Research On Solving A Robust Optimal Problems By Using Evolutionary Approach

In real world applications, problems usually have multiple attributes and the application environments are always changing from time to time. Thus the research on robust evolution (RE) has the desirable application value in practice. Consequently, this dissertation mainly investigates the following three main areas: the causes and influences of the overlapping individuals in the multi-objective evolution, the performance of different MOEAs searching for robust optimized solutions, and how to improve the efficiency of robust evolution. The main contribution includes 6 aspects as follows.1. Four types of uncertain factors that influence the process of engineering optimized design have been summarized. A systematic survey has been investigated on three aspects:the history of multi-objective evolutionary algorithms (MOEAs), the present research on single objective robust evolution (SRE) and the multi-objective evolution separately. Based on these, the difficulties and challenges which are faced by the research on robust evolution have been elaborated.2. The causes and influences of overlapping individuals in MOEAs have been analyzed. Take NSGA-?for example, the causes of overlapping individuals have been investigated through experimental methods. And a probabilistic method is used to analyze the number of overlapping individuals. In the meanwhile, an experimental method is used to investigate the influence of overlapping individuals.3. The ability of searching robust optimal solutions of MOEAs have been tested experimentally. In order to test the convergence and diversity of MOEAs under disturbance, two-dimensional and three-dimensional test functions have been utilized, and different levels of Gaussian noises have been introduced to conduct the experiments. Observed from the experimental results, under the disturbance, all three-dimensional test functions are sensitive to noises, only in different degrees.4. A Quasi-Monte Carlo method has been proposed to improve EA's searching ability of robust optimal solutions. The key to improve the searching ability is to estimate the effective objective function (EOF) efficiently. Traditionally, when using C-Monte Carlo (C-MC) method to calculate the approximation of the Monte Carlo Integration (MCI), the random sample would cause the low precision. Aimed at this case, this dissertation incorporate a Quasi-Monte Carlo (Q-MC) method to obtain the approximation of MCI. In order to increase the precision, three different low deviation sequences, namely, SQRT sequence, SOBOL sequence and Korobov lattice have been introduced. Experimental results show that Q-MC can effectively decrease the error caused by EOF estimation, and the performance of REA searching robust optimal solutions have been improved.5. An approach has been proposed to improve the searching efficiency of the robust optimized solutions for MOEAs. For the flaws of poor searching effect and low efficiency exist in the MOEAs, a Latin hypercube sampling (LHS) has been used to evaluate the EOF. It is proved that LHS get a better precision of the EOF evaluation by the experimental illustration and theoretical analysis. In order to get a further improvement of the efficiency, an adaptive sampling technique (ALHS) has been proposed. ALHS could adaptively adjust the size of sampling, decrease the frequency of sampled EOF evaluation and CPU time. Comparative experiments have been carried among ALHS?LHS and RS in two MROPs test functions. The results of the experiment illuminated that ALHS got a better efficiency and effect than rest two methods, LHS excelled RS.6. A hybrid genetic algorithm has been proposed to solve the multi-objective travelling sales man problem. An inversion operator (hill-climbing method) has been incorporated to improve the local search ability. Based on this, a novel hybrid genetic algorithm has been proposed. Experimental results demonstrate the capability of the proposed algorithm to solve the multi-objective TSP problem.