A dynamic archive niching differential evolution algorithm for multimodal optimization

Abstract

Abstract-Highly multimodal landscapes with multiple local/global optima represent common characteristics in real-world applications. Many niching algorithms have been proposed in the literature which aim to search such landscapes in an attempt to locate as many global optima as possible. However, to locate and maintain a large number of global solutions, these algorithms are substantially influenced by their parameter values, such as a large population size. Here, we propose a new niching Differential Evolution algorithm that attempts to overcome the population size influence and produce good performance almost independently of its population size. To this end, we incorporate two mechanisms into the algorithm: a control parameter adaptation technique and an external dynamic archive along with a reinitialization mechanism. The first mechanism is designed to efficiently adapt the control parameters of the algorithm, whilst the second one is responsible for enabling the algorithm to investigate unexplored regions of the search space and simultaneously keep the best solutions found by the algorithm. The proposed approach is compared with two Differential Evolution variants on a recently proposed benchmark suite. Empirical results indicate that the proposed niching algorithm is competitive and very promising. It exhibits a robust and stable behavior, whilst the incorporation of the dynamic archive seems to tackle the population size influence effectively. Moreover, it alleviates the problem of having to finetune the population size parameter in a niching algorithm.

Running Up Those Hills: Multi-modal search with the niching migratory multi-swarm optimiser

“…Interestingly, on the composite functions with 10-20D NMMSO can be seen to consistently hone just a few peaks until at some point the number of swarms rises quickly. [16] 0.2167 0.3676 0.3878 MSSPSO [15] 0.0000 0.2179 0.3901 A-NSGA-II [17] 0.0740 0.3275 0.4044 CMA-ES [7] 0.7750 0.7137 0.2807 CrowdingDE [18] 0.6667 0.5731 0.3612 dADE/nrand/1 [8] 0.7488 0.7383 0.3010 dADE/nrand/2 [8] 0.7150 0.6931 0.3174 DECG [19] 0.6567 0.5516 0.3992 DELG [19] 0.6667 0.5706 0.3925 DELS-aj [19] 0.6667 0.5760 0.3857 DE/nrand/1 [20] 0.6386 0.5809 0.3338 DE/nrand/2 [20] 0.6667 0.6082 0.3130 IPOP-CMA-ES [21] 0.2600 0.3625 0.3117 NEA1 [6] 0.6496 0.6117 0.3280 NEA2 [6] 0.8513 0.7940 0.2332 N-VMO [9] 0.7140 0.6983 0.3307 PNA-NSGA-II [22] 0.6660 0.6141 0.3421 This is probably due to tendency of NMMSO to merge local modes that live on larger landscape features. Figure 3 shows the growth of a swarm population over time as visualised in X for some of the 2D test problems.…”

“…Additionally, NMMSO is compared to the problem level results which are published in [9] and [8] for the niching variable mesh optimisation (N-VMO) and the dynamic archiving niching differential evolution (dADE) algorithms.…”

“…The NMMSO algorithm is compared to the results of a wide range of multi-modal optimisation algorithms [17], [7], [18], [8], [19], [20], [21], [6], [9], [22], which were applied to the 20 benchmark problems of the CEC 2013 "Competition on Niching Methods for Mutlimodal Optimization" [23], [1]. We follow the algorithm assessment protocol used in the CEC 2013 competition; our results can therefore be directly compared to the combined competition results.…”

“…This leads to another property of this approach -it is dynamic in the number of modes it maintains and returns (although limited to a maximum number, set a priori). The second best performing multi-modal optimiser [8] also has dynamic mode maintenance, storing an external dynamic archive of estimated mode locations which supports a reinitialisation mechanism, along with an adaptive control parameter technique for the differential evolution algorithm driving the search. The third best was the standard CMA-ES algorithm.…”

Multiple Optima Identification Using Multi-strategy Multimodal Genetic Algorithm

“…We have compared the results of the SelfMMOGA runs with some efficient techniques from the competition. The techniques are DE/nrand/1/bin and Crowding DE/rand/1/bin [14], N-VMO [15], dADE/nrand/1 [16], and PNA-NSGAII [17]. The settings for the SelfMMOGA are:…”