New global optimization algorithm via dynamic control

This paper proposes a new algorithm for the unconstrained optimization problem, which is derived as an application of the control theory called Direct Gradient Descent Control. The static optimization problem is solved by using a dynamic controller in which the convergence speed can be greatly accelerated. The major idea is to consider the objective function F(x) and its time derivative dF(x(t))/dt as the evaluation criteria, and to apply the gradient descent method. It is verified by simulation that the proposed dynamic mathematical programming has a very great capability to converge to the optimal solution. It is also interesting to note that the method has to a certain extent the ability to find not only local optimal solutions, but also global optimal solutions. This paper improves the basic algorithm of dynamic mathematical programming so that it is suited to global optimization. The new algorithm generates movement toward the global optimal solution by utilizing two different trajectories with interaction (the chaotic trajectory and convergence trajectory). It is verified by simulation that the new algorithm functions as a global optimization procedure with a high success probability. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(6): 20–27, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20094