萤火虫算法的改进分析及应用

针对萤火虫算法(FA)在求解有约束全局优化问题时，存在初始种群不易产生、相对吸引力的大小与萤火虫的绝对亮度无关、惯性权重没有充分利用目标函数信息、不能更好地控制和约束萤火虫的移动距离等缺点，提出一种改进的萤火虫算法。首先，给出了一种基于遗传算法(GA)的初始种群产生方法，提高了初始种群的产生速度；其次，给出了一种基于目标函数的动态自适应惯性权重萤火虫算法，以提高萤火虫算法收敛速度；另外，给出了一种相对吸引力大小与萤火虫的绝对亮度有关的吸引力的计算方法；最后，为了控制和约束萤火虫位置的移动距离，将压缩因子引入到萤火虫算法的位置更新公式中，从而提高了算法收敛速度。4个测试函数的计算结果表明，与标准FA和基于惯性权重的萤火虫算法相比，改进的萤火虫算法运算速度明显提高，迭代次数明显减少，从而验证了改进萤火虫算法的有效性。

Improvement analysis and application of firefly algorithm

The Firefly Algorithm (FA) has a few disadvantages in solving the constrained global optimization problem, including that it is difficult to produce initial population, the size of relative attractiveness has nothing to do with the absolute brightness of fireflies, the inertia weight does not take full advantage of the information of objective function, and it cannot better control and constrain the mobile distance of firefly. Therefore an improved FA was proposed. Firstly, Genetic Algorithm (GA) was used to produce an initial population, which improved the production speed of initial population. Secondly, on the basis of the objective function, a dynamic self-adaptive inertia weight was added to FA to improve the convergence speed. Furthermore, a calculation method of relative attractiveness was given, and the size of relative attractiveness had something to do with the absolute brightness of fireflies. Finally, the compression factor was introduced into the location update formula of FA to control and constrain the movement distance of firefly, and thus improved the convergence speed of FA. The experimental results of four test functions show that, compared with standard FA and FA with inertia weight, the improved FA is more effective, which significantly improves computing speed and reduces iteration number.