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Questions tagged [integer-programming]

Solving systems of linear equations where variables are integers.

An integer program is a problem where, in addition to the linear inequalities constraints, the variables are also constraint to be integers only.

While can be solved in polynomail time, integer-programming is NP-hard.

A good solver for such optimization problems is lp_solve. See also GLPK (http://www.gnu.org/software/glpk/) and CBC (https://projects.coin-or.org/Cbc)

However, for large or hard instances you may need a commercial solver such as CPLEX or Gurobi.

For more information see wikipedia.

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Is there an easy-to-use 0-1 IP solver for java?

I would like to use a 0-1 integer programming solver as a tool in a java program. I cannot find anything easy to use on the web. I tried the pseudo-boolean library from sat4j but this is not well documented, some classes are not consistent with…
user109711
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Sets and Indexing in GAMS

I am trying to solve a mathematical optimization model. I want to define a set in my model, say, i and I want it to be from 0 to 15. Is it possible? Or I have to define from 1 to 16? I am using the demo version of GAMS (General Algebraic Modeling…
Gobryas
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How to use integer and binary variables with matlab GA toolbox?

I used matlab GA toolbox to solve an integer programming problem. The problem has some binary variables. I used nonlinear constraints such as x*(1-x) = 0 for binary variables, but matlab outputs real values for these variables. One another problem…
JalalJaberi
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Conditional Constraint for Interger Linear Programming

I'm working on a problem on Trees. I'm trying to write an ILP formulation. I have a tree T=(V,E) V are vertices E are edges. One of my constraints is about connectivity and i want to formulate my statement which is: if X[i,j] =1; then X[parent_i,i]…
Berkehan
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Can this specific Linear Program constraint be expressed?

Thanks for your time. I have a linear program and no idea how I could express a form of constraint and even if it's possible. Maybe someone here know a solution. A company assembly and sells a mixture which is composed of 3 ingredients, a, b and…
infiniteLoop
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How to assign N numbers into M pack that minimize some target function?

I have N(for example 30) integer numbers V[i], and M(for example 8) packs, each pack have an expected value P[j]. I want to assign each integer number to one pack, the following expression calculate the difference between the sum of V[k] that in…
HYRY
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Computation time of LP Relaxation of an IP higher than optimizing the IP itself

This is a follow up of my previous question on LP Relaxation of a MIP using SCIP. Though I'm able to compute a LP Relaxation solution of my MIP by simply passing the MIP (in CPLEX format) to SoPlex, I observe that the computation time taken by…
Rohit Girdhar
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Solving nonlinear integer programming with exponential variable

everyone. I formulate some formulas for my research. I want to ask is there any tool can solve this problem. I survey some tools such as GLPK, some MATLAB toolbox… But my formula seems to be nonlinear. I find some information on the Internet, it is…
Liam
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number of levels in a branch and bound tree

Given a ILP (Integer-linear programming) optimization with n integer variables and m constraints and implementing a branch and bound tree for solving a canonical problem, how many levels (height of tree) does tree require to reach the…
Mohammad Namakshenas
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Formulating a bilinear optimization program as an integer linear program

In my work, I came across the following problem: Given a similarity matrix D, where $d_{i,j} \in \Re$ represents the similarity between objects $i$ and $j$, I would like to select $k$ objects, for $k \in {1, \dots, n}$, in such a way that minimizes…
user2947877
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What size tour can I reasonably expect to solve with GLPK?

I'm playing around with the travelling salesman example provided with GLPK, and trying to get a feel for what problem size I can reasonably expect to solve. I've managed to solve a 50 node graph, but 100 nodes doesn't seem to be converging in a…
ire_and_curses
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How can I order the basic solutions of a min cost flow problem according to their cost?

I was wondering if, given a min cost flow problem and an integer n, there is an efficient algorithm/package or mathematical method, to obtain the set of the n-best basic solutions of the min cost flow problem (instead of just the best).
Giacomo
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Nurse Scheduling for Shifts with Different Lengths

I am trying to adapt the shift scheduling problem from this code to use shifts with different lengths, but I didn't succeed any of my attempts to do. What is the best approach to include this feature? In the code, we input the type of shitfs in the…
j3r3mias
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Resource Constrained Project Scheduling such that tasks are scheduled based on highest priority

This is regarding a Resource Constrained Project Scheduling Problem (RCPSP). This involves scheduling certain tasks in time windows on machines subject to availability of manpower. This is set up in the form of an Integer Program. I'm using a…
Ryuu Agamaki
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Generalized Assignment Problem with Genetic Algorithms in R

How can I implement a Generalized Assignment Problem: https://en.wikipedia.org/wiki/Generalized_assignment_problem to be solved with Genetic Algorithms https://cran.r-project.org/web/packages/GA/GA.pdf in R. I have a working example of the code but…
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