Research On Cooperative Co-evolution With Online Decomposition Strategy For Large Scale Global Optimization

Optimization problems encountered in science and engineering have become increasingly complicated.A feasible approach to deal with large-scale optimization problem(LSGO)is the cooperative co-evolutionary(CC)algorithm.It decomposes the original complex problem into some subproblems which just acquire parts of the complete decision variables.Compared with traditional evolutionary algorithms,the "divide and conquer" strategy used by CC brings two new tasks:(1)design problem decomposition strategy;(2)design cooperation strategy for subproblems.The two new tasks have significant effects on the performance of the algorithm.In this paper,the two tasks are studied and corresponding improved methods are put forward respectively.(1)Focusing on the cooperative strategy among subproblems,the main contributions are as follows:(1)A large scale cooperative coevolution algorithm with imbalanced multi-modal optimization is proposed.The multi-modal optimizer is introduced into the framework of CC,and the imbalanced search of multi-modal optimizer is implemented based on a bi-objective(fitness and diversity)selection principle.In this way,the subproblems of CC can get more sufficient information so as to better cooperate with each other.In addition,imbalance can also save computational resources in multi-modal optimizer,so that CC procedure can be fully implemented.A multi-modal optimization by covariance matrix self-adaptation evolution strategy with repelling populations is employed as optimizer in the proposed method.A series of experiments are conduct on large-scale benchmark functions and statistical analysis of experimental results show that the proposed IMMO-CC significantly outperforms other 7 CC algorithm.(2)A cooperative co-evolution with selective multiple population for large scale optimization is proposed.Through the analysis of the dynamic characteristics of subproblems in CC,a selection strategy is designed in multiple populations mechanism.By the dynamic selection in multiple population CMA-ES(covariance matrix adaptation evolution strategy),population with higher quality can obtain more opportunities to evolve.The powerful local search capability of CMA-ES is utilized to find multiple optima,and the adaptability to dynamic problems is increased due to the selection strategy.The test results on CEC'10 functions confirm the effectiveness of the CC-SMP algorithm.(2)In view of the problem decomposition strategy,the main research contents are as follows:A cooperative co-evolution algorithm with online grouping is proposed by using the marginal distribution product model.Inspired by the linkage learning method of genetic algorithm,the gene grouping method in the extended compact genetic algorithm is employed to design a online variable grouping method under the framework of CC.A marginal product modal and minimum description length based decomposition strategy is combined with CC-SMP algorithm,then a cooperative coevolution algorithm with online grouping CC-SMP-MDL is proposed.By testing on LSGO benchmark,it is proved that the algorithm has a good performance.