Study Of Multimodal Optimization Algorithm Based On Mixed Niche

Multimodal optimization problem(MMOP)is a complex optimization problem with multiple global optimal solutions,which requires the algorithm to find as many global optimal solutions as possible in the search space with high precision.Therefore,locating more peaks and improving convergence accuracy are two challenging tasks.Differential Evolution(DE)algorithm with embedded niching technique is a commonly used method for solving MMOP.The main feature of niching techniques is that each niche evolves independently to find a global optimal solution through the use of multiple subpopulations.Common niching techniques include speciation-based differential evolution(SDE)and crowding-based differential evolution(CDE).SDE maintains niche stability through distance thresholds but requires prior knowledge of the search space.CDE improves population diversity by replacing similar individuals but struggles to determine if individuals belong to the same peak,leading to replacement errors.To combine the advantages of SDE and CDE,recent studies have proposed hybrid niching techniques.In this paper,we introduce the concept of hybrid niching into the DE algorithm and design two implementation methods based on population and individual levels.The main contributions are as follows:(1)A population-based hybrid niching differential evolution(PHNDE)algorithm is proposed,which employs two different niching techniques to accelerate the search for global optima.Specifically,the algorithm first divides the population into two parts based on their fitness values,with the better-performing individuals using SDE and the remaining individuals using CDE.These two niching techniques work together to discover more global optima and improve convergence speed.To determine the mixing ratio of these two niching techniques,the algorithm uses fitness-distance correlation(FDC)to quantify problem complexity.FDC adjusts the mixing ratio based on problem complexity to achieve better performance when dealing with optimization problems of varying difficulties.To test the performance of the algorithm,the PHNDE is compared with 11 existing multimodal optimization algorithms,including the competition champion algorithm,using the CEC2013 benchmark test suite.The experimental results show that the PHNDE exhibits highly competitive performance compared to the11 related algorithms,discovering more global optima.(2)An individual-based hybrid niching differential evolution(IHNDE)algorithm is proposed.The core idea is to partition the population into several sub-populations,where individuals are classified into two categories,namely,the good and bad individuals based on their objective function values.The good individuals are evolved using SDE,while the bad ones are updated using CDE.Moreover,the proportion of SDE and CDE can be adjusted in different evolution stages to enhance the efficiency and accuracy of the algorithm.To further improve the performance of the algorithm,a new mutation strategy is designed to better explore the search space.In addition,to prevent individuals from jumping to another peak and to preserve the good ones already found,IHNDE employs one archiving strategy to manage the individuals in the population.In experiments,IHNDE is applied to 20 different dimensions of multimodal optimization problems and compared with 11 existing multi-modal optimization algorithms.The results demonstrate that IHNDE outperforms the other 11 algorithms on test functions.This confirms the effectiveness and practicality of IHNDE in solving multi-modal optimization problems.