2 présentations

• 
  13h00 - 13h22

  MathOptAI.jl: Embedding trained machine learning surrogates in JuMP models

  • Robert Parker, prés., Los Alamos National Laboratory
  • Oscar Dowson, Dowson Farms

  A natural approach to combine optimization and machine learning is to replace a difficult-to-model process with a machine learning surrogate then optimize over the trained model for future decision-making. To avoid the error-prone work of translating a trained machine learning model into a solver or modeling language's API, software packages such as OMLT and gurobi-machinelearning have been developed to incorporate trained surrogate models into the Pyomo and GurobiPy modeling frameworks. In this talk, we present MathOptAI.jl, a software package for embedding trained surrogates into JuMP optimization models. We highlight the design decisions that differentiate MathOptAI.jl from similar packages and present benchmarks comparing different formulations of a neural network surrogate in nonlinear optimization problems.

• 
  13h22 - 13h44

  Neural Embedded Mixed-Integer Optimization for Location-Routing Problems

  • Waquar Kaleem, Pennsylvania State University
  • Anirudh Subramanyam, prés., Pennsylvania State University

  We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical yet NP-hard problem that integrates strategic facility location with operational vehicle routing decisions, aiming to simultaneously minimize both fixed and variable costs. The proposed method first trains a permutationally invariant neural network that approximates the vehicle routing cost for serving any arbitrary subset of customers by any candidate facility. The trained neural network is then used as a surrogate within a mixed-integer optimization problem, which is reformulated and solved using off-the-shelf solvers. The framework is simple, scalable, and requires no routing-specific knowledge or parameter tuning. Computational experiments on large-scale benchmark instances confirm the effectiveness of our approach. Using only 10,000 training samples generated by an off-the-shelf vehicle routing heuristic and a one-time training cost of approximately 2 wall-clock hours, the method provides location-allocation decisions that are within 1% of the best-known solutions for large problems in less than 5 seconds on average. The findings suggest that the neural-embedded framework can be a viable method for tackling integrated location and routing problems at scale. Our code and data are publicly available.