Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

Computational Social Networks

Table 5 Results on MIS and MVC problems compared to classic methods and supervised deep learning methods.\(^{1}\)

	Graph Info		Classic			Supervised		Proposed
	Name	Size	MD-Greedy	Greedy	SA	S2V-DQN	GCNGTS	GSO^a/EvoGSO^b
MIS	Cora	2708	1451	672	1390	1381	1451	\({1443}\)*
	Citeseer	3327	\({1818}\)*	1019	1728	1705	1867	1795
	PubMed	19,717	15,912	5353	14,703	15,709	15,912	\({15,886}\)*
MVC	Cora	2708	1257	2036	1318	1327	1257	\({1265}\)*
	Citeseer	3327	\({1509}\)*	2308	1599	1622	1460	1533
	PubMed	19,717	3805	14,364	5014	4008	3805	\({3831}\)*

The best and the second best results are denoted in italic and asterisk, respectively
^aConfiguration: batch size = 128, fixed \(\tau\) = 1, learning rate = 0.01, \(\alpha\) = 3, and instance = 20
^bConfiguration: batch size = 512, fixed \(\tau\) = 1, learning rate = 0.01, \(\alpha\) = 3, instance = 20, cycle \(T_1\) = 100, substitution ratio 1/u = 1/8, cycle \(T_2\) = 10,000, mutation rate m = 0.001, and elite ratio = 0.0625