Steepest-Ascent Constrained Simultaneous Perturbation for Multiobjective Optimization

The simultaneous optimization of multiple responses in a dynamic system is challenging. When a response has a known gradient, it is often easily improved along the path of steepest ascent. On the contrary, a stochastic approximation technique may be used when the gradient is unknown or costly to obtain. We consider the problem of optimizing multiple responses in which the gradient is known for only one response. We propose a hybrid approach for this problem, called simultaneous perturbation stochastic approximation steepest ascent, SPSA-SA or SP(SA)(2) for short. SP(SA)(2) is an SPSA technique that leverages information about the known gradient to constrain the perturbations used to approximate the others. We apply SP(SA)(2) to the cross-layer optimization of throughput, packet loss, and end-to-end delay in a mobile ad hoc network (MANET), a self-organizing wireless network. The results show that SP(SA)(2) achieves higher throughput and lower packet loss and end-to-end delay than the steepest ascent, SPSA, and the Nelder-Mead stochastic approximation approaches. It also reduces the cost in the number of iterations to perform the optimization.