The present paper gives a new formulation for rough surface scattering in terms of a stochastic integral equation which can be dealt with by means of stochastic functional approach. The random surface is assumed to be infinite and a homogeneous Gaussian random process. The random wave field is represented in the stochastic Floquet form due to the homogeneity of the surface, and in the non-Rayleigh form consisting of both upward and downward going scattered waves, as well as in the extended Voronovich form based on the consideration of the level-shift invariance. The stochastic integral equations of the first and the second kind are derived for the unknown surface source function which is a functional of the derivative or the increment of the surface profile function. It is also shown that the inhomogeneous term of the stochastic integral equation of the second kind automatically gives the solution of the Kirchhoff approximation for infinite surface.

Reinforcement learning has been used to adaptive service composition. However, traditional algorithms are not suitable for large-scale service composition. Based on Q-Learning algorithm, a multi-task oriented algorithm named multi-Q learning is proposed to realize subtask-assistance strategy for large-scale and adaptive service composition. Differ from previous studies that focus on one task, we take the relationship between multiple service composition tasks into account. We decompose complex service composition task into multiple subtasks according to the graph theory. Different tasks with the same subtasks can assist each other to improve their learning speed. The results of experiments show that our algorithm could obtain faster learning speed obviously than traditional Q-learning algorithm. Compared with multi-agent Q-learning, our algorithm also has faster convergence speed. Moreover, for all involved service composition tasks that have the same subtasks between each other, our algorithm can improve their speed of learning optimal policy simultaneously in real-time.