A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

Table 4

Effects of and allocated time for the forest P1.

Forest		Time (min)		Iterations			Value	Improvement (%)
P1	1000000	15	20	1	6	0.95	371,524,817	—
			40	9	6	0.95	386,068,433	3.9
			50	18	6	0.95	T	NA
			60	20	6	0.95	T	NA
			70	21	6	0.95	T	NA
		30	20	1	6	0.95	373,450,417	—
			40	9	6	0.95	386,156,779	3.4
			50	18	6	0.95	385,676,118	3.3
			60	20	6	0.95	385,394,686	3.2
			70	21	6	0.95	385,258,771	3.2
		45	20	1	6	0.95	375,427,413	—
			40	9	6	0.95	386,156,779	2.9
			50	18	6	0.95	385,676,118	2.7
			60	20	6	0.95	385,394,686	2.7
			70	21	6	0.95	385,258,771	2.6
		60	20	1	6	0.95	375,804,390	—
			40	9	6	0.95	386,156,779	2.8
			50	18	6	0.95	385,676,118	2.6
			60	20	6	0.95	385,394,686	2.6
			70	21	6	0.95	385,258,771	2.5

T: termination because PHVF ran out of time while iterating; NA: not applicable; : penalty factor; : percentage of variables fixed; : cascading factor; : initial slamming factor.