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OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling

Maxime Bouscary, Saurabh Amin

TL;DR

OptiHive introduces a two-stage, batched LLM-based optimization framework that first generates and filters interpretable solver/instance/test components via an ILP, then uses an EM-based latent-class model to quantify true performance and calibrate solver selection under uncertainty. By treating solvers, instances, and tests as noisy contributors and leveraging a probabilistic ensemble, it achieves large gains in feasibility and optimality on complex MDVRP variants and WSCP benchmarks with minimal added latency. The approach eliminates iterative self-correction loops and provides principled uncertainty-aware solver ranking, enabling robust, low-latency deployment around existing solver-generation pipelines. The work demonstrates that high-quality solvers can be recovered from imperfect components, particularly when instance and test signals are diverse and informative, highlighting practical impact for scalable, NL-to-optimization workflows.

Abstract

LLM-based solvers have emerged as a promising means of automating problem modeling and solving. However, they remain unreliable and often depend on iterative repair loops that result in significant latency. We introduce OptiHive, a framework that enhances any solver-generation pipeline to produce higher-quality solvers from natural-language descriptions of optimization problems. OptiHive uses a single batched generation to produce diverse components (solvers, problem instances, and validation tests) and filters out erroneous components to ensure fully interpretable outputs. Accounting for the imperfection of the generated components, we employ a statistical model to infer their true performance, enabling principled uncertainty quantification and solver selection. On tasks ranging from traditional optimization problems to challenging variants of the Multi-Depot Vehicle Routing Problem, OptiHive significantly outperforms baselines, increasing the optimality rate from 5% to 92% on the most complex problems.

OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling

TL;DR

OptiHive introduces a two-stage, batched LLM-based optimization framework that first generates and filters interpretable solver/instance/test components via an ILP, then uses an EM-based latent-class model to quantify true performance and calibrate solver selection under uncertainty. By treating solvers, instances, and tests as noisy contributors and leveraging a probabilistic ensemble, it achieves large gains in feasibility and optimality on complex MDVRP variants and WSCP benchmarks with minimal added latency. The approach eliminates iterative self-correction loops and provides principled uncertainty-aware solver ranking, enabling robust, low-latency deployment around existing solver-generation pipelines. The work demonstrates that high-quality solvers can be recovered from imperfect components, particularly when instance and test signals are diverse and informative, highlighting practical impact for scalable, NL-to-optimization workflows.

Abstract

LLM-based solvers have emerged as a promising means of automating problem modeling and solving. However, they remain unreliable and often depend on iterative repair loops that result in significant latency. We introduce OptiHive, a framework that enhances any solver-generation pipeline to produce higher-quality solvers from natural-language descriptions of optimization problems. OptiHive uses a single batched generation to produce diverse components (solvers, problem instances, and validation tests) and filters out erroneous components to ensure fully interpretable outputs. Accounting for the imperfection of the generated components, we employ a statistical model to infer their true performance, enabling principled uncertainty quantification and solver selection. On tasks ranging from traditional optimization problems to challenging variants of the Multi-Depot Vehicle Routing Problem, OptiHive significantly outperforms baselines, increasing the optimality rate from 5% to 92% on the most complex problems.

Paper Structure

This paper contains 23 sections, 27 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Generation of Valid Components
  5. Batched Components Generation.
  6. Testing.
  7. Filtering.
  8. Solver Characterization and Selection
  9. Characterization.
  10. Selection.
  11. Experimental Results
  12. Experimental Setup
  13. Multi-Depot Vehicle Routing Problems
  14. Weighted Set Cover Problem
  15. Conclusion
  16. ...and 8 more sections

Figures (2)

  • Figure 1: OptiHive produces optimization solvers through a two-stage process. In the first stage, it produces candidate solvers, problem instances, and tests, then filters out components to retain only fully interpretable solver-instance-test triples (represented as cubes). In the second stage, it applies latent class analysis to estimate the performance of each solver and selects the most promising candidate. Red, yellow, and green bubbles denote solvers that return non-interpretable or infeasible, feasible but suboptimal, and optimal solutions, respectively.
  • Figure 2: Feasibility and optimality rates on DCMDVRP and MDVRP+OBS across varying numbers of generated solvers, instances, and tests. The purple curve shows the rate under perfect selection i.e. the probability that at least one of the generated solvers is optimal.