(484b) A Comparative Study of Hybrid Optimization Approaches

Local minima appear naturally in non-convex nonlinear optimization problems. In constraint problems they commonly lie on the bounds but even in unconstrained problems the hyper-surface given by the objective function can be full of local minima. In many cases it is not possible to transform the objective function to a convex problem, e.g. with a relaxation, or excluding local minima with the use of tailored constraint functions. One application, where local minima can not be obviated, is model-based experimental design. While local optimization tools (LO) are highly developed (e.g. NPSOL, SNOPT, IPS) the improvement of global optimization algorithms (GO) is quite slow-going. Recently, some algorithms became familiar in chemical engineering, such as Generic Algorithms, Simulated Annealing, or Particle Swarm Optimization. However, the performance of these algorithms is quite similar. They request plenty of tuning parameters and converge very slow. Often, there is not even a convergence criterion defined, but the algorithm stops after a certain number of iterations. Despite all these drawbacks, they are able to find some global optimum irrespective of bad initial guesses. The idea of hybrid optimization approaches is to combine this ability of GO's with the fast convergence properties of the LO's. Therefore, different combinations of GO and LO are possible. In this work, five approaches: GO (PSO algorithm), LO (NPSOL), and three hybrid approaches are compared, respectively. A multidimensional test function based on trigonometric functions featuring several local minima and an overall tendency is used for comparison.