Exploring the next generation of AI-empowered LP and MILP Optimizers using Agentic systems
Linear Programming (LP) and Mixed-Integer Linear Programming (MILP)
This notebook demonstrates two real-world optimization problems:
LP Problem: Diet Optimization (continuous variables)
MILP Problem: Facility Location (mixed integer/continuous variables)
NOTE: MOST OF THIS CODE WAS GENERATED BY CLAUDE CODE - NOV 2025
- Gurobi Optimizer One of the most powerful and widely-used commercial solvers, known for exceptional performance on large-scale problems. Offers parallel processing, excellent presolve techniques, and strong community support. Popular in industry and academia.
- CPLEX (IBM ILOG CPLEX Optimization Studio) IBM's flagship solver with decades of development. Excellent for enterprise applications with robust integration capabilities, strong performance, and comprehensive documentation. Widely used in supply chain, logistics, and operations research.
- FICO Xpress Optimizer A high-performance solver with strong modeling capabilities through its Mosel language. Known for good performance on both LP and MILP problems, with particular strength in handling difficult integer programming problems.
- MOSEK Excels particularly at conic optimization but also offers strong MILP capabilities. Known for numerical stability and efficiency, especially on problems with special structure. Often used in finance and engineering applications.
- COPT (Cardinal Optimizer) A relatively newer entrant from Cardinal Operations, showing impressive performance benchmarks and competitive pricing. Has been gaining traction particularly in Asia and among users seeking alternatives to established solvers.
- HiGHS A modern, MIT-licensed solver developed at the University of Edinburgh. Offers surprisingly competitive performance with commercial solvers, particularly on LP problems, with rapidly improving MILP capabilities. Written in C++ with interfaces for multiple languages.
- SCIP (Solving Constraint Integer Programs) One of the most comprehensive non-commercial solvers, distributed under Apache 2.0 license. Offers a flexible framework for branch-cut-and-price, with strong academic backing from Zuse Institute Berlin. Highly extensible for research.
- GLPK (GNU Linear Programming Kit) The veteran of open source optimization, widely used for educational purposes and smaller applications. While not competitive with commercial solvers on large problems, it's reliable, well-documented, and has minimal dependencies.
- CBC (COIN-OR Branch and Cut) Part of the COIN-OR project, this EPL-licensed solver is widely used in open source optimization stacks. Good performance for many practical problems and integrates well with other COIN-OR tools. Actively maintained.
- SYMPHONY Also part of COIN-OR, designed for solving large-scale MILP problems in parallel computing environments. Good for customization and research applications where you need access to the solution process internals.
Commercial solvers (Gurobi, CPLEX, Xpress) generally offer superior performance on large, difficult problems and provide professional support, but come with licensing costs. Open source options like HiGHS and SCIP have closed the gap significantly in recent years and are excellent choices for many applications, especially if budget is a constraint or if you need to embed a solver in open source software. OK! LET'S TEST & EXPLORE - using Open Source HiGHS for: (1) LP Problem: Diet Optimization (continuous variables) (2) MILP Problem: Facility Location (mixed integer/continuous variables)