Improving the Bin Packing Heuristic through Grammatical Evolution Based on Swarm Intelligence

Table 4

Results obtained by each heuristic over the instance set.

Instance	Fitness function	PSO			PESO
		Grammar 1	Grammar 2	Grammar 3	Grammar 1	Grammar 2	Grammar 3
bin1data	Equation (7)	316.106020	316.106050	68.167305	316.106020	316.106050	68.090770
	Bins used	101097	101097	101097	101097	101097	78660
	Leftover bins	22719	22719	22719	22719	22719	282
bin2data	Equation (7)	93.388510	93.025230	44.561455	93.388510	93.007030	44.560112
	Bins used	23094	23156	23583	23097	23156	20994
	Leftover bins	2848	2910	3337	2851	2910	748
bin3data	Equation (7)	1.885825	1.885825	1.390289	1.885825	1.885825	1.390289
	Bins used	613	622	650	613	622	596
	Leftover bins	51	60	88	51	60	34
binpack1	Equation (7)	2.604965	2.425894	0.914034	2.604965	2.425894	0.913949
	Bins used	1044	1131	1372	1044	1131	995
	Leftover bins	63	150	391	63	150	14
binpack2	Equation (7)	2.396851	2.259154	0.706004	2.396851	2.259154	0.705970
	Bins used	2162	2342	2851	2162	2342	2062
	Leftover bins	130	310	819	130	310	30
binpack3	Equation (7)	2.133326	2.014334	0.591543	2.133326	2.014334	0.591541
	Bins used	4255	4614	5647	4255	4614	4078
	Leftover bins	231	590	1623	231	590	54
binpack4	Equation (7)	1.935710	1.838669	0.495522	1.935710	1.838669	0.495512
	Bins used	8430	9154	11253	8430	9154	8108
	Leftover bins	419	1143	3242	419	1143	97
binpack5	Equation (7)	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Bins used	400	400	400	400	400	400
	Leftover bins	0	0	0	0	0	0
binpack6	Equation (7)	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Bins used	800	800	800	800	800	800
	Leftover bins	0	0	0	0	0	0
binpack7	Equation (7)	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Bins used	1660	1660	1660	1660	1660	1660
	Leftover bins	0	0	0	0	0	0
binpack8	Equation (7)	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	Bins used	3340	3340	3340	3340	3340	3340
	Leftover bins	0	0	0	0	0	0
hard28	Equation (7)	0.655350	0.655480	0.655350	0.655350	0.655480	0.655480
	Bins used	1995	2024	2755	1995	2024	1995
	Leftover bins	23	52	783	23	52	23
Remaining bins		26484	27934	33002	26487	27934	1282