Stochastic Steepest-Descent Optimization of Multiple-Objective Mobile Sensor Coverage

We propose a steepest descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensor's coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij. We use steepest descent to compute the transition probabilities for optimal tradeoff between two performance goals concerning the distributions of per-PoI coverage times and exposure times, respectively. We also discuss how other important goals such as energy efficiency and entropy of the coverage schedule can be addressed. For computational efficiency, we show how to optimally adapt the step size in steepest descent to achieve fast convergence. However, we found that the structure of our problem is complex in that there may exist surprisingly many local optima in the solution space, causing basic steepest descent to get stuck easily at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis, and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.