Localized Time-Distance-Based Multimodal Optimization Algorithm and Its Application in PID Control
MultiModal Optimization Problems(MMOPs)require finding multiple high-precision global optima of a problem simultaneously,necessitating algorithms that have strong global search capabilities and can well balance the diversity and convergence of the population.Currently,when dealing with MMOPs,there are typically the following difficulties:(1)Existing methods often only consider the current state of the population during the evolutionary process(such as the commonly used greedy selection strategy),which can easily lead to the population being trapped in local optima;(2)Traditional random search strategies have difficulty quickly and effectively finding global optima within complex search spaces;(3)Current multimodal optimization algorithm designs often require manual parameter setting(such as mutation and crossover factors),where the magnitude of these parameters directly impacts the population's diversity and convergence.To address these challenges,this paper introduces a new Localized Time-Distance-based Multimodal Optimization(LTDMO)algorithm,mainly contributing in three areas:First,a Random and Direction-based Mutation(RDM)strategy combining random search and directed guidance is proposed,using random mutation to increase the diversity of individuals within the population,and by dividing the population into different,possibly overlapping subpopulations for mutation operations in local search spaces,better locating global optima and thus avoiding individuals falling into local optima.Second,a Locality-based Crowding Selection(LCS)strategy is proposed,utilizing the principle of temporal locality in the evolutionary process to record more promising evolutionary directions for the current individual,generating new offspring in this direction to further converge the population towards global optima.Lastly,a Self-adaptive Parameter Control(SPC)strategy is proposed,which adaptively adjusts the algorithm's parameter values based on individual evolutionary information,reducing the algorithm's sensitivity to parameters like mutation and crossover factors during the evolutionary process.The LTDMO algorithm was tested on the CEC'2013 benchmark,and the results were compared with those of 11 other multimodal optimiza-tion algorithms,showing that the LTDMO algorithm can effectively handle complex multimodal optimization problems with many global optima.Specifically,on problems F1-F5,F8,and F10,the peak rate and success rate both reached 100％;on multimodal optimization problems with many local optima(F6 and F7),the peak rate of the LTDMO algorithm exceeded 86％,surpassing the performance of nine comparison algorithms;in dealing with composite multimodal optimization problems,the LTDMO algorithm achieved optimal performance on problems F11,F12,F14,and F16.Furthermore,applying the LTDMO algorithm to the Proportional-Integral-Derivative(PID)controller shows that the LTDMO algorithm can find various optimal control parameters for the PID controller,allowing the system to reach a stable state with smaller error.
multimodal optimization problemneighborhood mutationtemporal localityadaptively adjust parametersproportional integral derivative controller
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