The AEA Combined With Copula Estimation Of Distribution Algorithm And Its Application On Constrained Optimization Problems

Alopex-based Evolutionary Algorithm (AEA) is a new optimization Algorithm combined the heuristic way of Alopex and the swarm intelligence of Evolutionary Algorithm. It not only has the characteristics of gradient descent, but also has the characteristics of simulated annealing. In this paper, in order to overcome the shortcomings of the AEA algorithm in which the two contrastive populations contains the same evolutionary information, Copula Estimation of Distribution Algorithm is introduced to the AEA algorithm to generate the two populations for the operation of Alopex. Making the two populations include not only those related heuristic information learning from AEA, but also include the global evolutionary information provided by Copula which taking into account the correlation between variables. Thus, in each iteration, the Copula Estimation of Distribution Algorithm gives the probability distribution of the population’s macro model, and then the micro level evolution will be achieved by Alopex. Then the performance of CAEA is studied by using11benchmark functions and compared with the EDA and EDA-AEA algorithm. The result shows CAEA has a great advantage from multiple angles to process the optimization problem with strong correlation between the variables.Based on the CAEA and constrained optimization problems, a new constraint handling method is proposed. The algorithm gradually converges to the feasible region from the relatively feasible region. By the introduction of an adaptive relaxation parameter μ, the algorithm fully takes into account different functions corresponding to different sizes of feasible region. In addition, an adaptive penalty function method is employed, which adaptively adjust the penalty coefficient. Thus, it can ensure the punishment not too big or too small. By solving11benchmark test functions and comparing the result with other algorithms, the experiment results indicate that the new method is reliable and efficient for solving constrained optimization problems.