| A lower dimensional pattern search evolution algorithm, LDPSE for short, based on pattern search method and genetic algorithm is given in this paper and best effect is got for applying LDPSE to solve global optimization problems with box constraints.Searching for global optimal solution of the problem on LDPSE is based on arithmetic crossover operator, extreme value mutation operator and lower dimensional pattern search operator. Arithmetic crossover operator can make individuals exchange information among them in the current population and maintain the diversity of the population. Extreme value mutation operator can restrain the population to appear early-maturing phenomenon and improve the population in the whole level. Lower Dimensional pattern search operator focuses on a part of excellent individuals in the population, which can make the performance of LDPSE improved largely.LDPSE is a derivative free optimization (DFO) algorithm because pattern search method and genetic algorithm are both DFO method. And LDPSE contains fully the advantages of global optimization ability of evolution algorithm and local strong search ability of pattern search method.LDPSE is a kind of real-coded evolutionary algorithm and introduces the lower dimensional pattern search operator which general form is m-pattern search operator, where the parameter m is far less than the dimension of the search direction set. Compared to hybrid genetic algorithm which directly introduced pattern search method as its optimal operator, m-pattern search operator in LDPSE just select m different search directions in a certain rule as candidate search direction subset from the given search direction set when it is calling and in the operator we use struggle operation to ensure the effectiveness of the operator.In the end we have proven the correctness and high efficiency of LDPSE by lots of test numerical experiments about global optimization problem with box constraints. |
PDF Full Text Request