An Enhanced Grasshopper Optimization Algorithm to the Bin Packing Problem

Table 6

Results for fixed-dimension multimodal functions.

Function	Type	EGOA	GOA	DA	ALO	PSO	OBLGOA
F14	avg	0.9980	1.0641	2.0501	2.1827	4.0791	3.2005
	std	1.93E − 16	0.3622	2.0262	1.9746	3.2178	2.4733
	best	0.9980	0.9980	0.9980	0.9980	0.9980	0.9980
	worst	0.9980	2.9821	10.7632	7.8740	12.6705	10.7632
F15	avg	0.0005	0.0063	0.0023	0.0035	0.0004	0.0076
	std	0.0003	0.0087	0.0049	0.0067	0.0004	0.0098
	best	0.0003	0.0006	0.0004	0.0005	0.0003	0.0003
	worst	0.0013	0.0204	0.0204	0.0204	0.0016	0.0224
F16	avg	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316
	std	4.7012E − 16	1.0871E − 12	2.2380E − 06	9.7720E − 14	6.6486E − 16	3.5117E − 06
	best	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316
	worst	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316
F17	avg	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979
	std	0.0000	6.0985E − 13	7.5449E − 07	3.5239E − 14	0.0000	1.0888E − 06
	best	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979
	worst	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979
F18	avg	3.0000	13.8000	3.0000	3.0000	3.9000	8.4000
	std	4.6795E − 15	28.0054	1.5781E − 05	9.0080E − 13	4.929503018	20.5504
	best	3.0000	3.0000	3.0000	3.0000	3.0000	3.0000
	worst	3.0000	84.0000	3.0001	3.0000	30.0000	84.0006
F19	avg	−3.8628	−3.8091	−3.8628	−3.8628	−3.8628	−3.8357
	std	5.0160E − 07	0.155858005	1.2444E − 06	5.5947E − 13	2.6962E − 15	0.1481
	best	−3.8628	−3.8628	−3.8628	−3.8628	−3.8628	−3.8628
	worst	−3.8628	−3.0333	−3.8628	−3.8628	−3.8628	−3.0513
F20	avg	−3.2341	−3.2665	−3.2767	−3.2620	−3.2665	−3.2388
	std	0.0584	0.0603	0.0606	0.0611	0.0603	0.1028
	best	−3.3220	−3.3220	−3.3220	−3.3220	−3.3220	−3.3220
	worst	−3.1803	−3.2030	−3.1831	−3.2000	−3.2031	−3.0253
F21	avg	−8.2885	−4.7947	−6.3718	−6.7001	−5.0570	−7.8820
	std	2.4926	2.6812	2.8591	2.9905	2.8139	2.9107
	best	−10.1532	−10.1532	−10.1532	−10.1532	−10.1532	−10.1532
	worst	−5.0552	−2.6305	−2.6305	−2.6305	−2.6305	−2.6304
F22	avg	−8.5972	−7.3266	−6.1121	−7.4811	−5.8788	−7.7390
	std	2.8452	3.6392	3.1788	3.2560	3.5547	3.4005
	best	−10.4029	−10.4029	−10.4029	−10.4029	−10.4029	−10.4029
	worst	−2.7659	−2.7519	−2.7518	−2.7519	−2.7519	−2.7658
F23	avg	−9.4383	−5.5672	−4.7293	−6.0268	−5.2543	−7.0597
	std	2.5121	3.6810	2.8552	3.5713	3.3498	3.8262
	best	−10.5364	−10.5364	−10.5364	−10.5364	−10.5364	−10.5364
	worst	−3.1054	−1.8595	−2.4217	−2.4217	−2.4217	−2.4217