Study On Efficient Evolutionary Algorithms For Large Scale Global Optimization Problems

Large scale global optimization problems are ones with high-dimension and many local optimal solutions, and the goal of this dissertation is to study some efficient evolutionary algorithms for them. First, a variable grouping strategy is proposed to reduce the huge amount of computation caused by high dimension. Second, to handle the problems with a lot of local optimal solutions, a smoothing technique which can remove many local optimal solutions is presented. Third, two filled function algorithms are designed to jump out of the local optimal solution. Finally, by integrating all three technologies mentioned above, a new cooperative coevolution algorithm with variable grouping strategy and auxiliary functions is proposed. The main contributions of this dissertation are as follows:(1) When solving large scale global optimization problems, in order to reduce the large amount computation caused by high dimension, a variable grouping strategy, i.e. Formula-Based Grouping(briefly, FBG), is firstly proposed. FBG is able to group the variables into several non-interacting subcomponents while keeping the variables in each subcomponent interactive. In this way, the original problem is decomposed into several small scale sub-problems, which reduces the difficulty of solving process. Moreover, in order to improve the efficiency of the algorithm, a local search strategy is presented. Finally, on the basis of the variable grouping strategy and local search method, a new cooperative co-evolution algorithm with formula based grouping(briefly, CCF) is constructed.(2) In order to overcome the difficulty that there exist too many local optimal solutions whose number increases with the increase of dimension in global optimization problems, a smoothing function method is firstly proposed. The proposed approach can filter the local optimal solutions which are worse than the best solution found so far, and keep those local optimal solutions with better value than the best solution found so far unchanged. In addition, a uniform design search technique is further introduced in the algorithm to make the proposed algorithm converge much faster. Based on this new smoothing function and uniform design method, a new evolutionary algorithm with smoothing function and uniform design(Smoothing with Uniform Design Evolutionary Algorithm,briefly,SUDEA) is proposed.(3) To tackle the difficulty that global optimization method is easy to trap into a local optimal solution, a new filled function with one parameter is proposed. Comparing with the existing filled functions, our function just needs to adjust one parameter and contains no ill-conditioned terms, and is able to keep the continuously differentiable characteristic which is consistent with the original problem. Furthermore, in order to enhance the local optimization, a new randomly and uniformly local search(RULS) is presented. On the basis of the new filled function and RULS, a new filled function method(New Filled Function Algorithm with One Parameter, briefly, NFFA1) is proposed.(4) In order to jump out from a local optimal solution, a filled function with two parameters is proposed. Although two parameters are contained in this function, only one parameter needs to adjust since the values of the other one is fixed, and the continuously differentiable characteristic of the proposed filled function is also consistent with the original problem. In addition, the local search RULS is also utilized to enhance the local optimization. On the basis of the proposals mentioned above, a new filled function method(New Filled Function Algorithm with Two Parameter, briefly, NFFA2) is proposed.(5) There are three characteristics of large scale global optimization problems, i.e. the high dimension of the variable, the large number of local optimal solutions and the susceptibility of the solving algorithm to trap into local minima in the searching process. In order to overcome the difficulties caused by these characteristics, a novel algorithm, i.e. cooperative coevolution algorithm with variable grouping strategy and auxiliary function(briefly, CCVA), is proposed on the basis of formula-based grouping, smoothing function and filled function. In CCVA, formula-based is utilized to group all variables into several relatively non-interacting subcomponents while keeping variables in each subcomponent interactive; two auxiliary functions(smoothing function and filled function) are integrated into EA, and in particular, the smoothing function is used to eliminate all local optimal solutions that are not better than this obtained one for an obtained local optimal solution, while the filled function can help algorithm escape from the current local optimal solution to find a better one. Thus, CCVA can efficiently handle large scale optimization problems.In order to test the performance of the above several algorithms, the experiments are conducted on several standard benchmark suites respectively, and the proposed algorithms are compared with several well-known algorithms. The results of a large number of numerical experiments indicate that our proposal are both numerical stable and efficient.