An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems

Table 4

Flow test for state-of-the-art algorithms.

Dimension	Iterations			Time (sec)			Error
	Avg	Max	Min	Avg	Max	Min	—
FPA2
500000	6.2	8	5	0.010	0.018	0.008	0
1000000	6.5	9	5	0.021	0.040	0.017	0
10000000	6.4	11	4	0.372	0.446	0.311	0
50000000	6.5	9	5	1.813	2.027	1.628	0
Newton
500000	6.1	8	4	0.017	0.022	0.010	0
1000000	6.5	9	5	0.036	0.048	0.025	0
10000000	6.1	10	4	0.403	0.507	0.258	0
50000000	6.2	9	5	1.978	2.604	1.542	0
Variable fixing
500000	6.2	8	5	0.015	0.021	0.010	0
1000000	6.5	9	5	0.033	0.044	0.022	0
10000000	6.5	11	4	0.376	0.467	0.223	0
50000000	6.6	9	5	1.860	2.395	1.340	0
FPA
500000	6.2	8	5	0.011	0.021	0.009	0
1000000	6.5	9	5	0.024	0.046	0.020	0
10000000	6.4	11	4	0.438	0.531	0.369	0
50000000	6.5	9	5	2.135	2.351	1.925	0
Secant
500000	14.4	16	9	0.018	0.022	0.013	0
1000000	14.6	19	11	0.040	0.052	0.029	0
10000000	14.3	21	10	0.425	0.791	0.283	0
50000000	14.2	17	9	2.026	3.088	1.511	0
Median search
500000	20.0	20	19	0.030	0.034	0.028	0
1000000	20.9	21	20	0.061	0.068	0.057	0
10000000	24.3	25	24	0.750	0.825	0.715	0
50000000	26.6	27	26	3.657	4.012	3.507	0