An Artificial Bee Colony Algorithm Based on Dynamic Penalty and Lévy Flight for Constrained Optimization Problems

Abstract

Artificial bee colony (ABC) algorithm is one of the most popular intelligence algorithms, which has been widely applied to some unconstrained optimization problems. Many improved versions of ABC algorithm are also used for solving constrained optimization problems (COPs). An artificial bee colony algorithm based on dynamic penalty function and Levy flight (DPLABC) is presented for COPs in this paper. Based on the original ABC algorithm, four modifications are put forward in this newly proposed algorithm: The dynamic penalty method is used to handle the constraints; Levy flight with logistic map is applied in the employed bee phase; according to the selection probability, a further search mechanism which is learned from the best solution and two other neighbor food sources is adopted for onlooker bees; different from pulling back to the upper and lower limits, the new boundary handling mechanism inspired by the best solution is also given to repair the invalid solutions. To validate the performance of DPLABC algorithm, it is tested on 13 constrained benchmark functions from 2006 IEEE Congress on Evolution Computation (CEC2006) and four engineering design problems. The experimental results indicate that DPLABC is competitive with the state-of-the-art algorithms including dynamic difference search algorithm and several improved variants of ABC for solving COPs.