Differential evolution for dynamic environments with unknown numbers of optima

Abstract

This paper investigates optimization in dynamic environments where the numbers of optima are unknown or fluctuating. The authors present a novel algorithm, Dynamic Population Differential Evolution (DynPopDE), which is specifically designed for these problems. DynPopDE is a Differential Evolution based multi-population algorithm that dynamically spawns and removes populations as required. The new algorithm is evaluated on an extension of the Moving Peaks Benchmark. Comparisons with other state-of-the-art algorithms indicate that DynPopDE is an effective approach to use when the number of optima in a dynamic problem space is unknown or changing over time.

Self-Adaptive Differential Evolution for Dynamic Environments with Fluctuating Numbers of Optima

“…However, a more robust approach, for example re-evaluating the best individual in each sub-population, can be introduced relatively easily should it be required. Dynamic Population Differential Evolution (DynPopDE) [27], an extension of DynDE and CDE [28], is aimed at dynamic optimization problems where the number of optima in the search space is unknown or fluctuates over time.…”

“…Equation (1.9) shows that the exclusion threshold increases with an increase in number of dimensions and decreases if the number of peaks is increased. Because knowledge of the number of peaks is generally not available, it was proposed that the exclusion threshold be calculated using the number of sub-populations as follows [27]:…”

“…It was shown [27] that even if the number of peaks is known, creating an equal number of sub-populations as peaks is not always an effective strategy. When the number of peaks is unknown, choosing the number of sub-populations to use would be, at best, an educated guess.…”

“…When the number of peaks is unknown, choosing the number of sub-populations to use would be, at best, an educated guess. It was therefore suggested [27] that the number of sub-populations should not be a parameter of the algorithm, but that sub-populations should be spawned as needed. The question that must be answered is: When should new populations be spawned?…”

“…It is possible that a situation could occur where some of the weaker sub-populations are not allocated enough fitness evaluation to reach the stagnation point as detected by equation (1.17). It was found experimentally that in order to detect stagnation effectively, it is necessary to distribute function evaluations more uniformly among all populations [27]. The final component of DynPopDE is the introduction of a penalty factor into the performance value, P(k,t) given in equation (1.13), to penalize populations for successively receiving the highest performance value without showing any improvement in fitness.…”