Distributed Individuals for Multiple Peaks: A Novel Differential Evolution for Multimodal Optimization Problems

Locating more peaks and refining the solution accuracy on the found peaks are two challenging issues in solving multimodal optimization problems (MMOPs). To deal with these two challenges, a distributed individuals differential evolution (DIDE) algorithm is proposed in this article based on a distributed individuals for multiple peaks (DIMP) framework and two novel mechanisms. First, the DIMP framework provides sufficient diversity by letting each individual act as a distributed unit to track a peak. Based on the DIMP framework, each individual uses a virtual population controlled by an adaptive range adjustment strategy to explore the search space sufficiently for locating a peak and then gradually approach it. Second, the two novel mechanisms named lifetime mechanism and elite learning mechanism (ELM) cooperate with the DIMP framework. The lifetime mechanism is inspired by the natural phenomenon that every organism will gradually age and has a limited lifespan. When an individual runs out of its lifetime and also has good fitness, it is regarded as an elite solution and will be added to an archive. Then the individual restarts a new lifetime, so as to bring further diversity to locate more peaks. The ELM is proposed to refine the accuracy of those elite solutions in the archive, being efficient in dealing with the solution accuracy issue on the found peaks. The experimental results on 20 multimodal benchmark test functions show that the proposed DIDE algorithm has generally better or competitive performance compared with the state-of-the-art multimodal optimization algorithms.