A Multi-Reference Relaxation Enforced Neighborhood Search Heuristic in SCIP

TL;DR

The paper addresses enhancing MILP primal heuristics by moving from a single reference solution to multiple references using MRENS, a generalization of RENS, integrated with SCIP via the Lagromory separator to harvest multiple fractional bases. By constructing sub-MILPs with bounds derived from a set of reference solutions, MRENS broadens the neighborhood and improves the likelihood of finding feasible and high-quality solutions. Computational experiments on the MIPLIB 2017 benchmark show that MRENS with three references yields higher best-known solution rates and sometimes faster solving times than single-reference RENS, with a manageable increase in search effort and fewer fixed integer variables. The results suggest that multi-reference strategies are a promising direction for primal heuristics in MILP solvers and could be extended to other heuristic frameworks and reference sources.

Abstract

This paper proposes and evaluates a Multi-Reference Relaxation Enforced Neighborhood Search (MRENS) heuristic within the SCIP solver. This study marks the first integration and evaluation of MRENS in a full-fledged MILP solver, specifically coupled with the recently-introduced Lagromory separator for generating multiple reference solutions. Computational experiments on the MIPLIB 2017 benchmark set show that MRENS, with multiple reference solutions, improves the solver's ability to find higher-quality feasible solutions compared to single-reference approaches. This study highlights the potential of multi-reference heuristics in enhancing primal heuristics in MILP solvers.