Dual-Performance Multi-Subpopulation Adaptive Restart Differential Evolutionary Algorithm

To cope with common local optimum traps and balance exploration and development in complex multi-peak optimisation problems, this paper puts forth a Dual-Performance Multi-subpopulation Adaptive Restart Differential Evolutionary Algorithm (DPR-MGDE) as a potential solution. The algorithm employs a novel approach by utilising the fitness and historical update frequency as dual-performance metrics to categorise the population into three distinct sub-populations: PM (the promising individual set), MM (the medium individual set) and UM (the un-promising individual set). The multi-subpopulation division mechanism enables the algorithm to achieve a balance between global exploration, local exploitation and diversity maintenance, thereby enhancing its overall optimisation capability. Furthermore, the DPR-MGDE incorporates an adaptive cross-variation strategy, which enables the dynamic adjustment of the variation factor and crossover probability in accordance with the performance of the individuals. This enhances the flexibility of the algorithm, allowing for the prioritisation of local exploitation among the more excellent individuals and the exploration of new search space among the less excellent individuals. Furthermore, the algorithm employs a collision-based Gaussian wandering restart strategy, wherein the collision frequency serves as the criterion for triggering a restart. Upon detecting population stagnation, the updated population is subjected to optimal solution-guided Gaussian wandering, effectively preventing the descent into local optima. Through experiments on the CEC2017 benchmark functions, we verified that DPR-MGDE has higher solution accuracy compared to newer differential evolution algorithms, and proved its significant advantages in complex optimisation tasks with the Wilcoxon test. In addition to this, we also conducted experiments on real engineering problems to demonstrate the effectiveness and superiority of DPR-MGDE in dealing with real engineering problems.