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Table 3 The results on optimization of ground state energy of SK model compared to extremal optimization (EO), genetic algorithm (GA), and simulated annealing (SA)

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

N I EO [28] GAa SA GSO (\(N_{{\text{bs}}}=1\))b
256 5000 \(-\,\)0.74585(2)/\(\sim\)268 s \(-\,\)0.6800(3)/16.3 s \(-\,\)0.7278(2)/1.28 s \(-\,\)0.7267(2)/0.99 s
512 2500 \(-\,\)0.75235(3)/\(\sim\)1.2 h \(-\,\)0.6580(3)/60.06 s \(-\,\)0.7327(2)/3.20 s \(-\,\)0.7405(2)/2.16 s
1024 1250 0.7563(2)/\(\sim\)20  h \(-\,\)0.6884(4)/236.21 s \(-\,\)0.7352(2)/15.27 s \(-\,\)0.7480(2)/4.49 s
2048 400 \(-\,\)0.7367(2)/63.27  s \(-\,\)0.7524(2)/7.23 s
4096 200 \(-\,\)0.73713(6)/1591.93 s \(-\,\)0.7551(2)/10.46 s
8192 100 \(-\,\)0.7562(1)/25.15 s
  1. The best results are denoted in italic. Corresponding standard error of the mean is given in brackets
  2. aConfiguration: population size = 64, crossover rate = 0.8, mutation rate = 0.001, and elite ratio = 0.125
  3. bConfiguration: initial \(\tau\) = 20, final \(\tau\) = 1, and learning rate = 1