Modified Firefly Algorithm

Table 1

Summery of simulation results, with maximum number of iterations as a termination criterion.

	𝑓1(𝑥)	𝑓2(𝑥)	𝑓3(𝑥)	𝑓4(𝑥)	𝑓5(𝑥)	𝑓6(𝑥)	𝑓7(𝑥)
𝑥^∗	(0,0)	(𝜋,𝜋)	𝑥1,𝑥2≥4.5	(2.8863, 1.8233)	(𝜋,𝜋)	(−2.9035,; −2.9035)	multiple
𝑓^∗=𝑓(𝑥^∗)	0	1	10	2.28395	[5,5.0794]	358.3323	186.73067
𝑥^∗𝑠	(−0.0207, 0.0140)	(3.2044, 3.0378)	(5.1149, 5.0934)	(2.8765, 1.9518)	(2.9504, 3.1789)	(−2.9495,; −2.8714)	(0.3895,; −0.1890)
𝑓^∗𝑠=𝑓(𝑥^∗𝑠)	−0.1239	0.9782	10	2.2308	4.8828	358.2775	183.4958
𝑥^∗𝑚	(0.0.0005)	(3.1420, 3.1413)	(5.12, 5.12)	(2.8864, 1.8234)	(3.1455, 3.1368)	(−2.904,; −2.904)	(−0.1989,; −5.8586)
𝑓^∗𝑚=𝑓(𝐱^∗𝑚)	−0.0001	1	10	2.2839	5.0279	358.3323	186.7290
CPU𝑠	0.1248	0.1404	0.1404	0.1560	0.2184	0.1716	0.1248
CPU𝑚	0.1404	0.1560	0.1404	0.1716	0.2340	0.1872	0.2028

𝑥^∗ the optimal solution with 𝑓^∗ as the global optimal value.
𝑥^∗_𝑠 is the solution of the ordinary firefly algorithm.
𝑓^∗_𝑠 is the final functional value in the ordinary firefly algorithm.
𝑥^∗_𝑚 is the solution of the modified firefly algorithm.
𝑓^∗_𝑚 is the final functional value in the modified algorithm.
CPU_𝑠 CPU time for the standard firefly algorithm.
CPU_𝑚 CPU time for the modified firefly algorithm.