arXiv:2608. 13079v1 Announce Type: new Abstract: This paper proposes a novel learning-based approach to approximately solve instances of mixed-integer optimization problems.
arXiv:2609. 22752v1 Announce Type: new Abstract: Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples.
The paper introduces Penalty + Sequential Linearized Feasibility Seeking (SLFS), a self‑supervised learning framework for solving multiphase AC optimal power flow (AC‑OPF) in distribution systems with topology reconfiguration. SLFS trains directly from the AC‑OPF objective and constraints using a differentiable fixed‑point power flow solver, avoiding the need for labeled optimal solutions. It achieves negligible optimality gaps and near‑zero constraint violations on IEEE feeders up to 8,500 nodes, delivering up to three orders of magnitude speedups over IPOPT while maintaining robustness to large distributional shifts.
arXiv:2607. 22550v1 Announce Type: cross Abstract: We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs.
The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.
arXiv:2609.25728v1 Announce Type: new Abstract: Self-supervised learning for combinatorial optimization has emerged as a promising paradigm for solving discrete optimization problems with neural netw...
arXiv:2606. 17192v1 Announce Type: new Abstract: This paper develops constrained diffusion models with primal-dual inference (PDI) to sample from optimal distributions of entropy-regularized optimization problems with \emph{average} constraints.
arXiv:2607. 22788v1 Announce Type: cross Abstract: AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations.
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
arXiv:2605. 30920v2 Announce Type: replace Abstract: Diffusion-based neural solvers have shown strong promise for combinatorial optimization (CO), but existing methods typically rely on supervised training with large collections of near-optimal solutions.
arXiv:2608. 02343v1 Announce Type: cross Abstract: Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints.
arXiv:2505. 04757v2 Announce Type: replace Abstract: This paper introduces a novel approach to contextual stochastic optimization, integrating operations research and machine learning to address decision-making under uncertainty.
arXiv:2608. 07040v1 Announce Type: new Abstract: Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations.