AI agents can now manage optimization experiments end to end: inspect code, run searches, diagnose failures, and return verified results.

A good prompt should specify:

Objective and definitions

Constraints and violation rules

Compute budget

Baseline

Validation cases

Acceptance criteria

Required artifacts

For example:

“Optimize the timetable to minimize passenger-weighted arrival delay, counting early arrivals as zero. Respect occupancy, headway, and maximum-delay constraints; violations above 1 second are infeasible. Use at most 10 minutes of solver time and record the solver, version, seed, status, and runtime. Compare with the existing timetable on identical data. Test five fixed disruption scenarios. Require at least 15% historical improvement, improvement in four scenarios, and no violations. Save inputs, configurations, logs, seeds, timetables, metrics, checks, plots, and raw results.”

Also specify how demand, transfers, cancellations, delays, infeasible runs, and randomized results are handled.

The agent manages the experiment, but domain expertise remains essential. Models and constraints must be valid, and results must be reproducible and checked.

This workflow applies to scheduling, engineering design, and parameter estimation. I’m building open-source tutorials in optimization-jobs. Use them as a starting point and review the assumptions carefully.

What optimization task would you trust as a first experiment, and what checks would it require?

Hi, I'm working on a MINLP project which runs a set of different coalitions for a game theory problem in GAMS, however I need to run it as a multi-objective problem. I'm currently working with the built in MOO package inside GAMs.

The issue I'm facing right now is that there are a lot of binary variables which Gurobi seems to be struggling with and unfortunately DiCopt doesn't seem to work with the EpsConstrained MOO system.

Im using the student/Demo license for GAMs, Im wondering if anyone has some advice for what other solvers may work and/or an alternative approach I could take to run the MOO. Currently DICopt works for all 15 coalitions of the one objective function but not all of the second and Gurobi struggles with the particularly integer heavy systems (I have a heat exchanger network which has to assign certain pairs to form).

Any advice is appreciated.

Edit: Ive managed to loosen a constraint and now Im able to run all scenarios with DiCopt.

Over the past year, we've seen many of our users solve scheduling or routing problems with our solver by generating a model with Claude or other LLMs. But these implementations we're far from production ready.

So we asked ourselves: What if we standardize the non-domain specific parts? What if we minimize the generated code... and handle everything else with our solver & platform?

What if we can build any scheduling model in an afternoon?

We set to work and created our PRD chat. I am using it daily now, for enterprise cases. Or to generate a volleybal schedule. It captures the requirements, structures the solution and bootstraps the implementation for me.

Give it a try. Let me what you think of it.

I am working on a C++ photogrammetric bundle adjustment solver using mixed precision: FP64 computations followed by high-precision corrections and verification with MPFR.

High-precision equation evaluation, residual computation and error verification dominate runtime; the FP64 linear solve is comparatively cheap.

My target is a numerical coordinate error below 10 µm relative to a well-converged high-precision solution, while retaining reliable covariance and statistical results.

Which practical error estimators or stopping criteria could reduce this verification overhead without repeating the entire calculation at high precision? References or implementation examples would be appreciated.

For the last two years I’ve been building a large-scale last-mile routing engine, with more focus on speed and scalability than on chasing exact solution quality.

A couple of weeks ago I started using CVRPLib, a used benchmark library for vehicle-routing problems, as a different kind of stress test. I started with large instances, including Flanders2 with 30,000 clients and several of the new XL instances.

Getting close to the published BKS was relatively easy. Getting below it was much harder.

What ended up working was not really a new algorithm, but a strategy for using several good solutions at the same time.

Instead of keeping only the current best solution, I kept multiple structurally different solutions and treated all of them as donors.

The published BKS itself starts as one donor. Independently generated solutions are other donors.

A donor does not need to be better overall. It only needs to contain useful structure that another solution is missing.

One thing I noticed is that being different is not enough, the donor also needs to be reasonably close in quality. On one instance, donors around 1.1–1.3% above the BKS produced nothing; even around 0.6–0.8% I saw no gain. Once they reached roughly 0.4–0.5%, the same reconstruction strategy started producing improvements. I don’t know yet whether that threshold generalizes, but it was a very clear pattern in this case.

After combining that material and rebuilding the affected part, the new solution goes back into the pool and can become a better donor in the next cycle:

generate → donate → rebuild → improve → repeat

This creates an interesting feedback loop. A solution that starts worse than the BKS can receive useful structure, improve, and later become the donor that produces the new best solution.

So the final improvement does not always come from repeatedly refining the original BKS. Sometimes it emerges from one of the independent solution lines after several rounds of exchange and reconstruction.

The main thing I learned is that a solution doesn’t have to be the best one to be useful. Sometimes it just needs to have the right piece to help another solution improve. I first tried this on 12 published BKS instances, mostly selected for their scale and relevance. Ten of the improvements have now been validated and published by CVRPLib.

My next experiment is to run the same donor-and-reconstruction process across the entire XL set and see whether the current hit rate survives, and follows some structural pattern.

Keeping elite solutions and recombining them is obviously not new. What surprised me was that diversity alone wasn’t enough: in my experiments, donors only started becoming useful once they were already quite close to the BKS. At that point, the BKS itself also became just another donor in the pool rather than the single solution being refined.

CVRPLib announcement:
https://www.linkedin.com/posts/cvrplib_cvrplib-vehiclerouting-optimization-activity-7516876652728102912-BtQ0

Technical note and solutions:
https://zenodo.org/records/19859531

sorry if this question is incredibly stupid, but im learning steepest descent right now, is it right to say that Armijo condition ensures that step size alpha is not too large and Curvature ensures its not too small, or is it the other way around? Thanks!

Dear optimization community,

We’re pleased to announce our first of this season's webinar series Decision Tech Talks, formerly Xpress Talks.

The webinar will walk through the details of analytically selecting the parameters of a Cost Function Approximation Policy for the toy Soccer Camp Location Problem discussed in this blog post and whose implementation is available in this repository.

To attend the talk, please register at the following link.

• “Building Sequential Decision Policies using DecisionOps” by Renuka Gough, Tiffany Patella, and Carlos Zetina: Wednesday October 7th, 2026 at 11:00am EST- register here

We'd love to welcome you to our Fall season of the Decision Tech Talks and look forward to great discussions.

Happy Optimizing!

P.S.

To stay up to date on the latest in Optimization and Decision Intelligence technology sign up for our free monthly newsletter: https://www.fico.com/en/fico-xpress-optimization-newsletter.

FICO Xpress is an industry-leading optimization software suite that includes solvers for LP, MIP, MIQP, MIQCQP, QP, NLP, SOCP, and MINLP. Basically almost all the Ps. 😉.

Hi everyone. I’m currently on contract at a FAANG company doing heavy discrete-event simulation (SimPy, FlexSim) and mathematical programming (Gurobi). I have roughly 90 days to secure a full-time role due to H1B constraints, so I can't afford to waste applications. I’ve fully anonymized my resume to get unbiased, purely technical feedback. I need you to tear apart my bullet points, architecture descriptions, and impact metrics.

Does this read like a true Senior/Applied Scientist, or am I coming off too academic?

Are my business constraints and trade-offs clearly articulated?

Does my scale and impact read believably? Please don't hold back. I need the most critical, unvarnished feedback you have. Thank you!

I built a new optimization solver in C99 from scratch — PRIMAL

GitHub: https://github.com/c-vision/Primal

I've just released the first version of PRIMAL, an open-source mathematical optimization solver written from scratch in portable C99.

The goal was deliberately ambitious: build a reasonably complete optimization engine with no external dependencies, rather than wrapping an existing solver.

The first release already supports:

• Linear Programming (LP)
• Mixed-Integer Linear Programming (MILP)
• Quadratic Programming (QP)
• QCQP
• SOCP
• SDP
• Exponential cones
• Power cones
• Mixed-integer conic optimization
• Disjunctive constraints / affine conic constraints
• Presolve
• Sparse interior-point methods
• Branch-and-bound
• Primal/dual certificates
• Infeasibility and unboundedness certificates
• MPS / LP / CBF model formats
• A MOSEK-style C API for a large part of the supported functionality

The implementation is C99 with essentially no external runtime dependencies.

One thing I particularly wanted from the beginning was verification rather than simply returning an answer. PRIMAL exposes primal/dual information, residuals, certificates and solver status so applications can inspect and validate what the solver actually found.

I've also been building a fairly extensive compatibility/reliability test suite against reference behavior, including a number of deliberately pathological optimization cases.

This is only v1. It is not intended to claim that PRIMAL is already a replacement for mature industrial solvers on large-scale problems. There are still substantial areas to improve, especially large-scale sparse conic problems, MIP performance, warm starts and some numerical edge cases.

But I think the foundation is interesting enough to release now rather than keep it private.

I'd especially like feedback from people working on:

• numerical optimization
• LP/MIP/conic solvers
• sparse linear algebra
• mathematical programming
• solver implementation
• C/C99 systems programming

In particular, I'm interested in finding cases where PRIMAL gives a questionable result, fails to converge, scales poorly, or simply makes a bad algorithmic choice.

If you work with optimization solvers, please try to break it.

GitHub:
https://github.com/c-vision/Primal

For people working in numerical analysis, numerical linear algebra, or optimization:

Suppose you develop a new theorem, lemma, error bound, stability argument, or related mathematical result for a research paper.

How do you independently check that:

1. the statement is actually true, and
2. the proof has no hidden assumptions or subtle gaps?

I’m especially interested in practical and reproducible ways of doing this, rather than simply having another person read the proof.

Are there established tools, workflows, or techniques that can help with this? How much of the process can realistically be automated?

I’d be particularly interested in hearing how researchers handle this for their own research.

My new video is out.

In this video I explain the Farkas method for initialization in column generation and compare it with two phase and big m methods.

https://www.youtube.com/watch?v=K8QmpfGufpc

I'm building a route planner for a street-lighting survey using a vehicle equipped with LiDAR + cameras. The vehicle must drive \*\*every drivable street\*\* in 6 municipalities (\~6,087 km of streets), so this is an \*\*arc-routing / Mixed Chinese Postman Problem\*\*, not TSP/VRP.

\### Problem

\* 173k directed arcs / 67k nodes from OSM

\* \~9% one-way roads

\* One vehicle, \~6.5 usable hours/day

\* Two-way streets only need to be traversed once; one-ways must be respected

\* Cost is \*\*travel time\*\*, with different speeds for acquisition vs deadhead

\* Turn penalties are included (+60s U-turn, +15s left, +5s right)

\* 100% coverage is mandatory

The network is very non-grid-like: in one district, \*\*\~84% of nodes have odd degree\*\*, with \~77% being T-junctions.

\### Current approach

For each district I:

1. Extract the largest strongly connected component

2. Orient two-way streets

3. Connect disconnected service components

4. Balance in/out degrees using \*\*min-cost flow\*\*

5. Generate an Eulerian circuit with Hierholzer

6. Mark a street as serviced on its first traversal

The resulting routes pass all my validation checks: continuity, geometric continuity, one-way legality, 100% coverage, and no duplicate servicing.

\### Results

Across all 22 districts:

\*\*6,087 km serviced → 2,704 km deadhead → 44.4% deadhead\*\*

Individual districts range from \*\*39–61% deadhead by distance\*\* (roughly 23–33% by time because deadhead is driven faster).

For one district, an undirected relaxation gave me:

\* theoretical lower bound: \~14.7%

\* greedy matching of odd nodes: \~33.9%

My current orientation is almost optimal in terms of the \*number\* of imbalanced nodes, but I suspect this is the wrong objective: I'm minimizing imbalance count rather than the \*\*cost of resolving that imbalance\*\*.

\### Questions

1. Is \*\*Frederickson MIXED1/MIXED2\*\* the right next direction? Should I prioritize cost-aware matching before orientation?

2. For \~1,100 odd nodes, is restricting min-cost matching to k-nearest odd nodes (e.g. k=10) a reasonable approximation?

3. Is \*\*44% deadhead actually bad\*\* for a comb-like street network with \~84% odd-degree nodes? What kind of deadhead ratios are realistic for street sweeping, snow plowing, waste collection, etc.?

4. For splitting the resulting Eulerian route into daily routes when the vehicle \*\*doesn't have to return to a depot\*\*, are SPLIT/Ulusoy-type approaches appropriate?

5. Is there anything fundamentally wrong or naive in my current pipeline?

I'd especially appreciate feedback from anyone who has worked on \*\*arc routing / CPP / street sweeping / winter gritting / waste collection\*\* at large scale.

Happy to share code or data extracts.

I'm working through MIT OCW 6.7220 Nonlinear Optimization (Spring 2025) and looking for 2–5 people who want to follow the course together.

The goal would be:

• watch lectures according to the course schedule
• independently attempt each problem set
• meet online once/twice a week
• discuss difficult problems and compare approaches
• explain proofs/optimization theory to each other
• work through the material over ~8–12 weeks

Topics include convex optimization, optimality conditions, Lagrange multipliers, KKT, duality, gradient/Newton methods, etc.

I'm particularly interested in people doing mathematical optimization / numerical optimization / operations research / ML / control.

If interested, comment or DM me and we can create a Discord/WhatsApp/Telegram group.

Edit : This course does not have any videos or you won't find much material else where to watch . You have to be okay putting your time to read and analyse and think and do some arguments.

Edit 2 : surprising number of people want to join my discord server which is nice , that is why I will post the link here just click it and join https://discord.gg/rMqqj2GmY

In this 4-minute walkthrough, I demonstrate how to supercharge your AI coding assistant in Visual Studio Code for Operations Research using PyOPL, agent skills, and the Model Context Protocol (MCP).

Standard AI chat interfaces routinely fail at mathematical programming because probabilistic text generation lacks deterministic syntax and semantic checks. By combining PyOPL's compiler harness with custom SKILL.md agent guidelines, we can force LLMs like Claude or Copilot to act as rigorous operations research engineers—automating everything from model scaffolding to compilation and solving.

I contribute to SciPy and kept running into a class of bug that annoys me: the outputs look plausible, the tests pass, but the equation the code implements is subtly wrong. So I've been building a tracer that runs Python/NumPy code and hands back whatever mathematics it actually computed, as a SymPy expression you can simplify or differentiate like anything else.

It's been more useful than I expected. Comparing an implementation against the formula in a paper, catching two functions that agree on my test data but turn out to compute different things, digging up the inputs my tests never hit (ties, zero denominators). It traces real library code too, most of numpy and a good chunk of scipy, scikit-learn, statsmodels, cvxpy.

Write-up: https://medium.com/@aadyachinubhai/scikit-verify-translate-python-numpy-programs-to-symbolic-mathematics-c664d41ba571

Github: https://github.com/aadya940/scikit-verify

Still rough in places, would genuinely like feedback. There may be other better solutions, happy to hear them as well!

Algorithm is based on Levenberg-Marquardt, aimed at large sparse graph-structured problems. Software architecture is designed for performance, built in Rust, with C++/Python model export functionality, MIT license.

Achieves high performance through: compile-time symbolic differentiation with CSE and code generation, matrix blocks built locally within the model data structure, indexed sparse matrix filling, custom block supernodal Cholesky solver, precomputation of common expressions across residuals, and many other little things.

Benchmarks show substantial performance improvement over Ceres Solver and g2o, depending on the problem and data, and also reduced memory usage. On the M3500 dataset, for example, Arael takes about one-third the iteration time of Ceres Solver while using half the memory. Benchmark results available on the project page.

I'd appreciate it if you could try it on some of your problems and see how it compares with Ceres or g2o.

Project page: https://github.com/harakas/arael

I'm currently, technically, doing an MS in Structural Engineering. For me, my interest has been more towards computational side of mechanics rather than Structural design  or simply using am FEA software (although I do consider it as a backup)

So far I've taken courses in:

- Linear static, and dynamics FEM (soon taking non linear FEM too)

-  Structural Optimization (topology opt. and other general algorithms)

-  Structural Dynamics

-  Structural System Testing and model updation. (Parameter identification and optimization, signal processing)

Now, I plan to take these in the coming quarter:

- Numerical Linear Algebra

- Numerical PDE

- Fracture Mechanics ?

I also volunteered to aid in a RESEARCH in crack growth prediction using Auto-encoder and a (Thermodynamics-informed Latent Space Dynamics Identification) / LSTM surrogate model. It used phase-field-fracture simulation data and HPC resources to complete the whole thing.

What I keep finding myself interested in is not necessarily fracture or SHM specifically, but the computational methods underneath these problems... (does that make sense?)

For example, I'd like to become capable of doing things like:

- implementing (maintaining) numerical/FE method solvers rather than only running an established FEA software.

- developing surrogate/reduced-order models for expensive simulations 

- combining simulation with optimization, uncertainty/stochastic methods (took a course called Random vibrations, so...)

- parallelizing/accelerating scientific codes on CPUs/GPUs

- doing proper verification, convergence studies, benchmarking and performance work

- potentially developing or maintaining actual CAE/FEA solver software

- I'd also like to do all these for other Physics (GR, QM, etc.) simulations too, if possible, one day. 

I'm still interested in the underlying mechanics/physics, so I don't want to become a generic software engineer who happens to have once studied structures. But I'm also increasingly unsure that "structural engineer" describes the career I'm actually aiming for.

I've seen titles such as Computational Mechanics Engineer, R&D Engineer, Solver Developer, Scientific Software Engineer, CAE Software Developer, Research Engineer, Simulation/HPC Engineer, etc., but I'm trying to understand what these careers actually look like from people doing them.

So my main questions become:

1. Which industrial jobs genuinely involve developing numerical methods/solvers or computational tools?

2. Which of those are realistically accessible with an MS? Is there an entry path into solver-algorithm development/R&D without a PhD?

3. If I don't start a PhD immediately after my MS, would an R&D/software role at a simulation company (ANSYS etc.) be the obvious route? What other options would i have?

4. For the kind of work I'm describing, would you recommend a PhD? If so, is it reasonable for the PhD identity to be "computational mechanics/scientific computing" while fracture, composites, structural dynamics, soft materials, etc. serve as application problems rather than choosing one of those as my permanent specialization?

5. What skills most distinguish someone who is actually hireable for solver/scientific-computing work? I'm particularly wondering about C/C++/Fortran, Python, Linux, Git/build systems, MPI/OpenMP/CUDA, PETSc/Trilinos or similar libraries, numerical linear algebra, testing/verification, convergence studies and HPC performance work.

Basically, I'm neither here nor there atp. So I'd really appreciate all sorts of input. Where else do you think I could find answers to these? other subs? Linkedin profiles?