Fast Polynomial Time Approximate Solution for 0-1 Knapsack Problem

Table 8

Relation between (-1.0003121) and the optimal solution in Example 1.

i				ej		d19l
2	4.877	5.8853	1.20674595	2	1.006714385	1	1	1	1
1	1.7856	2.7924	1.563844086	1	1.006219464	2	1	1	1
4	7.0943	8.0992	1.141648929	4	1.002593494	3	1	1	1
7	13.9249	14.9319	1.072316498	7	1.002472723	4	1	1	1
5	7.8807	8.885	1.127437918	5	1.001737819	5	1	1	1
3	6.3493	7.3521	1.15793867	3	1.000735709	6	1	1	1
10	24.2688	25.2767	1.04153069	10	1.000009703	7	1	1	1
6	8.5593	9.5616	1.117100697	6	0.999517192	8	1	1	1
9	21.0881	22.0925	1.047628757	9	0.997543816	9	1	1	1
16	37.1566	38.1662	1.027171485	16	0.997519609	10	1	1	1
8	19.6114	20.6148	1.051164119	8	0.997023922	11	1	1	1
13	32.7739	33.7797	1.030689054	13	0.995144517	12	1	1	1
18	39.6104	40.6175	1.025425141	18	0.994221827	13	0	1	1
11	27.3441	28.3472	1.03668433	11	0.994209859	14	1	1	1
27	47.8753	48.8848	1.02108603	26	0.993934735	15	1	0	1
20	40.7362	41.7432	1.024720028	20	0.993755806	16	1	0	1
21	42.4565	43.463	1.023706617	21	0.9926965	17	0	0	1
17	37.887	38.892	1.026526249	17	0.992682141	18	1	1	1
26	47.8583	48.866	1.021055909	27	0.992140262	19	1	0	0
14	32.787	33.7898	1.030585293	14	0.992140258	20	1	1	1
28	47.9746	48.9822	1.021002781	28	0.99200245	21	1	0	0
24	45.7868	46.7932	1.021980134	23	0.99151375	22	0	0	0
12	31.618	32.6189	1.031656019	12	0.990620324	23	0	1	0
15	33.9368	34.9379	1.029498951	15	0.990066434	24	0	1	0
19	40.014	41.0159	1.025038736	19	0.988890608	25	0	1	0
30	48.5296	49.5335	1.020686344	30	0.988122008	26	0	0	0
25	46.6997	47.7013	1.021447675	25	0.986416947	27	0	0	0
23	45.6688	46.6693	1.021907736	24	0.985652114	28	0	0	0
22	45.2896	46.2899	1.022086748	22	0.9855754	29	0	0	0
29	48.2444	49.2448	1.020736085	29	0.984714732	30	0	0	0

. is an initial solution constructed in descending order of efficiency.