Bat Algorithm And Application Research In Function Optimization

Bat algorithm(BA) is a new type of swarm intelligence algorithm, which is based on the echolocation features of micro-bats. It uses a frequency-tuning technique to diversify the solutions in the population, and uses the automatic zooming to balance exploration and exploitation during the search process by dynamically mimicking the variations of pulse emission rates and loudness of bats when searching for prey. For above characters, it proves to be very efficient with a typical quick start. However, similar to other intelligent algorithms, BA also has the weaknesses such as slow convergence speed and easy getting into the local extreme points. Moreover, the fields of its application should be further expanded.In this thesis, BA’ convergence analysis, as well as its application of solving the function optimization problem in continuous domain and discrete domain are mainly studied. The main research work includes:(1) The basic principle of BA is introduced briefly and a few existing variants of BA are summarized, three main reasons that explain why BA is superior to other algorithms are suggested and further research directions are pointed out.(2) BA is simplified to be one-dimensional single bat and two kind of modes about the speed and location updating are defined, BA’ convergence is studied with the method of characteristic equation. The conclusion shows that the convergence of mode 2 is better than mode 1’s, the selection method of parameters about the mode is given. Numerical simulation results demonstrate the validity of the theoretical analysis.(3) The position of the bat is encode with quantum bit, quantum rotation gate is used to search the optimal solution, the quantum non-gate is adopted to realize quantum mutation to avoid premature convergence, quantum bat algorithm is proposed for solving multimodal function optimization problem. The results of experiments on typical complex function optimization and comparison with other algorithms show that the algorithm can avoid local optimization and has a stronger global optimization capability.(4) Harmony search algorithm is used for global search, differential evolution algorithm is for local search, and the basic framework of BA is introduced to balance global search and local search, a hybrid algorithm is presented for solving multi-objective optimization problem. The results of experiments show that the hybrid algorithm has a certain advantages with the compared algorithms in convergence metric.(5) BA is combined with genetic algorithm, cellular theory, Pareto optimal solutions theory and quantum-behaved theory, respectively, genetic mutation bat algorithm for solving the 0-1 knapsack problem, cellular bat algorithm to solve 0-1 programming problem, bat algorithm for solving multi-objective and multi-choice knapsack problem, and quantum-behaved bat algorithm for solving integer programming problem are proposed. The experimental results show that the above algorithms have a certain optimization performance, and have better convergence than the compared algorithms.(6) The related operators about BA are redefined so as to solve traveling salesman problem(TSP) and minimum ratio traveling salesman problem(MRTSP), 2-opt is adopted to perform TSP’s local search and the reversing the city subsequence is introduced for MRTSP’s local search, two related algorithms are designed. The experimental results show that the above algorithms not only can effectively solve the related problems, but also have better optimization performance than the compared algorithms.In this thesis, the convergence theory and application of BA are analyzed and studied comprehensively. Finally, whole research contents are concluded, and further research directions are indicated.