# Questions tagged [mixed-integer-programming]

For questions about mathematical optimization problems involving both continuous and binary or general integer variables.

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### How to improve relative mip GAP using CPLEX in a MIP

Supose that I have an integer feasible solution for a MIP and I provide this one for CPLEX. I have tested this situation in a problem and CPLEX have reported the following: ...
134 views

### Problems finding a feasible solution in a MIP

I am using CPLEX with Julia using the package JuMP to solve a MIP problem. In a small instance, I have tested my problem but, after 10 minutes, nothing happens. I have defined the following parameters ...
135 views

### Formulating two non-negative variables without binary and/or big-M

There are two non-negative integer variables $q$ and $p$, where only one of them can take a positive value. To impose this relation, I write: \begin{align} q &\leq M(1 - y) \tag1 \\ p &\leq M(...
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### Are there strategies/rules/systematic approaches to derive alternative formulations for an optimization problem?

For a given optimization problem there are often many known math programming formulations. For example for the TSP here is a survey https://link.springer.com/chapter/10.1007/3-540-36626-1_5 of many ...
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### What are useful plots/statistics/metrics when analyzing the solution sensitivity in multi-objective optimization?

Consider an optimization problem with $n>3$ objectives. For handling this there exists often two approaches: a) some weighting of the objectives, b) fix an order of objectives and then optimize ...
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### MIP for resources to task assignments

I have few tasks t1, t2, t3, t4, t5 which need to be assigned to resources r1, r2, the tasks are located across multiple ...
111 views

### k -MST problem based on Miller-Tucker-Zemlin subtour elimination constraints

Where can I find the formulation of the $k$-MST ($k$-minimum spanning tree) problem as (mixed) integer linear program based on Miller-Tucker-Zemlin subtour elimination constraints (MTZ)?
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### Free solver for MINP problems

I have a mixed-integer nonlinear programming (MINP) problem. Is there a free solver for such a problem?
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### Lagrangian Relaxation The Weak Lower Bound

I am applying Lagrangian Relaxation with Subgradient Optimization Method and trying to solve a MIP model. Before testing the large-scale instances, I wanted to see how it performs on small-size ones. ...
155 views

### Working with large models

I am working with a variant of TSP, number of nodes that I need to test are in between 2500 to 3000 nodes, I am using docplex for modelling, I have a 8 gb Ram but it gets filled with only 400 nodes. ...
268 views

### If else condition to MILP

I have following problem: $c_i = 1$ if $X + \sum_j^N G_j = T$ else $c_i = 0$ Also there is another constraint which upper bounds equation $X + \sum_j^N G_j \le T$. $c_i$ is binary $X, T$ are ...
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### Modeling in integer programming vs modeling in constraint programming

I have some experience with linear and integer programming modeling (I read Model Building In Mathematical Programming by Williams). Now I am trying to learn how to model with constraint programming. ...
436 views

### What expresses the efficiency of an algorithm when solving MILPs

What is the appropriate measure to indicate the efficiency of an algorithm\model that solves a MILP through B&B? Is it the number of nodes examined to reach the optimum? the number of iterations ...
157 views

### Should I use Special Ordered Sets in MIP model

I investigating various aspects of MIP and I can see that my current modelling langaunge support Special Ordered Sets(https://python-mip.readthedocs.io/en/latest/sos.html) but looking at the papers ...
125 views

### Using LR-based method to solve mixed integer programming

When we use Lagrangian relaxation-based methods to solve mixed integer programming, does the convergence of multipliers to the optimum as well as convergence of primal variables to the optimum happen ...
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### In integer programming what's the difference between using lower upper bound constraints and using a big M constraints?

I've noticed that for integer programming models with binary variables some use upper bound constraints and others use big M constraints in order to have two mutually exclusive choices. I have trouble ...
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### How to describe the traveling salesman problem with an integer programming model?

I'm trying to describe the travelling salesman problem as an integer programming model. I'm interested in the asymmetric version of the problem. The problem can be summarized as finding the optimal ...
240 views

### Shortest path problem with underlying continuous variables

I recently got interested in the following variation of the shortest path problem. I've looked in the literature for days but I couldn't find any paper studying this problem. I'd like to ask if you ...
99 views

### What are the flow based formulations?

What are the flow-based formulations? For what optimization problems are they applied, and in which form? Which are the specificities of such a formulation? Also, the same question for the time staged ...
81 views

### How to model this chain of logical implication II

I would like to seek some advice on modeling the following (chain of) logical implication: For instance $\omega_{xz}$ might indicate precedence, i.e., $x$, $z$ being the nodes $x$ and $z$, ...
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### How to model this chain of logical implication

I would like to seek some advice on modeling the following (chain of) logical implication: For instance $\omega_{xy}$ might indicate precedence, i.e., $x$, $y$ being the nodes $x$ and $y$, ...
IF $\sum\limits_d X_{i,d}\ge6$ THEN $Y_i = 1$ (strictly) AND IF $\sum\limits_d X_{i,d}<6$ THEN $Y_i = 0$ (strictly) $X$ and $Y$ are binary variables. What I'm actually trying to do is to charge the ...