A Novel Harmony Search Algorithm Based on Teaching-Learning Strategies for 0-1 Knapsack Problems

Table 3

The result of 1-dimensional (weight versus value) knapsack problems.

Problem	D	Target weight	Total weight	Total values	Optimal result	Algorithm	Outcomes				Runtime
							Worst	Mean	Best	Std
KP1	15	375	741.9172	62.9963	481.069	HS	314.9297	423.191	481.069	67.92161	0.169532
						NGHS	481.069	481.069	481.069	𝟔.𝟒E  −𝟏𝟒	0.173909
						EHS	481.069	481.069	481.069	𝟔.𝟒E  −𝟏𝟒	0.814028
						ITHS	437.9345	472.4424	481.069	19.2905	0.447476
						HSTL	481.069	481.069	481.069	𝟔.𝟒E  −𝟏𝟒	0.330757
KP2	23	10000	19428	19309	9767	HS	9747	9760	9767	5.533596	0.313597
						NGHS	9767	9767	9767	0	0.305331
						EHS	9643	9751.6	9767	22.64509	1.595463
						ITHS	9756	9765.7	9767	2.641186	0.790986
						HSTL	9767	9767	9767	0	0.585312
KP3	20	878	1098	1085	1024	HS	924	987.4	1024	40.395544	0.254834
						NGHS	1024	1024	1024	0	0.245683
						EHS	1018	1022.8	1024	2.6832816	1.274226
						ITHS	1018	1022.8	1024	2.6832816	0.654352
						HSTL	1024	1024	1024	0	0.485799
KP4	40	15	374	14049	1149	HS	786	1109.4	1149	113.7494	12.51123
						NGHS	1138	1147.9	1149	3.478505	12.72128
						EHS	786	1109.4	1149	113.7494	15.64561
						ITHS	786	1112.7	1149	114.7907	13.6885
						HSTL	1138	1147.9	1149	3.478505	13.29233
KP5	100	27	1360	34965	1173	HS	1172	1172.5	1173	0.508548	37.14283
						NGHS	1172	1172.633	1173	0.490133	37.22416
						EHS	1172	1172.567	1173	0.504007	53.20237
						ITHS	1172	1172.567	1173	0.504007	41.50243
						HSTL	1172	1172.9	1173	0.305129	37.11053
KP6	10000	431	349354	3011792	unknown	HS	4795	4941	5338	228.20495	2902.844
						NGHS	5976	6270.4	6363	165.43821	1881.969
						EHS	4797	4929.8	5014	94.099416	16979.43
						ITHS	4899	4960.6	5064	72.081898	5047.957
						HSTL	6318	6474.4	6730	185.7156	1506.648
KP7	10000	1765326	5033006	2063406	unknown	HS	1068628	1070926.5	1073225	3250.5699	4526.0894
						NGHS	1126584	1127050.5	1127517	659.73063	5060.0062
						EHS	1041435	1043733.5	1046032	3250.5699	5435.1693
						ITHS	1124261	1129389	1134517	7252.0871	4555.54
						HSTL	1193743	1194524	1195304	1103.794	3326.1473
KP8	11000	1000000	5526981	2263955	unknown	HS	529153	532801.8	537353	3001.1646	10633.825
						NGHS	738654	762855.4	798991	26865.404	11912.341
						EHS	480038	486268.8	490627	4481.0616	13084.292
						ITHS	795202	800908	807164	4864.5424	10785.623
						HSTL	940656	944780	947850	2630.108	9606.735