基于标准蒙特卡洛与拟蒙特卡洛方法的萤火虫算法参数调优
Parameter Tuning of the Firefly Algorithm by Standard Monte Carlo and Quasi-Monte Carlo Methods
AI总结：
本文通过标准蒙特卡洛和拟蒙特卡洛方法随机初始化参数并调优萤火虫算法，在基准函数和弹簧设计问题上验证了 FA 对参数选择不敏感且具有较强鲁棒性。
摘要：
几乎所有优化算法都具有依赖于算法的参数，而这些参数值的设置会显著影响所考虑算法的行为。因此，应当进行适当的参数调优，以确保用于优化的算法表现良好，并且在求解不同类型优化问题时具有足够的鲁棒性。本研究采用萤火虫算法（Firefly Algorithm，FA）来评估其参数值对其效率的影响。参数值分别使用标准蒙特卡洛方法和拟蒙特卡洛方法随机初始化，随后将这些值用于调优 FA。使用两个基准函数和一个弹簧设计问题来测试调优后 FA 的鲁棒性。根据初步结果可以推断，蒙特卡洛方法和拟蒙特卡洛方法在最优适应度值方面产生了相似的结果。使用这两种不同方法在两个基准函数和弹簧设计问题上进行的数值实验表明，无论模拟过程中选择了何种不同的样本值，最终适应度值均未出现显著变化。这种不敏感性表明了 FA 的鲁棒性。
英文摘要：
Almost all optimization algorithms have algorithm-dependent parameters, and the setting of such parameter values can significantly influence the behavior of the algorithm under consideration. Thus, proper parameter tuning should be carried out to ensure that the algorithm used for optimization performs well and is sufficiently robust for solving different types of optimization problems. In this study, the Firefly Algorithm (FA) is used to evaluate the influence of its parameter values on its efficiency. Parameter values are randomly initialized using both the standard Monte Carlo method and the Quasi Monte-Carlo method. The values are then used for tuning the FA. Two benchmark functions and a spring design problem are used to test the robustness of the tuned FA. From the preliminary findings, it can be deduced that both the Monte Carlo method and Quasi-Monte Carlo method produce similar results in terms of optimal fitness values. Numerical experiments using the two different methods on both benchmark functions and the spring design problem showed no major variations in the final fitness values, irrespective of the different sample values selected during the simulations. This insensitivity indicates the robustness of the FA.
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