Table 1.

Analysis of the running time of BSO in six different situations.

Algorithm	Mutation Operator $\overrightarrow{\mathit{z}}$	Display Expression for $\mathit{E}\left({\mathit{T}}_{\mathit{\epsilon }}\right|{\mathit{X}}_0)$	Time Complexity $\mathbf{T}\left(\mathit{n}\right)$
BSO-I	$N(0,1)$	$E\left(T_{\epsilon }\right|X_0)\le 1+\sqrt{2\pi n}\frac{a}{k}-\sqrt{\frac{2\pi }{n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$
	$U\left(-\frac{1}{2},\frac{1}{2}\right)$	$E\left(T_{\epsilon }\right|X_0)\le 1+2\sqrt{6\pi n}\frac{a}{k}-\frac{2\sqrt{6\pi }}{\sqrt{n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$
	$U(-1,1)$	$E\left(T_{\epsilon }\right|X_0)\le 1+\sqrt{6\pi n}\frac{a}{k}-\sqrt{\frac{6\pi }{n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$
BSO-II	$N(0,1)$	$E\left(T_{\epsilon }\right|X_0)\le 1+\frac{5\sqrt{2\pi n}}{4+\sqrt{2}}\frac{a}{k}-\frac{5\sqrt{2\pi }}{4\sqrt{n}+\sqrt{2n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$
	$U\left(-\frac{1}{2},\frac{1}{2}\right)$	$E\left(T_{\epsilon }\right|X_0)\le 1+\frac{10\sqrt{6\pi n}}{4+\sqrt{2}}\frac{a}{k}-\frac{10\sqrt{6\pi }}{4\sqrt{n}+\sqrt{2n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$
	$U(-1,1)$	$E\left(T_{\epsilon }\right|X_0)\le 1+\frac{5\sqrt{6\pi n}}{4+\sqrt{2}}\frac{a}{k}-\frac{5\sqrt{6\pi }}{4\sqrt{n}+\sqrt{2n}}\frac{\epsilon }{k}$	$\mathrm{O}\left(\sqrt{n}\right)$