💎 Hidden gems in the solver world

🛠 In recent years, I have observed new products emerging in the mathematical solvers market. I am inspired by those who choose to create new products and establish a company and/or a brand from the ground up.

🏹 Having more of this innovation in the optimization space will increase the visibility of optimization and help maintain affordable prices.

1️⃣ HiGHS is a general purpose solver for LP, MIP and QP

HiGHS is based on solvers written by PhD students from the Optimization and Operational Research Group in the School of Mathematics at University of Edinburgh.

HiGHS is being developed very actively, with a new interior point solver and major improvements to the MIP solver in the pipeline, and its research software engineer is employed full-time by the university.

✅ Performance-wise, in general (based on the Mittelmann benchmarks) it's the best open-source linear optimization software, particularly for medium/large-scale MIP.

✅ It provides the default LP and MIP solvers in SciPy and MATLAB, has interfaces to C++, C, Python, Rust, C#, Julia, Javascript, Fortran and R, and can be used via modelling languages such as AMPL, GAMS, JuMP, Pyomo, PuLP and MathOpt (OR-Tools).

🚫 Documentation, add-ons like lazy constraints, and user-defined cuts and branching strategies.

2️⃣ Quantagonia solves LP, MIP, QUBO, scheduling, vehicle routing

They are combining LLM with their in-house built solver. Users can model and incorporate constraints without needing advanced math programming expertise.

✅ The solver closely matches the performance of the commercial solvers for LP & MIP (Gurobi etc.).

✅ A seamless experience with the friendly user interface.

✅ Start testing immediately for free without speaking to a sales representative.

✅ Access top-tier optimization capabilities at a fraction of the cost.

🚫 While the cloud-only availability this enhances accessibility and ease of use, it may not align with organizations requiring on-premises solutions.

🚫 Currently, non-convex optimization features are limited but are scheduled for inclusion in future updates.

3️⃣ Timefold solves field service routing, last mile routing, employee shift scheduling, job shop scheduling, task assignment, etc.

No math needed: Timefold Solver is the open source solver for software developers, with support OOP, FP, unit testing, integration and containers.

✅ Can handle complex constraints and objectives, such as fairness, lunch breaks, priorities, multi-resource visit, etc.

✅ Scales well to very large datasets

✅ Open source Solver (Apache License)

✅ Constraints as code in Java, Python or Kotlin with unit testing support

✅ Quickstarts code on GitHub and complete documentation.

🚫 Requires installing a JVM

🚫 Doesn’t always handle small problems ideally (work in progress)

🔷 InsideOpt’s Seeker solves, among others, inventory optimization, pricing, time tabling, network design, production scheduling, sports scheduling, fleet assignment, train yarding etc.

Seeker is a general purpose solver. It is hyper-parameterized. You can tune the solver exactly for the problem instances that you are facing, without having to do it manually, but by using InsideOpt tuning technology. You get a massive customization performance booster without hands-on work.

✅ Models are easier and intutive to setup up and change. Native support for non-linear, non-convex, non-differentiable, non-hierarchical multi-objective, and stochastic problems.

✅ You get better feasible solutions faster in many cases than with MIP tech. Ability to run distributed on as many cores as desired. Ability to add more cores during optimization. Crash resilience if individual pods crash. Ability to pick up optimization from where it stopped after hardware crashes.

✅ Solutions still work well even if futures turn out slightly differently than expected. More realistic models mean plans that execute better.

🚫 No dual bounds (not needed during deployment, only during development).

🔷 SAS Optimization is a set of solvers + algebraic modeling language + ModelOps deployment + open source integration.

It solves LP, MIP, QP, NLP, CLP and Conic type of problems.

They have
(1) built-in metaheuristics for feasible, and exact solutions for CVRP and VRPTW
(2) automated Benders and Dantzig-Wolfe decomposition for large LP and MIP (3) built-in, seamless distributed processing (see: the cofor{ } loop and groupby() statements)
(4) backward compatibility and version control throughout previous releases.

✅ One of the fastest solvers for large scale LP and MIP problems

✅ Robust algebraic modelling language with the syntax similar to AMPL

✅ Open source integration of solvers into Pyomo and PuLP, in addition to Python API (sasoptpy)

✅ Robust and scalable network algorithms available through the network solver (e.g., TSP, VRP, VRPTW, MST, min cut, shortest paths, cycle detection, etc.)

🚫 Expensive for commercial use
🚫 Unknown to many who still think SAS is only for statistics and machine learning applications


🔷 Worth mentioning is Hexaly, focused on non-linear problems. Their example tour on the website is a great place to check out the type of problems and already start practicing the formulation of various non-linear problems.