Run Time Analysis regarding Stopping Criteria for Differential Evolution and Particle Swarm Optimization

Due to the growing complexity of todays technical systems optimization is becoming an important issue within the design phase. The applicability of optimization algorithms in automatic design processes is strongly dependent on the stopping criterion. It is important that the optimum is reliably found but furthermore no time or computational resources should be wasted. Therefore a run time analysis is conducted for several promising stopping criteria. Amongst others a new criterion incorporating a quicksort algorithm is examined. In former work it proved to be particularly beneficial with regards to the needed number of function evaluations for Particle Swarm Optimization. However, it is considered to produce additional computational effort because of the sorting. An estimation of the complexity of the stopping criteria calculations supports this assumption. Nevertheless, the results of the run time analysis confirm that the new criterion is the best choice for Particle Swarm Optimization, especially when optimizing real-worlds problems with computationally expensive objective functions. As most technical systems require complex simulations this assumption is generally met. For Differential Evolution a simpler criterion is sufficient.