Efficient Differential Evolution algorithms for multimodal optimal control problems

Many methods for solving optimal control problems, whether direct or indirect, rely upon gradient information and therefore may converge to a local optimum. Global optimisation methods like Evolutionary algorithms, overcome this problem. In this work it is investigated how well novel and easy to understand Evolutionary algorithms, referred to as Differential Evolution (DE) algorithms, and claimed to be very efficient when they are applied to solve static optimisation problems, perform on solving multimodal optimal control problems. The results show that within the class of evolutionary methods, Differential Evolution algorithms are very robust, effective and highly efficient in solving the studied class of optimal control problems. Thus, they are able of mitigating the drawback of long computation times commonly associated with Evolutionary algorithms. Furthermore, in locating the global optimum these Evolutionary algorithms present some advantages over the Iterative Dynamic Programming (IDP) algorithm, which is an alternative global optimisation approach for solving optimal control problems. At present little knowledge is available to the selection of the algorithm parameters in the de algorithm when they are applied to solve optimal control problems. Our study provides guidelines for this selection. In contrast to the IDP algorithm the de algorithms have only a few algorithm parameters that are easily determined such that multimodal optimal control problems are solved effectively and efficiently.