Check seeded upper bounds before accepting the first incumbent #2142

Summary

A finite upper bound can be seeded through branch_and_bound_t::set_initial_upper_bound() before a solver-space incumbent exists. accept_new_incumbent() currently accepts the first candidate unconditionally.

Some solution-update paths then retain the seeded upper_bound_ through std::min or fetch_min, while storing the worse candidate in incumbent_. For example, a seeded upper bound of 100 and a first candidate objective of 110 can leave upper_bound_ at 100 and incumbent_.objective at 110.

This behavior predates PR #2131. Address it in a separate follow-up PR.

Required changes

• Define how a first solver-space incumbent must satisfy a finite seeded upper bound, including the appropriate numerical tolerance.
• Update accept_new_incumbent() and audit its callers so a worse candidate cannot create an inconsistent incumbent and upper bound.
• Preserve first-candidate acceptance when no finite upper bound exists.
• Preserve the objective-lattice, integral-objective, and general-objective comparison rules after an incumbent exists.
• Check the sub-MIP path, which seeds an upper bound from the main solve before it necessarily has a valid local incumbent.
• Add regression tests for the first-incumbent behavior.

Affected areas

• cpp/src/branch_and_bound/branch_and_bound.cpp
• branch_and_bound_t::accept_new_incumbent
• branch_and_bound_t::set_initial_upper_bound
• Heuristic, repaired, tree-search, deterministic, and sub-MIP incumbent handling

Acceptance criteria

• With a finite seeded upper bound, a first candidate that exceeds the allowed bound is rejected without modifying the incumbent.
• A first candidate that satisfies the seeded upper bound is handled consistently with the defined tolerance.
• Without a finite seeded upper bound, the first feasible candidate is accepted.
• Later incumbent updates retain the existing comparison rules.
• Regression tests cover candidates above, equal to, and below a seeded upper bound, plus the unseeded case.
• Tests verify that accepted incumbent objectives and stored upper bounds remain consistent under the defined contract.

Context

Requested by @nguidotti.

• PR: Uses objective lattice to accept or reject incumbents #2131
• Review thread: Uses objective lattice to accept or reject incumbents #2131 (comment)