Stopping Criteria for a Constrained Single-Objective Particle Swarm Optimization Algorithm

When using optimization algorithms the goal is usually clear: The global optimum should be found. However, in general it is not clear when this goal is achieved, especially if real-world problems are optimized for which no knowledge about the global optimum is available. Therefore, it is not easy to decide when the execution of an optimization algorithm should be terminated. Although different mechanisms can be used for the detection of an appropriate time for ending an optimization run, only two of them are frequently used in the literature. Unfortunately, both methods have disadvantages, particularly for the optimization of real-world problems. Because especially for practical applications it is important when an optimization algorithm is terminated as they usually contain computationally expensive objective functions, the performance of several stopping criteria that react adaptively to the state of an optimization run is evaluated for a Particle Swarm Optimization algorithm in this work. The examination is done on the basis of a constrained single-objective power allocation problem. Suggestions from former work concerning stopping criteria for unconstrained optimization are verified and comparisons with results for Differential Evolution are made.