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

Table 10

Comparison of solutions from PHVF and the extensive form.

				Same duration with PHVF			24 h
	Time (s)	Forest	PHVF	EF	Gap (%)	Gain (%)	EF	Gap (%)	Gain (%)
64	120	P1	2.99E + 08	3.08E + 08	0.14	−2.69	—	—	—
64	120	P34	1.04E + 06	1.05E + 06	0.14	−1.64	—	—	—
64	120	P36	3.48E + 06	3.73E + 06	0.32	−6.77	—	—	—
64	120	P75	4.71E + 07	4.75E + 07	1.59	−0.81	—	—	—
64	120	P83	4.70E + 07	4.72E + 07	0.43	−0.46	—	—	—
64	120	P100	6.53E + 07	6.54E + 07	0.51	−0.05	—	—	—
256	600	P1	3.86E + 08	3.87E + 08	0.05	−0.17	3.87E + 08	0.02	−0.28
256	600	P34	1.35E + 06	1.33E + 06	2.38	1.56	1.35E + 06	0.73	−0.05
256	600	P36	4.73E + 06	4.64E + 06	2.05	1.75	4.70E + 06	0.82	0.52
256	600	P75	5.94E + 07	5.94E + 07	0.69	−0.06	5.97E + 07	0.19	−0.55
256	600	P83	5.90E + 07	5.93E + 07	0.28	−0.47	5.93E + 07	0.22	−0.50
256	600	P100	4.34E + 07	4.34E + 07	0.34	−0.06	4.35E + 07	0.14	−0.22
512	900	P1	2.91E + 08	NA	NA		NA	NA
512	900	P34	2.07E + 06	2.05E + 06	1.2	0.84	2.07E + 06	0.27	-0.08
512	900	P36	6.85E + 06	6.78E + 06	1.876	1.13	6.79E + 06	1.64	0.89
512	900	P75	8.48E + 07	4.50E + 07	89.57	88.63	8.50E + 07	0.22	−0.28
512	900	P83	8.47E + 07	4.49E + 07	89.44	88.76	8.45E + 07	0.63	0.27
512	900	P100	4.74E + 07	5.49E + 06	767.9	763.3	5.49E + 06	767.9	763.3

NA: no results because of memory limitation.