| In field of engineering technology and scientific computing, more and more problems are described as mathematical programming problems. Especially in energy, finance, transportation and other fields, mathematical programming method reflects an extremely important role.General mathematical programming problems are composed of objective function and constraint conditions;it can be divided into single-objective programming and multiobjective programming according to the number of the objective function. With the depth study of the problems, the using of multi-objective problems is increasingly extensive, so study these problems has an important scientific and practical value.Firstly, we construct a new index penalty function, translating multi-objective programming problems with complex constraints into unconstrained multi-objective programming problems, forming a new model of multi-objective exponential penalty function, and prove the convergence of the feasible sequence about the model in theory. Then, based on fast and non-dominated sorting genetic algorithm(NSGA-II), we propose a new algorithm—Improved adaptive fast non-dominated sorting genetic algorithm(MANSGA-II), and apply this algorithm to solve the above model. The advantages of MANSGA-II is that it constructed by adaptive iterative operator(AIO) and extreme pseudo Pareto examine operator(EPNEO), overcome the difficulties caused by improper selected of the penalty, make the population quickly converge to Pareto solution, and in the process of iterative, excluding non-inferiority endpoint of the same pseudo-order values, maintaining the diversity of the population. Finally, the paper gives the specific steps of MANSGA-II, and for some examples, gives the optimization results. Through examples, we find that the MANSGA-II has a simple fitness function structure, the convergence speed fast, the final feasible solution ratio is high advantages, it can be used to solve practical problems. |
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