Figure 1.
The Lam target acceptance rate.
Figure 1.
The Lam target acceptance rate.
Figure 2.
OneMax (each 0-bit costs 1): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 2.
OneMax (each 0-bit costs 1): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 3.
OneMax (each 0-bit costs 10): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 3.
OneMax (each 0-bit costs 10): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 4.
OneMax (each 0-bit costs 100): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 4.
OneMax (each 0-bit costs 100): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 5.
TwoMax problem: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 5.
TwoMax problem: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 6.
Trap problem: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 6.
Trap problem: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 7.
Graphs of (a) ${f}_{1}\left(x\right)$ and (b) ${f}_{2}\left(x\right)$.
Figure 7.
Graphs of (a) ${f}_{1}\left(x\right)$ and (b) ${f}_{2}\left(x\right)$.
Figure 8.
Minimize ${f}_{1,1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 8.
Minimize ${f}_{1,1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 9.
Minimize ${f}_{1,10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 9.
Minimize ${f}_{1,10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 10.
Minimize ${f}_{1,100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 10.
Minimize ${f}_{1,100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 11.
Minimize ${f}_{1,1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 11.
Minimize ${f}_{1,1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 12.
Minimize ${f}_{2,1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 12.
Minimize ${f}_{2,1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 13.
Minimize ${f}_{2,10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 13.
Minimize ${f}_{2,10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 14.
Minimize ${f}_{2,100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 14.
Minimize ${f}_{2,100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 15.
Minimize ${f}_{2,1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 15.
Minimize ${f}_{2,1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 16.
Graph of $g\left(x\right)$.
Figure 16.
Graph of $g\left(x\right)$.
Figure 17.
Minimize ${g}_{1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 17.
Minimize ${g}_{1}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 18.
Minimize ${g}_{10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 18.
Minimize ${g}_{10}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 19.
Minimize ${g}_{100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 19.
Minimize ${g}_{100}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 20.
Minimize ${g}_{1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 20.
Minimize ${g}_{1000}\left(x\right)$: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 21.
TSP with cities in unit square: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 21.
TSP with cities in unit square: Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 22.
TSP (cities in 100 by 100 square): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Figure 22.
TSP (cities in 100 by 100 square): Self-Tuning Lam, Modified Lam, and target acceptance rates for (a) 1000 iterations, (b) 10,000 iterations, (c) 100,000 iterations, and (d) 1 million iterations.
Table 1.
Constants used in the specification of the Self-Tuning Lam, including the constant, its mathematical definition, and its double-precision floating point value.
Table 1.
Constants used in the specification of the Self-Tuning Lam, including the constant, its mathematical definition, and its double-precision floating point value.
Constant | Definition | Value |
---|
${\lambda}_{0.001}$ | $\mathrm{LamRate}\left(0.001N\right)$ | 0.9768670788789564 |
${\lambda}_{0.002}$ | $\mathrm{LamRate}\left(0.002N\right)$ | 0.9546897506857566 |
${\lambda}_{0.01}$ | $\mathrm{LamRate}\left(0.01N\right)$ | 0.8072615745900611 |
${\lambda}_{0.02}$ | $\mathrm{LamRate}\left(0.02N\right)$ | 0.6808590431613767 |
${\zeta}_{0.001}$ | $-1/ln\left(\frac{0.001}{1.001-{\lambda}_{0.001}}\right)$ | 0.3141120890121576 |
${\zeta}_{0.002}$ | $-1/ln\left(\frac{0.001}{1.001-{\lambda}_{0.002}}\right)$ | 0.260731492877931 |
${\zeta}_{0.01}$ | $-1/ln\left(\frac{0.001}{1.001-{\lambda}_{0.01}}\right)$ | 0.18987910472222955 |
${\zeta}_{0.02}$ | $-1/ln\left(\frac{0.001}{1.001-{\lambda}_{0.02}}\right)$ | 0.17334743675123146 |
Table 2.
Average solution cost for the OneMax problem, case when each 0-bit costs 1.
Table 2.
Average solution cost for the OneMax problem, case when each 0-bit costs 1.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $24.5$ | $16.5$ | <${10}^{-26}$ |
$\mathrm{10,000}$ | $0.01$ | $0.04$ | $0.17$ |
$\mathrm{100,000}$ | $0.00$ | $0.00$ | n/a |
$\mathrm{1,000,000}$ | $0.00$ | $0.00$ | n/a |
Table 3.
Average solution cost for the OneMax problem, case when each 0-bit costs 10.
Table 3.
Average solution cost for the OneMax problem, case when each 0-bit costs 10.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $25.2$ | $167.9$ | <${10}^{-66}$ |
$\mathrm{10,000}$ | $0.00$ | $0.08$ | $0.01$ |
$\mathrm{100,000}$ | $0.00$ | $0.00$ | n/a |
$\mathrm{1,000,000}$ | $0.00$ | $0.00$ | n/a |
Table 4.
Average solution cost for the OneMax problem, case when each 0-bit costs 100.
Table 4.
Average solution cost for the OneMax problem, case when each 0-bit costs 100.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $231.0$ | $1661.0$ | <${10}^{-66}$ |
$\mathrm{10,000}$ | $0.00$ | $6.00$ | $0.01$ |
$\mathrm{100,000}$ | $0.00$ | $0.00$ | n/a |
$\mathrm{1,000,000}$ | $0.00$ | $0.00$ | n/a |
Table 5.
Average solution cost for the TwoMax problem.
Table 5.
Average solution cost for the TwoMax problem.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $60.00$ | $312.62$ | <${10}^{-36}$ |
$\mathrm{10,000}$ | $15.36$ | $10.78$ | $0.69$ |
$\mathrm{100,000}$ | $20.48$ | $0.00$ | $0.04$ |
$\mathrm{1,000,000}$ | $0.00$ | $0.00$ | n/a |
Table 6.
Average solution cost for the Trap problem.
Table 6.
Average solution cost for the Trap problem.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $539.63$ | $683.63$ | <${10}^{-65}$ |
$\mathrm{10,000}$ | $512.00$ | $512.43$ | $0.04$ |
$\mathrm{100,000}$ | $512.00$ | $512.00$ | n/a |
$\mathrm{1,000,000}$ | $512.00$ | $512.00$ | n/a |
Table 7.
Average solution for minimizing ${f}_{1,1}\left(x\right)$. The minimum is ${f}_{1,1}\left(x\right)\approx -6.02074$.
Table 7.
Average solution for minimizing ${f}_{1,1}\left(x\right)$. The minimum is ${f}_{1,1}\left(x\right)\approx -6.02074$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-4.309034$ | $-3.651338$ | $0.06$ |
$\mathrm{10,000}$ | $-5.416610$ | $-4.965097$ | $0.09$ |
$\mathrm{100,000}$ | $-6.020740$ | $-5.970393$ | $0.32$ |
$\mathrm{1,000,000}$ | $-6.020740$ | $-6.020740$ | n/a |
Table 8.
Average solution for minimizing ${f}_{1,10}\left(x\right)$. The minimum is ${f}_{1,10}\left(x\right)\approx -60.2074$.
Table 8.
Average solution for minimizing ${f}_{1,10}\left(x\right)$. The minimum is ${f}_{1,10}\left(x\right)\approx -60.2074$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-33.524983$ | $-40.061769$ | $0.07$ |
$\mathrm{10,000}$ | $-28.994029$ | $-54.713137$ | <${10}^{-14}$ |
$\mathrm{100,000}$ | $-48.628247$ | $-60.207395$ | <${10}^{-6}$ |
$\mathrm{1,000,000}$ | $-60.207401$ | $-60.207401$ | $0.14$ |
Table 9.
Average solution for minimizing ${f}_{1,100}\left(x\right)$. The minimum is ${f}_{1,100}\left(x\right)\approx -602.074$.
Table 9.
Average solution for minimizing ${f}_{1,100}\left(x\right)$. The minimum is ${f}_{1,100}\left(x\right)\approx -602.074$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-340.284138$ | $-349.329322$ | $0.80$ |
$\mathrm{10,000}$ | $-350.353270$ | $-520.506232$ | <${10}^{-6}$ |
$\mathrm{100,000}$ | $-360.422102$ | $-598.098820$ | <${10}^{-14}$ |
$\mathrm{1,000,000}$ | $-602.074006$ | $-602.074006$ | $0.06$ |
Table 10.
Average solution for minimizing ${f}_{1,1000}\left(x\right)$. The minimum is ${f}_{1,1000}\left(x\right)\approx -6020.74$.
Table 10.
Average solution for minimizing ${f}_{1,1000}\left(x\right)$. The minimum is ${f}_{1,1000}\left(x\right)\approx -6020.74$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-3402.841736$ | $-3637.881712$ | $0.51$ |
$\mathrm{10,000}$ | $-3251.811974$ | $-5199.982268$ | <${10}^{-8}$ |
$\mathrm{100,000}$ | $-3201.467852$ | $-5970.395531$ | <${10}^{-18}$ |
$\mathrm{1,000,000}$ | $-6020.740052$ | $-6020.740056$ | $0.14$ |
Table 11.
Average solution for minimizing ${f}_{2,1}\left(x\right)$. The minimum is ${f}_{2,1}\left(x\right)\approx 0.665095$.
Table 11.
Average solution for minimizing ${f}_{2,1}\left(x\right)$. The minimum is ${f}_{2,1}\left(x\right)\approx 0.665095$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $1.044128$ | $1.690334$ | $0.002$ |
$\mathrm{10,000}$ | $0.703067$ | $0.665095$ | $0.32$ |
$\mathrm{100,000}$ | $0.665095$ | $0.665095$ | $0.32$ |
$\mathrm{1,000,000}$ | $0.665095$ | $0.665095$ | $0.07$ |
Table 12.
Average solution for minimizing ${f}_{2,10}\left(x\right)$. The minimum is ${f}_{2,10}\left(x\right)\approx 6.65095$.
Table 12.
Average solution for minimizing ${f}_{2,10}\left(x\right)$. The minimum is ${f}_{2,10}\left(x\right)\approx 6.65095$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $22.978824$ | $13.303961$ | <${10}^{-4}$ |
$\mathrm{10,000}$ | $18.422196$ | $6.650951$ | <${10}^{-8}$ |
$\mathrm{100,000}$ | $6.650951$ | $6.650951$ | $0.69$ |
$\mathrm{1,000,000}$ | $6.650951$ | $6.650951$ | $0.95$ |
Table 13.
Average solution for minimizing ${f}_{2,100}\left(x\right)$. The minimum is ${f}_{2,100}\left(x\right)\approx 66.5095$.
Table 13.
Average solution for minimizing ${f}_{2,100}\left(x\right)$. The minimum is ${f}_{2,100}\left(x\right)\approx 66.5095$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $203.207943$ | $149.615304$ | $0.03$ |
$\mathrm{10,000}$ | $172.830434$ | $66.509514$ | <${10}^{-7}$ |
$\mathrm{100,000}$ | $66.509512$ | $66.509512$ | $0.58$ |
$\mathrm{1,000,000}$ | $66.509512$ | $66.509512$ | $0.51$ |
Table 14.
Average solution for minimizing ${f}_{2,1000}\left(x\right)$. The minimum is ${f}_{2,1000}\left(x\right)\approx 665.095$.
Table 14.
Average solution for minimizing ${f}_{2,1000}\left(x\right)$. The minimum is ${f}_{2,1000}\left(x\right)\approx 665.095$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $2563.685013$ | $1720.298119$ | $0.001$ |
$\mathrm{10,000}$ | $1994.106640$ | $665.095131$ | <${10}^{-10}$ |
$\mathrm{100,000}$ | $665.095123$ | $665.095123$ | $0.22$ |
$\mathrm{1,000,000}$ | $665.095123$ | $665.095123$ | $0.22$ |
Table 15.
Average solution for minimizing ${g}_{1}\left(x\right)$. The minimum is ${g}_{1}\left(x\right)\approx -0.869011$.
Table 15.
Average solution for minimizing ${g}_{1}\left(x\right)$. The minimum is ${g}_{1}\left(x\right)\approx -0.869011$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-0.682822$ | $-0.547887$ | <${10}^{-5}$ |
$\mathrm{10,000}$ | $-0.851176$ | $-0.846336$ | $0.62$ |
$\mathrm{100,000}$ | $-0.869011$ | $-0.869011$ | $0.24$ |
$\mathrm{1,000,000}$ | $-0.869011$ | $-0.869011$ | $0.26$ |
Table 16.
Average solution for minimizing ${g}_{10}\left(x\right)$. The minimum is ${g}_{10}\left(x\right)\approx -8.69011$.
Table 16.
Average solution for minimizing ${g}_{10}\left(x\right)$. The minimum is ${g}_{10}\left(x\right)\approx -8.69011$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-4.555178$ | $-5.712597$ | $0.0002$ |
$\mathrm{10,000}$ | $-8.187308$ | $-8.416688$ | $0.08$ |
$\mathrm{100,000}$ | $-8.690111$ | $-8.690111$ | $0.01$ |
$\mathrm{1,000,000}$ | $-8.690111$ | $-8.690111$ | $0.63$ |
Table 17.
Average solution for minimizing ${g}_{100}\left(x\right)$. The minimum is ${g}_{100}\left(x\right)\approx -86.9011$.
Table 17.
Average solution for minimizing ${g}_{100}\left(x\right)$. The minimum is ${g}_{100}\left(x\right)\approx -86.9011$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-38.269621$ | $-52.774954$ | <${10}^{-5}$ |
$\mathrm{10,000}$ | $-76.827533$ | $-85.156692$ | <${10}^{-5}$ |
$\mathrm{100,000}$ | $-86.901113$ | $-86.901113$ | $0.60$ |
$\mathrm{1,000,000}$ | $-86.901113$ | $-86.901113$ | $0.07$ |
Table 18.
Average solution for minimizing ${g}_{1000}\left(x\right)$. The minimum is ${g}_{1000}\left(x\right)\approx -869.011$.
Table 18.
Average solution for minimizing ${g}_{1000}\left(x\right)$. The minimum is ${g}_{1000}\left(x\right)\approx -869.011$.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $-340.359950$ | $-565.666535$ | <${10}^{-10}$ |
$\mathrm{10,000}$ | $-715.997501$ | $-855.184880$ | <${10}^{-12}$ |
$\mathrm{100,000}$ | $-869.011133$ | $-869.011126$ | $0.14$ |
$\mathrm{1,000,000}$ | $-869.011135$ | $-869.011135$ | $0.10$ |
Table 19.
Average cost of solution to TSP with 1000 cities distributed within a unit square.
Table 19.
Average cost of solution to TSP with 1000 cities distributed within a unit square.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $440.91$ | $411.18$ | <${10}^{-52}$ |
$\mathrm{10,000}$ | $250.52$ | $246.80$ | <$0.0001$ |
$\mathrm{100,000}$ | $108.88$ | $109.21$ | $0.22$ |
$\mathrm{1,000,000}$ | $47.01$ | $46.88$ | $0.21$ |
Table 20.
Average cost of solution to TSP with 1000 cities distributed within a 100 by 100 square.
Table 20.
Average cost of solution to TSP with 1000 cities distributed within a 100 by 100 square.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
1000 | $40,825.52$ | $41,095.38$ | $0.003$ |
$\mathrm{10,000}$ | $25,235.56$ | $24,691.62$ | <${10}^{-8}$ |
$\mathrm{100,000}$ | $10,895.33$ | $10,902.40$ | $0.80$ |
$\mathrm{1,000,000}$ | $4686.09$ | $4692.92$ | $0.56$ |
Table 21.
Runtime comparison, measured in seconds of CPU time, of the Modified Lam and Self-Tuning Lam annealing schedules. Averages of 100 runs of each run length.
Table 21.
Runtime comparison, measured in seconds of CPU time, of the Modified Lam and Self-Tuning Lam annealing schedules. Averages of 100 runs of each run length.
N | Modified Lam | Self-Tuning Lam | T-Test p-Value |
---|
$16,000$ | $0.00063$ | $0.00094$ | $0.52$ |
$32,000$ | $0.00156$ | $0.00172$ | $0.82$ |
$64,000$ | $0.00313$ | $0.00328$ | $0.86$ |
$128,000$ | $0.00594$ | $0.00625$ | $0.77$ |
$256,000$ | $0.01156$ | $0.01328$ | $0.054$ |
$512,000$ | $0.02406$ | $0.02547$ | $0.20$ |
$1,024,000$ | $0.04875$ | $0.05000$ | $0.14$ |