Propagate the bounds from the parent to the child nodes

[nguidotti]

With this PR, the solver propagates the bounds from the parent to the child nodes. If the solver reaches the end of a branch (i.e., when the node becomes infeasible or an integer feasible solution is found), the bounds are recomputed from scratch.

Average (Primal) Gap over the MIPLIB2017 dataset:
main (91a19f8): 15.917959 with 224 feasible solutions
This PR: 15.519858 with 224 feasible solutions

Checklist

• I am familiar with the Contributing Guidelines.
• Testing
  • New or existing tests cover these changes
  • Added tests
  • Created an issue to follow-up
  • NA
• Documentation
  • The documentation is up to date with these changes
  • Added new documentation
  • NA

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[nguidotti]

/ok to test f44b134

[greptile-apps]

Greptile Overview

Greptile Summary

This PR implements bounds propagation optimization in the branch-and-bound solver for mixed-integer programming (MIP). The key change is that bounds (variable upper/lower limits) are now efficiently propagated from parent nodes to child nodes during tree traversal, rather than being recomputed from scratch at every node. The implementation tracks which bounds have changed using a bounds_changed vector and selectively triggers full recomputation only when necessary (when nodes become infeasible or integer feasible solutions are found). The changes span three core files: branch_and_bound.hpp updates the method signature, mip_node.hpp refactors bounds update logic into separate methods, and branch_and_bound.cpp implements the conditional bounds update mechanism with performance optimizations for the dual simplex solver.

Important Files Changed

Changed Files

Filename	Score	Overview
cpp/src/dual_simplex/branch_and_bound.hpp	5/5	Updated solve_node method signature to support bounds propagation tracking
cpp/src/dual_simplex/mip_node.hpp	4/5	Refactored bounds update logic with new update_variable_bound method and optimized traversal
cpp/src/dual_simplex/branch_and_bound.cpp	4/5	Implemented conditional bounds recomputation logic with performance optimizations

Confidence score: 4/5

• This PR implements a well-understood optimization for branch-and-bound algorithms with clear performance benefits
• Score reflects solid implementation but complexity in bounds management logic could introduce subtle bugs if bounds tracking becomes inconsistent
• Pay close attention to the bounds update logic in mip_node.hpp to ensure tighter bounds are never overwritten by looser ones

Sequence Diagram

sequenceDiagram
    participant User
    participant BranchAndBound as "Branch & Bound Solver"
    participant Node as "MIP Node"
    participant LP as "LP Solver"
    
    User->>BranchAndBound: "solve(solution)"
    
    BranchAndBound->>BranchAndBound: "solve_node()"
    
    Note over BranchAndBound: Bounds propagation logic
    BranchAndBound->>Node: "get_variable_bounds(lower, upper, bounds_changed)"
    Node->>Node: "update_variable_bound() for current node"
    
    loop For each parent node up to root
        Node->>Node: "update_variable_bound() from parent"
        Note over Node: Propagates bounds from parent to child
    end
    
    Node-->>BranchAndBound: "Updated bounds with bounds_changed flags"
    
    BranchAndBound->>LP: "bound_strengthening()"
    LP-->>BranchAndBound: "feasible status"
    
    alt Node is feasible
        BranchAndBound->>LP: "dual_phase2() with updated bounds"
        LP-->>BranchAndBound: "LP solution"
        
        alt Solution is integer feasible
            BranchAndBound->>BranchAndBound: "add_feasible_solution()"
        else Solution is fractional
            BranchAndBound->>Node: "branch() - create child nodes"
            Note over Node: Children inherit parent bounds
            Node->>Node: "add_children(down_child, up_child)"
        end
    else Node is infeasible
        BranchAndBound->>Node: "set_status(INFEASIBLE)"
    end
    
    BranchAndBound-->>User: "Final solution with bounds propagation"

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