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Complement Submodular Information Measures for Balanced and Robust Data Selection On The Morse Ensemble Polynomial Of Simplicial Complexes A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations
TriVAL: A Tri-Validation Framework for Faithful Automatic...
Ziyang Fang, JinXi Wang, Jinghui Zhong, Yew-Soon Ong · 2026-05-13 · via math.CO updates on arXiv.org

Optimization modeling serves as the pivotal bridge between natural-language problem descriptions and optimization solvers, and remains a cornerstone for bringing operations research (OR) into real-world decision making. Recent advances in large language models (LLMs) have driven significant progress in automatic optimization modeling. However, existing methods still lack explicit validation during the modeling process, allowing errors introduced in earlier stages to carry through the pipeline and ultimately reduce final modeling accuracy. To address this challenge, we introduce TriVAL, a tri-validation framework that performs explicit validation at three stages of automatic optimization modeling: semantic specification, mathematical formulation, and code generation. At each stage, TriVAL follows a construct-validate-revise loop that assesses the current result against stage-specific criteria and revises it when needed. This design helps identify and correct errors before they accumulate across stages, helping preserve faithfulness throughout the modeling process. To evaluate automatic optimization modeling on more challenging combinatorial problems, we further introduce NL4COP, a benchmark of 150 instances across 50 diverse problem types with more complex decision logic, more tightly coupled constraints, and more demanding modeling requirements than existing benchmarks. Experiments on NL4COP and established benchmarks show that TriVAL consistently outperforms state-ofthe-art methods, with the largest gains on the most challenging problems.