Distributed Knowledge Transfer for Evolutionary Multitask Multimodal Optimization

Evolutionary multitasking optimization (EMTO) is a paradigm that optimizes multiple tasks simultaneously to improve the overall performance of all tasks by seamlessly transferring useful knowledge among them. Although EMTO has received significant interest, rare studies consider handling tasks that are multimodal optimization problems (MMOPs) with multiple global optimal solutions. Due to the multiple different modalities of each task, a major challenge of solving multiple MMOPs is how to extract and transfer knowledge across modalities of different tasks. To this end, this article designs a distributed knowledge transfer-based evolutionary multitask multimodal optimization (EMTMO-DKT) approach for solving multiple MMOPs simultaneously by discovering and utilizing local knowledge across modalities of different tasks. Specifically, we first divide the population of each task into multiple subpopulations, where each subpopulation explores a modality. Then, we propose an evolution path-based similarity measurement to measure the local similarities between subpopulations of different tasks. Since the modalities can be locally similar across tasks, we develop a subpopulation cross matching strategy according to the obtained similarities to pair subpopulations of different tasks. In this stage, the successfully paired subpopulations are allowed to transfer knowledge. Finally, the knowledge transfer probability self-adjusting strategy is applied to each subpopulation to balance knowledge transfer and self-evolution, so as to improve search efficiency. In this article, a set of multitask multimodal optimization test problems are constructed to assess the efficacy of compared algorithms. Experimental results on both the benchmark functions and the real-world optimization problem demonstrate that the proposed algorithm can quickly locate more global optima in comparison with state-of-the-art EMTO and multimodal optimization algorithms.