[zayenz]

Problem

Restart-based search with no-goods can report a solution as optimal when it is not.

Space::slave() returning false means the slave search is incomplete: it explores a restricted search space, such as an LNS neighbourhood. The no-goods recorded by that search only rule out parts of the restricted space. RBS::next still passed them to Space::master(), whose default posts them in the master. The master then lost solutions that the restriction had excluded only in that one slave.

Small example (the new test): four distinct variables over 0..3, minimise x0. The first slave restricts x2 and x3 to {0,1} and returns false. That search finds x0 = 2 and records no-goods that rule out x0 = 0 and x0 = 1. Posted in the master, those no-goods fail it, and RBS finishes, claiming x0 = 2 is optimal, although x0 = 0 is feasible (0,1,2,3).

The first slave is configured in Gecode::RBS::RBS (gecode/search/rbs.hpp), which discarded its result. Its no-goods were always treated as valid, even for a restricted first slave.

This also made the relax crash fixed in #276 frequent: in photo -nogoods true, the wrong no-goods remove values from the master that relax later tries to keep from the last solution.

Fix

• RBS::master_nogoods() returns the empty no-goods (NoGoods::eng) when the search that recorded them was incomplete, and the engine's no-goods otherwise. Both restart paths in RBS::next use it.
• The result of the first slave configuration is now passed to the engine and determines whether that search yields valid no-goods. A new Search::Seq::rbsengine overload takes it; the old overload stays for binary compatibility and passes true.
• The first search is still treated as complete for termination. FlatZinc's slave() returns false on the first restart for on_restart models, so honouring it there would change when those models finish. Only no-goods are affected.
• The Doxygen of Space::slave() and MetaInfo::nogoods() states the contract.

No public API changes. Searches whose slaves are complete behave exactly as before. Searches with incomplete slaves post fewer no-goods, so they may explore more but no longer lose solutions.

Test

Search::RBS::IncompleteNoGoods is the example above with nogoods_limit = 128. Without the fix it reports x0 = 2 and finishes. With the fix it finds x0 = 0.

A two-thread variant passed without the fix as well, so it is not included.

Validation

Linux (erebor), GCC 15 Release:

Run	Result
gecode-test -test Search::RBS::IncompleteNoGoods	1/1
gecode-test -threads 4 -tag check	517/517
gecode-test -threads 4 -tag standard -test ^Search::	796/796
gecode-test -threads 4 -tag standard -test ^NoGoods::	160/160
gecode-test -threads 4 -tag standard -test ^FlatZinc	136/136
photo -restart constant -restart-scale {1,5,8} -nogoods true -seed {1..8} -time 1500 1	0/24 crashed (unfixed main: 15/24 on 6.5.0)

Linux, Clang 21 Debug with ASan and UBSan: -test ^Search::RBS 37/37 and -tag check -test ^NoGoods:: 96/96.

macOS Release: the new test fails without the fix and passes with it. uv run misc/tidy.py --check passes.

Relation to #276

The two fixes are independent. With only this fix, photo -restart constant -nogoods true did not crash in the sweep above, because the relax failures become rare. The relax bug is still there, so #276 is still needed.

Not fixed here

• DFS and BAB check the stop object before exhaustion, so RBS with no-goods on an unsatisfiable model does not terminate for some cutoffs.
• When the master fails during a restart, RBS::stopped() can give the wrong answer and statistics are counted twice.