A White-box Cooperative Co-evolution For Large Scale Global Optimization

In real world, many scientific and engineer problems can be modeled as real-valued optimization problems. For example, engineering design, artificial neural network training etc.Due to their simple, easy implementation, parallel search and no requiring the continuity and differentiability of the objective function, nature inspired optimization algorithms which are a class of population-based metaheuristic methods, have received intensive attention in the area of real-valued optimizations, but for large scale optimization problems with more than1000 variables, traditional evolutionary algorithms are often ineffective and inefficient.Cooperative co-evolution which uses ”divide and conquer” strategy is a very effective framework to solve large scale global optimization. The general steps of cooperative co-evolution for large scale optimization problems are as follows: first, large-scale problems(variable dimension above 1000) should be broken down into a number of small scale(the number of variable less than 200) sub-problems, then one can use evolutionary algorithm to optimize each sub-problem, and finally one can merge the solutions of these sub-problems. In other word, firstly, grouping large scale variables, then optimizing each group using evolutionary algorithm, finally merge variables of all groups to get the optimal solution.However, due to the existence of complex correlation between variables, variables grouping becomes difficult. If the correlated variables are assigned to the same group, then the final result will be good, however, if the correlated variables are assigned into different group, the final result will be poor. Therefore, how to identify and assign the correlated variables to the same group and assign the irrelated variables to different groups are hot and difficult issues in this research area. This paper propose an improved variable grouping strategy for whitebox problems which use objective function expressions information to group large scale variables. The detail is as follows: a high dimensional objective function is usually an elementary function which is constituted by finite number of add, subtract, multiply, divide and compound operations of basic elementary functions. These operations(basic functions are also treated as operations) are divided into two categories: one will result in the variables correlated, the other will result in the variables irrelated. This variable grouping strategy scans objective function expression, analyzes the operations, get correlated variable groups and irrelated variable groups. So this variable grouping strategy can accurately assign correlated variables into the same group. White-box cooperative co-evolution(Wb CC) algorithm for large scale problem optimization based on this improved variable grouping strategy is proposed in this paper. This algorithm uses the improved variables grouping strategy to group variables and the improved generalized adaptation differential evolution algorithm(Ga DE-I)to optimize each group(sub-problem). The proposed algorithm is test on CEC'2013 large scale global optimization problems set, and the results show that the algorithm is effective and significantly better than other algorithms.