Questions tagged [solver]

For questions related to software designed to solve very general classes of optimization problems to guaranteed optimality.

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41 votes
3 answers
13k views

How to select a Constraint Programming Solver

I would like to clarify that I am absolutely not an expert when it comes to constraint programming (I happen to use it when it seems to be the right tool for the right job). It is my understanding ...
Renaud M.'s user avatar
  • 2,398
34 votes
6 answers
2k views

Where can I find open source LP solvers?

I'm familiar with COIN-OR and have also used a couple packages in R to solve LPs. Today I found out Google has their own open source optimization software, and it got me wondering what other open ...
Zohar Strinka's user avatar
31 votes
4 answers
3k views

"Best practices" for formulating MIPs

Often there are many alternatives ways for formulating a MIP. For example: The model contains inequality constraints that must hold with equality in an optimal solution. The model contains ...
Rolf van Lieshout's user avatar
30 votes
3 answers
2k views

Feeding known lower bounds to solvers

Given an optimization problem that aims at minimizing some objective function, a lower bound that is valid for all feasible solutions, and your solver of choice: For what theoretical and/or practical ...
fbahr's user avatar
  • 1,016
29 votes
4 answers
14k views

What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?

I come from an ML background, and occasionally have to dive into the OR world. I am trying to figure out whether I need to purchase a commercial solver license for a certain problem set. In the ML ...
Skander H.'s user avatar
  • 2,139
29 votes
5 answers
12k views

Which GPUs to get for Mathematical Optimization (if any)?

The Machine Learning community has largely benefited from modern GPUs and several large companies are investing in new dedicated hardware. Unfortunately, academic and commercial mathematical ...
Stefano Gualandi's user avatar
26 votes
4 answers
1k views

Stochastic programming MIP solvers

I am aware that Benders Decomposition is readily available in CPLEX and in SCIP; but are there any (free) solvers that provide off the shelf stochastic programming MIP algorithms or a nice to work ...
Albert Schrotenboer's user avatar
23 votes
4 answers
5k views

What instances can be solved today by modern solvers (pure LP)?

I have found a PowerPoint presentation in which the presentor Hall claims instances could be of the size of 108 in variables and constraints to be solved today. I assume that he meant sparse problems. ...
Gehhilfe's user avatar
  • 443
20 votes
7 answers
3k views

Is there a Linear Programming Library that natively supports fractions instead of floating point arithmetic?

If one recalls how the Simplex method is taught by hand in most LP classes it takes place entirely in $\mathbb{Q}$. All operations yield exact fractions. For this reason I'm looking for linear ...
Sidharth Ghoshal's user avatar
20 votes
3 answers
2k views

Are valid inequalities worth the effort given modern solvers?

In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also ...
SecretAgentMan's user avatar
19 votes
6 answers
8k views

When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs

Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
AndyT's user avatar
  • 193
19 votes
4 answers
4k views

How to evaluate the performance of open source solver?

I am looking for a reliable open source solver to solve LP and MILP (with a few thousand variables). How can I evaluate the performance of a given solver for a particular use case?
Rajasekhar Kadambur's user avatar
19 votes
2 answers
857 views

How do we decide/plan an SLA for an NP-hard optimization process running in production?

How do you decide or plan an SLA (Service Level Agreement) for an application that depends on an optimization process when the problems you deal with are NP-hard? That is, if you are developing an ...
Skander H.'s user avatar
  • 2,139
17 votes
3 answers
3k views

How Close Is Linear Programming Class to What Solvers Actually Implement for Pivot Algorithms

As part of a final project for my linear programming course, I have been asked to discuss implementations of pivot algorithms, including which combinations of the ideas we have talked about in class ...
Sean Kelley's user avatar
17 votes
5 answers
723 views

Presolve is cutting down a lot of binary variables. Should I rethink my formulation?

I built my model on Python and am passing it to Gurobi to solve the problem. The presolve phase of Gurobi cuts down ~80% of the integer/binary variables and I am wondering if I should rethink my ...
Abhishiekh Ramesh's user avatar
14 votes
4 answers
959 views

How to progress with CPLEX/Gurobi

I've been learning and playing with CPLEX/Gurobi for a year using C++/Python API. I know some basic stuff like writing a model, callbacks, basic playing with solvers' parameters. I am wondering what ...
Antarctica's user avatar
  • 2,917
14 votes
4 answers
4k views

YALMIP-like modeling environment in Python

What are the handiest optimization parsers out there? Is COIN-OR's PyPy being used actively? I am currently trying to do an optimization project in Python, but I am used to using MATLAB + YALMIP ...
independentvariable's user avatar
14 votes
4 answers
940 views

Model conversion as fast as gurobipy and solved by open source solvers

Gurobipy is a fast solver and can convert a mathematical programming model to its underneath language very fast compared to some open source wrappers (e.g., PuLP, OR-tools, etc.). However, a ...
Yihe Zhuo's user avatar
  • 141
14 votes
4 answers
2k views

CPLEX non-convex Quadratic Programming algorithms

CPLEX solves non-convex quadratic problems to global optimality with a global optimality option (in version 12). The relevant pages are this and this. I benchmarked many solvers, and see that CPLEX ...
independentvariable's user avatar
14 votes
2 answers
235 views

Solver rounding precision vs programming language rounding precision

Often times I have this issue. For example, I need to have a non-negative coefficient, say $c_0$, in my optimization problem (otherwise the problem is not convex). Moreover, to obtain this $c_0$ I ...
independentvariable's user avatar
13 votes
3 answers
1k views

How could we simplify solving the large scale MIPs without using any advanced methods like decompositions?

Many practical optimization models (specially MIPs) are NP-Hard and solving them need much time even with the modern solvers like CPLEX or GUROBI. One of the best way (but not easy) is using ...
A.Omidi's user avatar
  • 8,717
13 votes
1 answer
1k views

Difference between lazy callbacks and using lazy constraints directly

I'm trying to use lazy constraints to solve an optimization problem. In some software such as CPLEX or GUROBI, they have some tools to handle them directly (in the original model) or using callback ...
A.Omidi's user avatar
  • 8,717
13 votes
2 answers
1k views

What is the difference between optimization software APIs based on performance and speed?

The state-of-art solvers like CPLEX or Gurobi and some of the open-source solvers have had the different APIs (like Python, C/C++, Java, etc.) in which users could write their MP model in own ...
A.Omidi's user avatar
  • 8,717
13 votes
1 answer
1k views

Sum of Max terms maximization

Maximizing sum-of-max terms is an NP-hard problem. The objective function is a convex function and maximizing a convex function is a hard problem. Also, this is a non-differentiable function. CPLEX ...
independentvariable's user avatar
13 votes
2 answers
991 views

How fair is limit solver threads when publishing?

Reading gurobi reference manual I found this: We have also found that certain classes of MIP models benefit from reducing the thread count, often all the way down to one thread. Starting multiple ...
seimetz's user avatar
  • 513
12 votes
4 answers
4k views

What do solvers like Gurobi and CPLEX do when they run into hard instances of MIP?

MIP is NP-Hard, so it is possible that an instance is very difficult and has multiple local minima that the search can get stuck in. With a Metaheuristic Algorithm, the stochastic and approximate ...
Skander H.'s user avatar
  • 2,139
12 votes
4 answers
3k views

Citing CPLEX 12.9

Simple question, but very hard to find an answer. How can I cite version 12.9 of CPLEX? Shall I cite the very first CPLEX and indicate that I am using the version 12.9 of this, or shall I cite the ...
independentvariable's user avatar
12 votes
2 answers
600 views

Dedicated solver for convex problems

Are you aware of a fast solver (open source or commercial) for convex NLPs that is faster than IPOPT? I'm interested in problems in the 50K+ variable range, both dense and sparse. Ideally, it would be ...
Nikos Kazazakis's user avatar
12 votes
3 answers
6k views

How to find all vertices of a polyhedron

I have a convex polyhedron given by a set of linear inequalities, for example: $$ x_1 \geq 0,~~ x_2 \geq 0, ~~x_3\geq 0 \\ x_1+x_2\leq 1,~~ x_2+x_3\leq 1,~~ x_3+x_1\leq 1 $$ I want to list all the ...
Erel Segal-Halevi's user avatar
12 votes
3 answers
2k views

Is using gradient descent for MIP a good idea?

I'm researching ways of solving constrained optimization problems on a cloud platform. I stumbled across this: https://cloud.google.com/blog/products/data-analytics/distributed-optimization-with-...
Skander H.'s user avatar
  • 2,139
12 votes
2 answers
498 views

Can Tuning Knitro Solver Considerably Make A Difference?

I have an NLP that I am hoping to solve with Knitro and I am aware of a multitude of different settings that you can "tune" in order to improve solution performance. I am not familiar with ...
GrayLiterature's user avatar
12 votes
1 answer
3k views

What are the pros and cons of LocalSolver?

LocalSolver is a company which provides a global optimization solver, combining exact and heuristic techniques. The benchmarks on their website are quite impressive. For example, they claim they can ...
Kuifje's user avatar
  • 13.2k
12 votes
3 answers
309 views

Connection between solver and Julia's JuMP

I am looking for ways or tips to connect a solver with the JuMP package. I started reading the manual of Math Opt Interface — I don't know the right terms, but I'll call it the backend of JuMP. Also, ...
Josa Ferreira's user avatar
12 votes
0 answers
173 views

which method has been used to automatically reformulate logical constraints in a standard MIP solver?

There are many of the formulations to linearize logical constraints by introducing new auxiliary binary or any appropriate variables and adding the corresponding constraints to the model. It can be ...
A.Omidi's user avatar
  • 8,717
12 votes
0 answers
224 views

Unpopular/Obscure solvers/algorithms that you used

There are many (numeric) optimizers which solve some subset of the set of multi-objective, black-or-grey-or-white box, robust, stochastic, mixed-integer, non-linear, non-smooth, manifold-constrained ...
worldsmithhelper's user avatar
11 votes
6 answers
2k views

How to read open-source code of a solver (Or-tools, OptaPlanner, Minotaur, etc.)?

I want to learn more about solvers by reading the code of some open-source projects such as MINOTAUR, Optaplanner and OR-Tools. However, I am struggling. I don't know where to start from there are a ...
Best_fit's user avatar
  • 567
11 votes
5 answers
1k views

How to implement a "generic" solver for scheduling problems?

I have been accepted for an internship for 6 months. The aim of this internship is to implement a "generic" solver for scheduling/production planning problems. This solver will bill a small prototype ...
Antarctica's user avatar
  • 2,917
11 votes
3 answers
970 views

From a performance/speed perspective, does the programming language matter if the solver used is the same?

Perhaps a silly question, I know... But just wondering if the programming language has an impact here if the solver used is the same? For instance, the same model formulation being solved using Gurobi ...
epilefst's user avatar
  • 159
11 votes
3 answers
1k views

Parallel nonlinear solvers

I've noticed that parallel (CPU or GPU) nonlinear programming solvers are few and far between. It seems that if any parallelization is involved at all, it generally applies to solving the underlying ...
Josh Allen's user avatar
11 votes
2 answers
886 views

Do LP solvers convert LPs to standard form?

To solve a linear program (LP) using the simplex method one first needs to bring the LP to standard form. This requires replacing every equality constraint with two inequalities and replacing every ...
Rolf van Lieshout's user avatar
11 votes
1 answer
563 views

Solvers and saddle points

It seems like most solvers that can tackle nonlinear nonconvex optimization problems (e.g. IPOPT) operate on ultimately solving for the first-order optimality conditions. Can it therefore be assumed ...
Josh Allen's user avatar
11 votes
1 answer
614 views

I've formulated my optimization model; now what?

I've formulated my linear/nonlinear/integer/mixed-integer optimization problem in algebraic form (possibly with the help of the folks on this site). Now what? How do I solve it?
LarrySnyder610's user avatar
11 votes
1 answer
192 views

Heuristics for mixed integer linear and nonlinear programs

What are some primal heuristics that mixed-integer linear and nonlinear program solvers use to quickly obtain a reasonably good feasible solution?
Sriram Sankaranarayanan's user avatar
10 votes
4 answers
15k views

What is the best open source solver for large scale LP optimization in pyomo?

I have used Gurobi and cplex for solving large scale LP problems with Pyomo. However, I do need to use open source solver. Any advise? glpk and cbc seems to be very slow in solving the problem (with ...
Optimization team's user avatar
10 votes
3 answers
785 views

Graph problems as integer programs

Suppose I give a solver (CPLEX, Gurobi, SCIP or anything else) an IP which is a reformulation of a stable set problem (or vertex cover problem or coloring problem) of some graph, is there a way I can ...
Sriram Sankaranarayanan's user avatar
10 votes
3 answers
981 views

Do solvers use GUB/SOS1 branching?

GUB/SOS1 branching is an old and well-known idea (see for example page 9 of Jeff Linderoth's notes). Is this implemented in commercial solvers these days? The Gurobi documentation mentions SOS1 ...
Austin Buchanan's user avatar
10 votes
1 answer
318 views

Partial Relaxation

In the context of a larger optimization problem I realized that I am missing the skill to implement/exploit the following observation: In the problem I was faced with two related sets of indicator ...
CMichael's user avatar
  • 1,333
9 votes
3 answers
4k views

Matlab fmincon for a problem with many nonlinear constraints

Using Matlab to solve a problem which has linear objective function and many nonlinear constraints, I am trying to generate the inequality nonlinear constraints by a function and pass it to fmincon ...
Oguz Toragay's user avatar
  • 8,642
9 votes
2 answers
820 views

Softwares for Operations Research. Is Excel Outdated or Useless for the OR industry?

I am looking over for softwares recommendation in Introduction to Operations Research Hillier 11th, there are tens of options for learn and apply OR theory using software. I normally check how much ...
rubengavidia0x's user avatar
9 votes
3 answers
973 views

Constraint programming resources

I am looking for resources to learn constraint programming. I will divide the resources I am looking for in three types: Modeling Is there resources (books, articles, courses, etc.) that are ...
Joffrey L.'s user avatar

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