Questions tagged [solver]

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

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8
votes
1answer
102 views

Formulating a MINLP for CPLEX in PYOMO

I am trying to do my first MINLP problem using PYOMO and CPLEX - although I am not committed to using CPLEX, but it was recommended to me. To my understanding you need to formulate your problem in ...
8
votes
2answers
70 views

Warm-start SCIP with a solution

I am trying to solve a MIP using SCIP. I let my solver run for some initial time-bound - let's say 10min. After 10min, I check if the problem is solved to optimality or 1% gap. If not, then I would ...
19
votes
3answers
1k 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 ...
24
votes
5answers
5k 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 ...
17
votes
4answers
2k 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?
13
votes
1answer
261 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 ...
21
votes
4answers
4k 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. ...
24
votes
4answers
1k 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 ...
8
votes
1answer
55 views

Read an LP/MPS file in the PuLP

I was trying to read a MPS file by using the PuLP package in the Python, but I can't find any related documents on it. Does ...
8
votes
3answers
596 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 ...
8
votes
1answer
111 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?
16
votes
2answers
251 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 ...
13
votes
3answers
175 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 ...
7
votes
2answers
171 views

Simplex-Implementations in professional Solvers

Which non-textbook variants (primal/dual, revised) and techniques (e.g. steepest-edge) do professional solvers like Xpress, CPLEX, CLP use, to get the best out of the simplex algorithm? This ...
7
votes
1answer
93 views

Java source code for branch and price

Is there any Java source code (or framework) to implement and solve MILP using the branch and price method? AFAIK, jORLib is a framework to implement B&P using Java, but it does not have any ...
20
votes
3answers
181 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 optimal solutions, and your solver of choice: For what theoretical and/or practical (...
11
votes
1answer
83 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 ...
14
votes
4answers
330 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 ...
7
votes
2answers
68 views

Does the API affect the time Gurobi requires to find an optimum?

When working with Gurobi, CPLEX and the like the user can choose between many different APIs, for example Python, C++, R, Java, Matlab or C. Some of these API are more efficient than others. For ...
11
votes
2answers
112 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 ...
14
votes
5answers
211 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 ...
19
votes
3answers
185 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 ...
27
votes
6answers
471 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 ...