Firefly algorithm (FA) is a novel optimization algorithm in the field of swarm intelligence, which mimics the flashing and communication behavior of fireflies and is a kind of stochastic algorithm. Because of its simple structure, fewer parameters to tune and preferable search capability, many researchers pay attention to it. Now, FA has been applied widely in many fields such as engineering, computer, management, economics and biology, et al. However, similar to other population based stochastic algorithms, FA has inherent defects. For instances, the algorithm converges slowly at later period, easy to premature convergence and fall into the local optima. Thus may result to the low precision.This thesis presents six improved algorithms from different angles based on the studies of the basic FA. Then we apply three of these algorithms to improve the performance of the cluster analysis algorithm. The main work can be summarized as follows:(1) Two improved algorithms based on step change strategies are proposed. In basic FA, it adopts uniform fixed step value for all fireflies and ignores individual differences in search capability. This is not rational. So we propose two improved algorithms including selfadaptive step FA and variable step FA considering the position of the best firefly. The first improved algorithm uses the functionâ€™s fitnesses of former two iterations and current iterationâ€™s fitness to adjust step value for every firefly; The second improved algorithm tunes the step value of a firefly dynamically based on the position of the best firefly till now and its selfbest position. These two improved algorithms overcome the fault that FA use the fixed step value for all fireflies, enhance the algorithmâ€™s search performance and improve the accuracy. Finally, simulations on the benchmark functions show that our algorithms are efficient.(2) Two modified FAs based on the population diversity are presented. FA has a tendency to converge to local optima. This premature convergence is caused by various algorithmic properties, but a major reason is due to loss of population diversity. In order to promote the population diversity of FA and enhance the FAâ€™s search ability, the thesis proposes two improved algorithms. The first one can dynamically guide the searching process by the value of population diversity. It can increase the population diversity by adjusting a fireflyâ€™s position when the value of population diversity is below the given threshold, and help the algorithm to avoid premature convergence; The second modified FA can adjust the step of a firefly at every iteration by computing the population distribution entropy. When the population distribution entropy is large, it shows that the population of fireflies gather seriously. Then the step value should increase. This operation can help a firefly to jump out of the agminated region and enhance the algorithmâ€™s search ability and accuracy. Experiments on benchmark functions show that two proposed algorithms can improve the performance of the basic FA.(3) Two improved FAs based on learning strategies are proposed:enhancing firefly algorithm using generalized oppositionbased learning and an improved firefly algorithm based on the selfregulating strategy. The idea of first improved FA is to replace the worst firefly with a new constructed firefly when a random number is bigger than the given learning probability. This new constructed firefly is created by taken some elements from the opposition number of the worst firefly. Otherwise it learns from the position of the brightest firefly; In second improved FA, according to the human cognitive psychology, it uses a larger step for the best firefly to improve its exploration and a linearly decreasing step for the rest of the fireflies for better exploitation. Simulations show that two methods outperform the basic FA and can improve the FAâ€™s performance significantly.(4) To further evaluate the performance of the improved algorithms, we apply them to integration into Kmeans clustering algorithm. Although Kmeans clustering algorithm is simple and popular, it has a fundamental drawback of falling into local optima that depends on the randomly generated initial centroid values. Becasuse of the better global search ability and the faster convergence rate of FA, we apply three of the modified FA to integration into Kmeans clustering algorithm to overcome its defect and obtain the globally optimal solutions. Experiments on six datasets of UCI show that the modified FAs are effective optimization tool and can obtain the better clustering results.
