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The initial temperature is the larger of the standard deviation of 32 random pilot objective values and 0.001. This scales early acceptance of uphill moves to the local objective’s observed variability while imposing a positive floor. It is recomputed within each independent search under the fixed benchmark protocol.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| T_0 | Initial annealing temperature |
| SD | Standard deviation of pilot scores |
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\subsection*{Queyranne: direct normalized-objective search}
We use pendant-pair contraction with a deterministic starting order and cache objective values within each search. The minimum candidate is returned without an added local-search step. Queyranne has a guarantee for symmetric submodular functions [3]; that guarantee is not assumed for normalized stochastic interaction. Consequently, its outputs are judged against enumeration, not treated as reference answers. Each run has a fresh on-demand oracle and cannot read the exhaustive table.
\subsection*{Simulated annealing: independently repeated searches}
Each of ten independent runs per network uses four random restarts and 512 single-bit proposals per restart. Metropolis acceptance is $\min\{1,e^{-\Delta J/T}\}$. Temperature decreases geometrically from $T_0$ to $10^{-3}T_0$, with $T_0=\max\{\operatorname{SD}(32\text{ random pilot scores}),0.001\}$. All-in-one proposals are rejected and consume a proposal step. The best visited valid partition, including pilot points, is retained. Each run uses a fresh cached oracle; it receives neither the optimum nor the reference table. Maximum budget: 2,048 proposals plus 36 pilot/initial evaluations.
[Context excerpt; full source linked.]Exact original notation
T_0=\max\{\operatorname{SD}(32\text{ random pilot scores}),0.001\}