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1500 questions
22
votes
5 answers

How can I best handle symmetries in my MIP?

When dealing with mixed-integer-programs with many symmetric solutions it can take very long until the branch-and-bound-tree search is finished because symmetric optimal solutions cannot be pruned. What techniques can I use for a MIP with…
YukiJ
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22
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2 answers

How does a warm start work in LP/MIP?

Can someone explain how warm starts/ MIP starts work? How do solvers like CPLEX/GUROBI use warm start with the Simplex algorithm? I am interested in understanding how the entire warm start pipeline works in a MILP solver. I would appreciate links to…
Palaniappan Chellappan
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22
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5 answers

Validation and verification of mathematical models

Within the subject of simulation I have found some literature on validation and verification (e.g. Sargent's paper). My question is, what techniques do you use to validate and verify your mathematical (optimization) models and their implementation?
Djames
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22
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3 answers

How to minimize an absolute value in the objective of an LP?

I want to solve the following optimization problem $$\begin{array}{ll} \text{minimize} & | c^\top x |\\ \text{subject to} & A x \leq b\end{array}$$ Without the absolute value, this a standard form for linear programs. Can such a problem be…
Discrete lizard
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22
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4 answers

Linearize or approximate a square root constraint

I encounter a nonlinear constraint that contains the square root of a sum of integer variables. Of course one could use nonlinear solvers and techniques; but I like linear programming. Are there any standard results on linearizing or approximating a…
Albert Schrotenboer
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21
votes
3 answers

Using Neural Networks For Solving Optimization Problems

Recently, I came across the below paper and found it very interesting. Solving Mixed Integer Programs Using Neural Networks; https://arxiv.org/abs/2012.13349 The idea is to use (train with neural network models) similar problem instances to help the…
alamaranka
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21
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5 answers

Tightness of an LP relaxation without using objective function

How can we measure the tightness of a linear programming relaxation for a mixed integer linear program without using the objective value? I would like to get a measure in terms of the feasible set and independent of the objective function. This is…
Mertcan Yetkin
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21
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2 answers

Real-world examples of supply chain contracts?

Does anyone know of any real-world examples in which supply chain contracts, of the type introduced by Pasternack (1985) and reviewed by Cachon (2003), are actually used in practice? I'm talking about contracts formulated as Stackelberg games, with…
LarrySnyder610
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21
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10 answers

What are Operations Research problems which occur in everyday life?

What are Operations Research problems which occur in your everyday life? Things that come to mind are for example: driving to work: shortest path problem packing your backpack for vacation: knapsack problem or bin-packing planning for every…
user3680510
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21
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9 answers

What kind of optimization problems are solved most often in practice?

I think that the shortest path problem is probably the problem that is solved most often. But if we move to problems where we need more complicated solvers, like Gurobi, Cplex, and Baron? What are the problems which are solved most often in industry…
user3680510
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21
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3 answers

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 Ch 9). In the application-oriented literature,…
SecretAgentMan
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21
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9 answers

Applications of pure mathematics in operations research

This is a question that I've been thinking about for a while, as my background is mainly on pure mathematics. From a few OR papers that I've looked at, I could identify some areas of pure mathematics that can be applied to OR: (Analytic) Number…
ə̷̶̸͇̘̜́̍͗̂̄︣͟
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21
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8 answers

How to innovate in OR

I am a graduate student in OR and I want to build one or two independent projects that go beyond academic projects in my university. I would like to target average people and/or those in the industry who may or may not use an existing…
Antarctica
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20
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3 answers

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] which, in my case, should be solved using column generation…
Djames
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20
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7 answers

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 programming library that doesn't use floats/doubles and…
Sidharth Ghoshal
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