Research On Efficient Differential Evolution Algorithms For Global Optimization Problems

Many practical problems in science and engineering always involve global opti-mization problems.With the rapid development of computer science and the wide application of big data,the structures of practical problems are more and more com-plex and their scales are larger and larger,which increases the difficulty of solving them.In fact,the main difficulties in solving these problems can be attributed as follows:1)they usually do not have some good properties such as differentiability and continuity,so many classical and effective optimization methods can not be directly used to solve them;2)The rapid increasement of decision variables and their increas-ing complex relationship make the search space exponentially enlarge and the local optimum significantly increase,which makes it difficult for the existing algorithms to find the global optimal solution;3)The characteristics of some problems can not be predicted in advance,and the search environment is always changing during the optimization process,so the algorithm should be robust to different types of prob-lems and different search environments.Although researchers have proposed many heuristic stochastic optimization algorithms for global optimization,such as genetic algorithm,particle swarm optimization,ant colony algorithm,immune algorithm and so on,they always converge slowly and easily fall into local minima.In particular,differential evolution algorithm owns simple operation,high convergence accuracy and strong robustness,and has been widely used in various practical engineering problems.However,the differential evolution algorithm still can not effectively adjust the search performance(search range or direction and control parameters)and avoid the waste of computing resources(premature convergence and stagnation).To solve these prob-lems,this paper designs four efficient differential evolution algorithms,and the main works and innovations are as follows:1.In order to alleviate the shortcomings that the information of the basic individ-ual is only used to set the control parameters in the guiding-based mutation operator and the fitness value of individual is only used to update the population,by further utilizing the fitness of the guiding individual and the local information of individual respectively,a novel differential evolution algorithm with improved individual-based parameter setting and selection strategy is proposed.First,to effectively adjust the search range of mutation operator,an individual-guided parameter setting is designed by using the fitness values of both original and guiding individuals,so that the pro-posed algorithm can always search along with a promising direction and make full use of the promising information of individual.Then,to avoid waste a large num-ber of search information during selection process,a new weighted fitness value is defined by utilizing the fitness value and position of each individual,and a diversity-based selection strategy is designed by assembling it with greedy selection strategy,which can maintain the diversity of population effectively.Compared with the exist-ing guiding-based algorithms,the proposed algorithm has a simple structure,makes use of the information of the base individual and guiding individual to set the control parameters,and the fitness value and location information of individual to update the population,such that the optimization efficiency of algorithm can be effectively improved.2.In order to alleviate the shortcomings that the probability selecting parameter in the combined mutation strategies can not effectively meet the search requirements in the late evolution stage and the subpopulations lack of the information dissemination,by incorporating a cosine perturbation and exchanging the information of individual individuals respectively,a novel differential evolution algorithm with information inter-crossing and sharing mechanism is proposed.First,to enhance the ability of algorithm to jump out of the local optima in the later evolution stage,a stochastic mixed muta-tion strategy is proposed by incorporating a cosine perturbation into the probability parameter setting,which can improve the randomness of selecting the different opera-tors during the evolutionary process.Then,an information intercrossing and sharing mechanism is developed to make good use of the information of different individual-s by dividing the population into superior and inferior subpopulations according to their fitness values and exchanging or sharing their information with the opposite and binomial crossover operations,which can further enhance the exploitation of superior individuals and the global exploration of the whole search space.Compared with the existing combined strategies and multi-population algorithms,the proposed algorithm has a simple structure,employs the cosine disturbance to enhance its global search ability in the later evolution stage,and uses the opposite and binomial crossover oper-ations to promote the information transmission between various subpopulations,thus effectively balancing the exploitation and exploration of algorithm.3.In order to alleviate the shortcomings that the existing neighborhood-based mutation strategies rarely consider the search characteristic of the current individual and the existing restart mechanisms rarely consider the local state of population,by describing and fully using the search characteristic of individual,a new differential evo-lution algorithm with neighborhood-based adaptive evolution mechanism is proposed.First,to effectively adjust the search ability of each individual,a neighborhood-based mutation strategy is designed by designing two neighborhood-based mutation oper-ators and an individual-based selection probability,which can dynamically assign a suitable search operator for each individual.In addition,a neighborhood-based adap-tive evolution mechanism is developed by identifying the evolutionary states of neigh-borhood with its performance and diversity and designing a dynamic neighborhood model and two exchanging operations to avoid its evolutionary dilemmas,which can reduce the invalid search during the evolution process effectively.Compared with the existing neighborhood-based and evolution state-based algorithms,the proposed algo-rithm employs the performance of both the current individual and its neighborhood to select appropriate mutation operator,and uses the performance and diversity of the neighborhood to alleviate its evolution dilemma,such that the search performance of each individual can be effectively enhanced,and the optimization ability of algo-rithm can be strengthened.The numerical result of 1000 independent runs on IEEE CEC2014 benchmark functions show the stability of the proposed algorithm.4.In order to accurately describe the search characteristics of individual by the probability selection parameter and simultaneously adapt to different individu-als and evolution stages by the control parameters setting,by making full use of the information of the neighborhood,a new adaptive differential evolution algorith-m with neighborhood topology is proposed.First,to effectively adjust the search performance of each individual,a neighborhood-based adaptive mutation strategy is developed by using the ring topology to construct an elite individual set and adaptive-ly choosing a suitable elite individual for each individual to create the search direction according to its neighborhood performance,which can effectively not only enhance the search efficiency of individual,but also maintain the diversity of population.Then,a neighborhood-based adaptive parameter setting is designed to meet the search re-quirements of different individuals and evolution stages by utilizing the feedback infor-mation of population and its neighbors simultaneously,which can further improve the applicability of algorithm to different search environments.Compared with the ex-isting algorithm,the proposed algorithm adaptively constructs the appropriate search direction for each individual,and updates its control parameters by using the feed-back information of population and its neighbors,such that the search efficiency and robustness of algorithm can be effectively improved.A large number of numerical experiments are carried out on the benchmark func-tions from IEEE CEC2005 and CEC2014,and the comparison results with typical algorithms show the effectiveness of the proposed algorithms.