A Hybrid Harmony Search Algorithm with Distribution Estimation for Solving the 0-1 Knapsack Problem

Table 4

Comparison with nonharmony search algorithm variants for low dimensional instances.

Instance	Measure	HHSEDA	GA	PSO	BFPA	BABC-DE
KP1	Best	130	130	130	130	130
	Median	130	130	130	130	130
	Worst	130	130	130	130	130
	Mean	130	130	130	130	130
	Std	0	0	0	0	0
KP2	Best	107	107	107	107	107
	Median	107	107	107	107	107
	Worst	107	107	107	107	107
	Mean	107	107	107	107	107
	Std	0	0	0	0	0
KP3	Best	23	NA	NA	23	23
	Median	23	NA	NA	23	23
	Worst	23	NA	NA	23	23
	Mean	23	NA	NA	23	23
	Std	0	NA	NA	0	0
KP4	Best	35	NA	NA	35	35
	Median	35	NA	NA	35	35
	Worst	35	NA	NA	35	35
	Mean	35	NA	NA	35	35
	Std	0	NA	NA	0	0
KP5	Best	1025	1025	1025	1025	1025
	Median	1025	1025	1025	995	1025
	Worst	1025	1025	1025	922	1025
	Mean	1025	1025	1025	989.77	1025
	Std	0	0	0	28.98	0
KP6	Best	52	52	52	52	52
	Median	52	52	52	52	52
	Worst	52	52	52	52	52
	Mean	52	52	52	52	52
	Std	0	0	0	0	0
KP7	Best	295	295	295	295	295
	Median	295	295	295	295	295
	Worst	295	295	295	295	295
	Mean	295	295	295	295	295
	Std	0	0	0	0	0
KP8	Best	1024	1024	1024	1024	1024
	Median	1024	1024	1024	1013	1024
	Worst	1024	1024	1024	922	1024
	Mean	1024	1024	1024	1003.1	1024
	Std	0	0	0	24.35	0
KP9	Best	481.07	481.07	481.07	481.07	481.07
	Median	481.07	481.07	481.07	481.07	481.07
	Worst	481.07	481.07	481.07	481.07	481.07
	Mean	481.07	481.07	481.07	481.07	481.07
	Std	0	0	0	0	0
KP10	Best	9767	NA	NA	9767	9767
	Median	9767	NA	NA	9765	9767
	Worst	9767	NA	NA	9761	9767
	Mean	9767	NA	NA	9764.7	9767
	Std	0	NA	NA	1.8257	0