Compressing branch-and-bound trees

Journal Article · 05 April 2024 · Mathematical Programming

DOI: https://doi.org/10.1007/s10107-024-02080-5 · OSTI ID:2500845

Muñoz, Gonzalo ^[1]; Paat, Joseph  ^[2]; Xavier, Álinson S. ^[3]

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1. Universidad de O’Higgins, Rancagua (Chile)
2. Univ. of British Columbia, Vancouver, BC (Canada)
3. Argonne National Laboratory (ANL), Argonne, IL (United States)

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? Here we believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.

• Research Organization: Argonne National Laboratory (ANL); Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Electricity (OE)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2500845
• Journal Information: Mathematical Programming, Journal Name: Mathematical Programming Vol. 210; ISSN 0025-5610
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English