Benchmarking Derivative-Free Global Optimization Methods on Variable Dimension Robotics Problems

Several real-world applications introduce derivativefree optimization problems, called variable dimension problems, where the problem's dimension is not known in advance. Despite their importance, no unified framework for developing, comparing, and benchmarking variable dimension problems exists. The robot arm controlling problem is a variable dimension problem where the number of joints to optimize defines the problem's dimension. For a holistic study of global optimization methods, we studied 14 representative methods from 4 different categories, i.e., (i) local search optimization techniques with random restarts, (ii) state-of-the-art DIRECT-type methods, (iii) established Evolutionary Computation approaches, and (iv) state-of-the-art Evolutionary Computation approaches. To investigate the effect of the problem's dimensionality on the solution we generated 20 instances of various combinations among the number of predefined and open decision variables, and we performed experiments for various computational budgets. The results attest that the robot arm controlling problem provides a proper benchmark for variable dimensions. Furthermore, methods in-corporating local search techniques have dominant performance for higher dimensionalities of the problem, while state-of-the-art EC methods dominate in the lower dimensionalities.