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BasicILS is the fixed-evaluation variant of ParamILS. In $\mathrm{BasicILS}(N)$, competing parameter settings are compared using the same $N$ benchmark runs, with matched instances and random seeds.^[ref] The comparison rule supplies the cost estimates used by the surrounding iterated local search.

For mean runtime, writewhere $r_i$ is the recorded cost on the specified run. Consider invented costs $A=(1,1,19)$ seconds and $B=(5,5,5)$ seconds. With only the first run, $A$ appears better, $1<5$. Across all three runs, its mean is $7$ seconds while $B$ remains at $5$ seconds. Choosing $N$ therefore affects both evaluation expense and how much instance variation the estimate captures.

Using the same run list makes that example a comparison on common evidence. Comparing $A$ only on easy instances with $B$ on harder ones would answer a different question. Even a matched finite sample can be unrepresentative of future workloads, so the final configuration still needs evaluation on unused instances.

FocusedILS changes the allocation of runs rather than requiring the same fixed $N$ for every explored candidate. Adaptive capping can avoid completing an already-lost runtime comparison under a valid lower-bound rule. Neither modification makes a finite observed mean a proof of the best possible setting in the entire algorithm parameter space.

FocusedILS is the ParamILS variant that adapts the number of evaluation runs assigned to different configurations. Its pairwise comparisons use common benchmark instances and random seeds, extending the evidence when necessary instead of comparing arbitrary means from different run lists.^[ref]

An original example shows why unequal evidence needs care. Suppose configuration $A$ has completed two runs with costs $(2,2)$ seconds, while $B$ has four costs $(3,3,30,30)$ seconds. Their available means, $2$ and $16.5$, mix different instance coverage. On the two shared runs the comparison is $2$ against $3$. If extending $A$ to the same four runs gives $(2,2,40,40)$, its mean becomes $21$, reversing the ranking against $B$'s $16.5$. Matching the evidence does not prevent a ranking from changing when more evidence arrives.

The run allocation and the configuration search are different layers. Iterated local search proposes which settings to compare; the FocusedILS comparison procedure determines how much measured evidence supports the decision. BasicILS instead uses a fixed evaluation count $N$. Both still depend on a declared cost statistic and a representative workload.

The example is a finite-data illustration, not a confidence interval or proof about unseen inputs. A setting selected after adaptive evaluation should be assessed on unused instances, with the full tuning budget recorded. The cost of finding the configuration and the subsequent cost of running it answer different questions.

ParamILS is a framework for algorithm configuration based on iterated local search. It explores an algorithm parameter space using improvements to nearby configurations, perturbations and occasional restarts. BasicILS compares configurations on a fixed number of matched training runs; FocusedILS adapts how many runs support a comparison.^[ref]

The distinctive efficiency idea of adaptive capping is to stop spending evaluation time on a candidate once it cannot win the comparison under the stated cost model. Consider an original example with three fixed instances and mean nonnegative runtime as the objective function. A fully evaluated incumbent has total time $12$ seconds, hence mean $4$ seconds. If the first two candidate runs already total $13$ seconds, even a zero-time final run leaves mean at least $13/3>4$. Rejecting that candidate does not require finishing the last run.

This argument depends on its assumptions: the comparison uses the same fixed instance set and a lower bound on unfinished cost. It cannot be transferred unchanged to arbitrary quality scores or a different timeout penalty. The paper distinguishes trajectory-preserving capping from a more aggressive heuristic variant; faster rejection does not always carry the same guarantee.^[ref]

The method turns tuning into a measured optimization experiment, but a good observed configuration is not a proof of a global minimum. The neighborhood, evaluation budget and deployment workload remain relevant to what the returned setting establishes.