Derivative Free Optimal Thrust Allocation in Ship Dynamic Positioning Based on Direct Search Algorithms

In dynamic positioning systems, nonlinear cost functions, as well as nonlinear equality and inequality constraints within optimal thrust allocation procedures cannot be handled directly by means of the solvers like industry-standardized quadratic programing (QP), at least not without appropriate linearization technique applied, which can be computationally very expensive. Thus, if optimization requirements are strict, and problem should be solved for nonlinear objective function with nonlinear equality and inequality constraints, than one should use some appropriate nonlinear optimization technique. The current state-of-the-art in nonlinear optimization for gradient-based algorithms is surely the sequential quadratic programing (SQP), both for general applications and specific thrust allocation problems. On the other hand, in recent time, one can also notice the increased applications of gradient-free optimization methods in various engineering problems. In this context, the implementation of selected derivative free direct search algorithms in optimal thrust allocation is proposed and discussed in this paper, and avenues for future research are provided.