ID-PaS+: Identity-Aware Predict-and-Search for Solving General Mixed-Integer Linear Programs

Learning Early-to-Final Solution Consistency for MILP Acceleration

This paper finds that solutions produced at the early search stage of MILP solvers are often structurally close to the solutions found after full-budget search, and proposes a new solver-informed paradigm that shifts the learning target from variable assignment to early-to-final consistency.

SHSP: Structure-Aware Hierarchical Solution Prediction for Mixed-Integer Linear Programming

The Structure-Aware Hierarchical Solution Prediction (SHSP) framework is proposed that replaces the parallel marginal decoding of one-shot methods with a novel hierarchical conditional decoding mechanism and significantly outperforms existing one-shot prediction baselines.

LLM-guided Cutting-plane Management for Mixed-integer Linear Programming

This work proposes an LLM-guided cutting-plane management framework that removes dependence on domain-specific training data and substantially reduces reliance on expert-crafted configurations.

UvA-DARE (Digital Academic Repository) Mixed-Integer Optimization with Constraint Learning

The quadratic multidimensional knapsack problem: exact, heuristic, and machine learning methods

This paper presents a multi-faceted approach to solving the quadratic multidimensional knapsack problem (QMDKP), an NP-hard nonlinear combinatorial optimization problem that has received limited attention in the literature. We introduce a new testbed of QMDKP instances with induced profit-weight correlations and evaluate four linearization strategies for solving the problem exactly. To address scalability, we propose several heuristic and metaheuristic methods, including a greedy algorithm, a supervised machine learning (ML)-based approach, and a genetic algorithm. Our underlying ML framework employs binary classification to predict item inclusion probabilities, guiding a greedy construction process. Building on this framework, we explore hybrid strategies such as reduce-fill, expand-repair, and a genetic algorithm with ML-driven repair operators. Extensive computational results show that these ML-enhanced hybrid methods improve upon their baseline heuristics and that the genetic algorithm consistently yields near-optimal solutions. This work provides a generalizable template for hybrid optimization and learning-based approaches to challenging combinatorial problems.

AutoPref: Automatic Discovery of Task-Specific Preference Objectives for Neural Combinatorial Optimization

Combinatorial optimization problems (COPs) underpin many real-world decisions, but their exponentially large search spaces make high-quality solutions costly to obtain. Neural combinatorial optimization (NCO) learns fast construction policies, typically with reinforcement learning (RL), while preference-based NCO improves sample efficiency by learning from relative solution quality. However, existing preference objectives combine two distinct design choices in manually specified, one-size-fits-all formulations: what learning signal to extract from each solution pair and how to weight each pair relative to the sampled set. We present AutoPref, the first LLM-guided framework for automated preference-objective discovery in NCO. AutoPref factorizes the objective into a pairwise loss program, which defines the learning signal, and a set-aware weighting program, which determines each pair's relative contribution. Their composition forms a unified programmatic objective space containing existing preference objectives as special cases. To make its search tractable, we introduce a staged conditional search strategy with behavioral gates that filter inadmissible programs before short-horizon training and evaluation. Across TSP, CVRP, FFSP, and JSSP, AutoPref consistently outperforms strong hand-designed baselines across problem scales, demonstrating the benefits and scalability of automated objective discovery for NCO.