In order to improve the optimization efficiency of the biogeography-based optimization (BBO) algorithm, an improved BBO algorithm, that is, worst opposition learning and random-scaled differential mutation BBO (WRBBO), is presented in this paper. First, BBO's mutation operator is deleted to reduce the computational complexity and a more efficient random-scaled differential mutation operator is merged into BBO's migration operator to obtain global search ability. Second, in order to balance exploration and exploitation, the BBO's migration operator is replaced with a dynamic heuristic crossover to enhance the local search ability. Finally, a worst opposition learning is merged into the improved algorithm to avoid trapping into local optima. A large number of experiments are made on 18 various kinds of classic benchmark functions and some complex functions from the CEC-2013 test set. In addition, WRBBO is applied to clustering optimization and medical image segmentation. The experimental results show that WRBBO has better optimization efficiency on benchmark function optimization, clustering optimization, and medical image segmentation than quite a few state-of-the-art BBO variants and other algorithms.

Lévy flight Shuffle Frog Leaping Algorithm (LSFLA) is a SFLA variant and enhances the performance of SFLA largely, however, it still has some defects, such as poor convergence and low efficiency. So an improved LSFLA, namely, LSFLA based on Differential perturbation and Quasi-Newton search (DQLSFLA), is proposed in this paper. Firstly, the way of updating only one solution which is the worst one at every sub-iteration in LSFLA is replaced with an all-solution updating way in the subgroup to improve the probability of obtaining the best solution, to omit one sorting step at every sub-iteration and the sub-iteration number parameter setting, to reduce the computational complexity and to enhance the optimization efficiency. Secondly, a random differential perturbation approach and an improved Lévy flight updating one are created and used in the subgroup updating to form DLSFLA, that is, the first half frogs in the subgroup use the random differential perturbation updating approach to improve the global search ability, and the last half adopt the improved Lévy flight updating method to keep the advantage of the Lévy flight updating method and overcome its defects. Finally, quasi-Newton local search is integrated into DLSFLA near the end of the algorithm to improve the convergence speed. Experimental results on the complex functions from CEC-2014 show that DQLSFLAb’s convergence quality and optimization efficiency are much better than LSFLAb’s and that compared with quite a few other state-of-the-art algorithms, DQLSFLA has better performance. The results on medical image enhancement and Quadratic Assignment Problem (QAP) also show that DQLSFLA can solve the real word optimization problems better than LSFLA can.

Laplacian Biogeography-Based Optimization (LxBBO) is a BBO variant which improves BBO’s performance largely. When it solves some complex problems, however, it has some drawbacks such as poor performance, weak operability, and high complexity, so an improved LxBBO (ILxBBO) is proposed. First, a two-global-best guiding operator is created for guiding the worst habitat mainly to enhance the exploitation of LxBBO. Second, a dynamic two-differential perturbing operator is proposed for the first two best habitats’ updating to improve the global search ability in the early search phase and the local one in the late search one, respectively. Third, an improved Laplace migration operator is formulated for other habitats’ updating to improve the search ability and the operability. Finally, some measures such as example learning, mutation operation removing, and greedy selection are adopted mostly to reduce the computation complexity of LxBBO. A lot of experimental results on the complex functions from the CEC-2013 test set show ILxBBO obtains better performance than LxBBO and quite a few state-of-the-art algorithms do. Also, the results on Quadratic Assignment Problems (QAPs) show that ILxBBO is more competitive compared with LxBBO, Improved Particle Swarm Optimization (IPSO), and Improved Firefly Algorithm (IFA).