clinical use in cancer diagnosis and monitoring the method should be robust to sources of decorrelation between ultrasound images. A regularized Dynamic Programming (DP) approach was used for displacement estimation in compressed tissue. In the Analytic Minimization (AM) extension of DP, integer displacements are calculated just for one RF-line, and later propagated laterally throughout the entire image. This makes the seed RF-line very important; faulty seed lines could propagate erroneous displacement values throughout the image resulting in the appearance of false "lesions". In this paper we analyze the robustness of this method in free-hand palpation of laboratory tissue phantoms. We are proposing an update to the algorithm which includes a random search for the most robust seed RF-line. Axial integer displacements are obtained on each random seed line individually with DP optimization. For each random axial RF-line, multiple random values for decorrelation compensation are used in the displacement estimation. The displacement values are then compared and several metrics of stability and consistency are considered. A ranking is established and the line deemed most robust will become the seed line for displacement propagation, while also selecting the most stable value for decorrelation compensation. The random search can be achieved at no additional computational cost in a parallel implementation. The results indicate significant improvement in the robustness of the DP approach, while maintaining real-time computation of strain images.