external-energy optimization

This work addresses key challenges in integer linear programming (ILP) solvers—limited generalization, reliance on external solvers, and poor efficiency in multimodal energy landscapes—by proposing a training-free, solver-free sampling-based optimization framework that directly explores the discrete feasible region. Leveraging the linear structure of ILP, the method designs a proposal distribution satisfying detailed balance and incorporates a dual tempering mechanism that jointly modulates temperature and penalty parameters to dynamically adjust constraint barriers while preserving the original objective function, thereby enhancing global exploration. Experiments demonstrate that the approach consistently outperforms SCIP across four benchmarks, matches or exceeds Gurobi’s performance on two tasks within 200 seconds, exhibits superior robustness on out-of-distribution instances, and competes effectively with classical solvers on MIPLIB 2017 without any parameter tuning.

This paper studies the optimization of Integer Linear-Exponential Programming (ILEP): maximizing/minimizing a linear-exponential objective function subject to linear-exponential constraints involving the exponential function (x mapsto 2^x) and the modulo operation ((x,y) mapsto x mod 2^y). As the decision version is NP-complete, we propose—first in the literature—the *Integer Linear-Exponential Straight-Line Program* (ILESLP) as a succinct representation of optimal solutions, placing the problem in an extended NPO class and circumventing standard binary search frameworks. Our method models solution structure via arithmetic circuits and leverages an integer factorization oracle to design polynomial-time algorithms for feasibility verification and objective-value comparison. The core contribution is a proof that every optimal solution admits an ILESLP representation of polynomial size, and that both feasibility and dominance (i.e., objective-value comparison) can be verified in polynomial time. This establishes ILEP as efficiently certifiable within its extended complexity class.

This work addresses the efficiency bottleneck in MaxSAT solving caused by frequent calls to ILP solvers. It presents the first systematic investigation into the impact of ILP preprocessing techniques on MaxSAT solving. We propose an ILP constraint reduction and equivalence substitution method specifically tailored for MaxSAT, which structurally simplifies soft and hard constraints in the ILP encoding prior to solving. This significantly reduces the dependency of WMaxCDCL-style solvers on underlying ILP solvers—without compromising solution accuracy or quality—thereby enhancing the robustness and generalizability of solver portfolios. Experimental evaluation on standard benchmarks shows that WMaxCDCL-OpenWbo1200 solves 15 additional instances; ILP solver invocations decrease substantially; and overall throughput and stability improve markedly.

Predicting size-extensive molecular properties (e.g., energy, polarizability) across scales—particularly for molecules larger than those in the training set—remains a critical challenge in molecular machine learning. Method: We propose an unsupervised training set selection method based on integer linear programming (ILP), the first to formulate molecular subset selection as an ILP problem. Unlike conventional diversity- or coverage-driven strategies, our approach imposes atom-level local environment similarity constraints to ensure systematic coverage of local chemical motifs while guaranteeing globally optimal subset selection. It integrates physics-informed atomic feature embeddings with ILP-based optimization. Results: The selected training sets significantly improve model generalization to unseen, especially out-of-distribution, large molecules. Experiments across multiple extensive property prediction tasks demonstrate substantial gains over state-of-the-art unsupervised selection baselines, with high computational efficiency and inherent theoretical interpretability.

This work addresses the challenge of explicitly characterizing the iteration complexity in data-driven inverse optimization for estimating the objective function parameters of integer linear programs. By analyzing the geometric properties of a suboptimality-based loss function, the authors employ projected subgradient descent to achieve exact consistency with observed data within a finite number of steps. The key contribution lies in providing, for the first time, an explicit polynomial bound on the required number of iterations in terms of the sample size, feature dimension, feature range, and structural properties of the constraint matrix—thereby overcoming the prior reliance on unknown geometric constants. Leveraging fundamental quantities such as the Lipschitz continuity of the loss function and the diameter of the weight set, the study establishes a theoretically transparent and practically informative upper bound on the iterations needed to attain exact consistency.

Integer Linear Programming (ILP) suffers from low computational efficiency on conventional CPUs and GPUs due to its inherent sparsity and strong branching behavior, making it ill-suited for real-time decision-making. This work proposes SPARK, a near-cache accelerator integrated alongside the CPU L1 cache, which for the first time co-designs sparsity awareness, computation reuse, and near-cache architecture, incurring only 1.4% area overhead. By leveraging sparse pattern detection, reuse-aware scheduling, and a low-power data path, SPARK efficiently supports both sparse and dense ILP as well as Linear Programming (LP) problems. Evaluated on the MIPLIB 2017 benchmark suite, SPARK achieves 15–20× speedup over a Zen3 CPU and an NVIDIA V100 GPU for sparse ILP instances, with energy efficiency improvements ranging from 152× to 740×.

This study addresses the problem of minimizing makespan on a fixed number of parallel machines. It introduces, for the first time, an efficient approach based on short integer linear programming (Short ILP) to design a quasipolynomial-time algorithm. When the maximum processing time $p_{\text{max}}$ is moderate, the algorithm achieves a running time of either $\widetilde{O}(p_{\text{max}}^{O(1)} + n)$ or $\widetilde{O}(p_{\text{max}}^{O(1)} \cdot n)$, significantly outperforming existing methods. This work not only extends the applicability of Short ILP techniques to scheduling problems but also provides a more efficient solution pathway for instances of moderate scale.

This work addresses mixed-integer linear programming (MILP) and stochastic optimization problems by proposing a probabilistic solution framework grounded in the Boltzmann distribution. The original problem is reformulated as a Monte Carlo optimization task—sampling from truncated multivariate exponential and Gaussian distributions over the feasible constraint set—and solved efficiently via the Kent–Davis sampling algorithm. Unlike conventional deterministic solvers, this approach avoids strong structural assumptions on the problem, thereby enhancing scalability and stochastic exploration capability. Experiments on portfolio optimization and the canonical stochastic farmer problem demonstrate that the method achieves solution quality comparable to state-of-the-art commercial solvers (e.g., Gurobi) on medium-scale instances, while exhibiting superior robustness to high-dimensional, non-convex, or black-box constraints. The framework introduces a novel probabilistic modeling and optimization paradigm for MILP, bridging statistical sampling theory with discrete and stochastic decision-making.

This study addresses the problem of extracting an optimal subplan from an existing plan under a budget constraint, while preserving the original actions and their execution order. The goal is to identify a subplan that respects a given cost upper bound, remains executable, and maximizes utility. The decision variant of this problem is proven to be NP-complete. To tackle it, the authors propose a refined integer linear programming (ILP) formulation that significantly reduces model size and enhances computational efficiency without sacrificing solution accuracy. Together with over-subscription planning (OSP), this ILP approach constitutes one of two exact solution methods. Compared to prior work, the proposed ILP method demonstrates marked improvements in both scalability and empirical performance.