Genetic Algorithms Based On Smoothing Technique And Line Search For Global Optimization

Evolutionary algorithms are new kinds of modern optimization algorithms that are inspired by principle of nature evolution. As new kinds of random search algorithms, they have some advantages over the traditional optimization algorithms, and are of the great importance and have a wide range of applications. The traditional optimization algorithms usually have strict limitations on the functions such as their differentiability, however, evolutionary algorithms do not require the differentiability of the functions and have parallel property. Therefore, they are often be used to solve some complex, large scale, nonlinear and non-differentiable optimization problems.First, a new evolutionary algorithm for unconstrained optimization problems is proposed in this paper. In the proposed algorithm a new fitness function based on smoothing technique is designed, and a novel line search scheme is integrated into the algorithm design to improve the efficiency of the algorithm. The new fitness function has the advantages that the many local optimal solutions can be removed by using this fitness function. As a result, it is less possible for the proposed algorithm to trap into the local optimal solutions. Moreover, the new crossover operator designed in this paper and the new line search scheme can make the proposed algorithm find the global optimal solutions more quickly.Second, the constrained optimization problem considered is transformed into a multi-objective optimization problem with two objectives, and new genetic operators are designed for the multi-objective optimization problem model. Based on these a new genetic algorithm is proposed for the new model. By solving the multi-objective optimization problem we can get the optimal solutions for the constrained optimization problem. The simulation results show the effectiveness of the proposed algorithm.