arXiv subjects

Mengchuan Zou

Publications and source records attributed to Mengchuan Zou.

4 recordsLinked to original sources

arXiv2025

AutoPBO: LLM-powered Optimization for Local Search PBO Solvers

Pseudo-Boolean Optimization (PBO) provides a powerful framework for modeling combinatorial problems through pseudo-Boolean (PB) constraints. Local search solvers have shown excellent performance in PBO solving, and their efficiency is highly dependent on their internal heuristics to guide the search. Still, their design often requires significant expert effort and manual tuning in practice. While Large Language Models (LLMs) have demonstrated potential in automating algorithm design, their application to optimizing PBO solvers remains unexplored. In this work, we introduce AutoPBO, a novel LLM-powered framework to automatically enhance PBO local search solvers. We conduct experiments on a broad range of four public benchmarks, including one real-world benchmark, a benchmark from PB competition, an integer linear programming optimization benchmark, and a crafted combinatorial benchmark, to evaluate the performance improvement achieved by AutoPBO and compare it with six state-of-the-art competitors, including two local search PBO solvers NuPBO and OraSLS, two complete PB solvers PBO-IHS and RoundingSat, and two mixed integer programming (MIP) solvers Gurobi and SCIP. AutoPBO demonstrates significant improvements over previous local search approaches, while maintaining competitive performance compared to state-of-the-art competitors. The results suggest that AutoPBO offers a promising approach to automating local search solver design.

cs.AI↗

arXiv2024

New Characterizations and Efficient Local Search for General Integer Linear Programming

Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop a new local search algorithm Local-ILP, which is efficient for solving general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. Two new operators are proposed, namely the tight move and the lift move operators, which are associated with appropriate scoring functions. Different modes apply different operators to realize different search strategies and the algorithm switches between three modes according to the current search state. Putting these together, we develop a local search ILP solver called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our algorithm in solving large-scale hard ILP problems. In the aspect of finding a good feasible solution quickly, Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our algorithm establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions.

math.OC↗

arXiv2021

(α, β)-Modules in Graphs

Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very strict, especially when dealing with real world graphs. We study new ways to relax this exactitude condition. However, generalizing modular decomposition is far from obvious. Most of the previous proposals lose algebraic properties of modules and thus most of the nice algorithmic consequences. We introduce the notion of an (α, β)-module, a relaxation that allows a bounded number of errors in each node and maintains some of the algebraic structure. It leads to a new combinatorial decomposition with interesting properties. Among the main results in this work, we show that minimal (α, β)-modules can be computed in polynomial time, and that every graph admits an (α,β)-modular decomposition tree, thus generalizing Gallai's Theorem (which corresponds to the case for α = β = 0). Unfortunately we give evidence that computing such a decomposition tree can be difficult.

cs.DM↗

arXiv2017

Approximation Strategies for Generalized Binary Search in Weighted Trees

We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node $t$ in a given tree $T$. Upon querying a node $v$ of the tree, the strategy receives as a reply an indication of the connected component of $T\setminus\{v\}$ containing the target $t$. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total query cost for a worst-case choice of the target. Designing an optimal strategy for a weighted tree search instance is known to be strongly NP-hard, in contrast to the unweighted variant of the problem which can be solved optimally in linear time. Here, we show that weighted tree search admits a quasi-polynomial time approximation scheme: for any $0 \textless{} \varepsilon \textless{} 1$, there exists a $(1+\varepsilon)$-approximation strategy with a computation time of $n^{O(\log n / \varepsilon^2)}$. Thus, the problem is not APX-hard, unless $NP \subseteq DTIME(n^{O(\log n)})$. By applying a generic reduction, we obtain as a corollary that the studied problem admits a polynomial-time $O(\sqrt{\log n})$-approximation. This improves previous $\hat O(\log n)$-approximation approaches, where the $\hat O$-notation disregards $O(\mathrm{poly}\log\log n)$-factors.

cs.DS↗