Research On Artificial Raindrop Algorithm And Its Applications

Evolutionary algorithms(EAs)are a kind of intelligent search and optimization techniques inspired by natural phenomena or laws.Due to their high efficient optimization performance and huge application potentials,EAs have attracted wide attention by domestic and foreign researchers over the past half century.At present,EAs have been broadly applied to diversified fields,and solve a lot of very valuable practical problems.The research fruits of EAs have already permeated into disciplines.In the process of solving,however,we still need to focus on the following two aspects:1)how to balance the ability of exploration and development,and 2)how to combine the characteristics of the problem in the process of EA design.In response,this thesis aims at developing a new EA-artificial raindrop algorithm(ARA),and thus solving complex continuous optimization problems based on the ARA,the main contributions of which can be summarized as follows.1)The raindrop calculation model and its algorithm design are studied.Firstly,the process of nature rainfall is abstracted into six stages:raindrop generation process,raindrop descent process,raindrop collision process,raindrop flowing process,raindrop pool process and vapor updating process.The purpose of doing so is to construct the raindrop calculation model.Secondly,the corresponding evolution operators are designed for ARA based on the raindrop calculation model.Furthermore,under the condition that the variables are not related,it is proved that ARA can converge to a satisfactory population with probability one using the relevant mathematical theory.Finally,ARA is compared with twenty-four state-of-the-art EAs on the CEC2005 test platform.The experimental results have indicated its efficiency.2)When using ARA to solve single optimization problems,the key point is how to balance the ability of exploration and development.For this reason,an extended artificial raindrop algorithm(ARAE)is proposed by drawing on the parallel search mechanism of multiple raindrops.Firstly,the current population is dynamically divided into several sub-populations by clustering technology for co-evolution.The purpose of doing so is to enhance the diversity of population.Secondly,the raindrop formation operator and the raindrop flow operator are modified using the information of objective function and global optimal individuals,respectively.Finally,ARA is compared with ARA and other twenty-three state-of-the-art EAs on the CEC2005 test platform.The experimental results have shown that the performance of ARAE is not only better than the ARA,but also competitive with the other twenty-three compared algorithms.3)When using ARA to solve single optimization problems,the important aspect to improve the search efficiency is how to combine the characteristics of the problem in the algorithm design process.For this reason.an enhanced artificial raindrop algorithm with ensemble of self-organizing map and covariance matrix learning(ARAE-SOM+CML)is proposed.Firstly,the current population is mapped from high dimensional input space to low dimensional hidden layer space.The purpose of doing so is to construct the neighborhood structure of every individual based on its topological invariance.Secondly,the data association characteristic of population distribution is identified by CML,which is to establish the feature vector as the coordinate axis of new coordinate system.The purpose of doing so is to improve the calculation efficiency by cooperative search in different coordinate systems.Finally,ARAE-SOM+CML is compared with ARA,ARAE and other five state-of-the-art EAs on the CEC2005 test platform.The experimental results have shown that the performance of ARAE-SOM+CML is not only better than ARA and ARAE,but also competitive with the other five compared algorithms.4)When using ARA to solve multi-objective optimization problems,two primary goals are how to achieve the convergence and diversity.For this reason,a multi-objective evolutionary algorithm based on decomposition with ARA and simulated binary crossover(SBX)is proposed(MOEA/D-ARA+SBX).Firstly,to improve the convergence ability,SBX is introduced to accelerate the filling of the Pareto front(PF)by recombining diverse solutions.Secondly,to improve the diversity of non-dominated individuals in the PF,the k-nearest neighbors approach is introduced to prune of redundant non-dominated solutions.Furthermore,based on the relevant mathematical theory,it is proved that MOEA/D-ARA+SBX can converge to the ideal Pareto optimal set with probability one.For performance evaluation and comparison purposes,the proposed approach has been applied to two set of benchmark multi-objective optimization problems(MOPs),and compared with eight state-of-the-art multi-objective evolutionary algorithms based on non-dominated sorting.The experimental results have indicated the efficiency of the proposed algorithm over other compared approaches.5)When using ARA to solve multi-objective optimization problems,the important aspect to improve the search efficiency is how to combine the characteristics of the problem in the algorithm design process.For this reason,an efficient multi-objective artificial raindrop algorithm(MOARA)with prior knowledge is proposed.To improve the exploratory ability,the center point sampling strategy(CPSS)and SBX is integrated into MO ARA.The primary role of SBX is to accelerate the filling of the Pareto front by recombining diverse solutions,whereas CPSS serves as the domain knowledge of MOPs for guiding other points towards the target PF.Furthermore,based on the relevant mathematical theory,it is proved that MOARA can converge to the ideal Pareto optimal set with probability one.For performance evaluation and comparison purposes,the proposed approach has been applied to two set of benchmark MOPs,and compared with eight state-of-the-art multi-objective evolutionary algorithms based on non-dominated sorting.The experimental results have indicated its efficiency over other compared approaches.6)IM-MOEA is a regularity model-based multi-objective estimation of distribution algorithm,which is very suitable to solve MOPs with regular PFs.Due to the limitations of uniformly distributed reference vectors and inverse model sampling,however,IM-MOEA encounters big challenges for MOPs with irregular PFs.To alleviate these limitations,both ARA and inverse model are integrated into the IM-MOEA.Firstly,the raindrop pool of ARA is to store non-dominated solutions and dynamically adjust the reference vectors,which promotes the IM-MOEA to explore the sparse region.Secondly,incorporating ARA and inverse model sampling is used to improve the search efficiency of IM-MOEA.By incorporating both of them into IM-MOEA,an enhanced IM-MOEA variant,IM-MOEA+ARA for short,is presented in this paper.Finally,IM-MOEA+ARA is compared with other six state-of-the-art multi-objective evolutionary algorithms on eighteen MOPs with irregular PFs.The experiment results show that the proposed approach has better overall performance.7)Due to the complexity of the chaotic system,some parameters in the system are difficult to be determined or unknown in practical applications.The most important problem in the control and synchronization of chaotic systems is how to estimate the system parameters effectively.Firstly,the parameter estimation problem is converted to a multi-dimensional optimization problem by establishing an appropriate fitness function.Secondly,ARA is used to solve the problem based on the global search ability.Finally,ARA is compared with eight state-of-the-art EAs on the six different chaotic systems.The experimental results show that ARA is an effective approach of parameter estimation for chaotic systems.