Questions tagged [mixed-integer-programming]

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

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4
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1answer
97 views

How do I formulate constraints that check if a parameter is between certain values, using binary variables?

I have $3$ parameters $a_1,a_2,a_3$ and a variable $d$ and $3$ binary variables $b_1,b_2,b_3$ and a "result" variable $s$. How do I model constraints so that: If $d$ is between $0$ and $a_1$...
2
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0answers
94 views

Scheduling minimization Integer Programming problem formulation

I am working with integer optimization. I have a problem with $t$ tasks and every task $i$ needs $w_i$ weeks to be completed and $p_{il}$ workers on a specific week $l$. There is a total time in weeks ...
5
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1answer
83 views

Breadth First Search vs. Best First Search

What is the main difference between Breadth First Search and Best First Search? What is meant by saying Breadth First Search requires previous knowledge?
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0answers
49 views

Multiple conditions in indicator constraint of Gurobi

I'm working on a vehicle routing problem, in which a vehicle need to pick up amounts of things in some nodes. I'm trying to solve it by Gurobi optimizer. Except for meeting the time windows of each ...
6
votes
1answer
92 views

Upper and lower bounds of a variable equal

I'm working on a MILP (Mixed-Integer Linear Programming) problem with the Java API of Cplex. In order to easily exclude some variables from my problem I thought about setting both their lower and ...
2
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1answer
92 views

Problem with vehicle routing problem in Gurobi Python

I have a vehicle routing problem solved by linear programming, but I'm confused about the constraints (see the model in figure 1). In the model, $u$ and $x$ are decision variables, and we set node $0$ ...
0
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1answer
127 views
2
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0answers
48 views

Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program

I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function: \begin{equation} x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
3
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0answers
40 views

MIP: Do binary variables perform better that integers? [duplicate]

I have a model where investments can be done in blocks. Now I could model this with integer or binary variables. Does anybody know which one is the better choice in terms of computational performance?
5
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1answer
140 views

Does exchanging integer variables by binary variables strengthen a MIP?

Suppose that I have an MIP with a whole lot of continuous variables and some integer variables. In my case, this takes a very long to solve (in fact I wasn't able at all to solve it to optimality). So ...
4
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1answer
366 views

How is this type of function treated in mathematical programming?

I'm trying to solve a problem for human resource allocation that has a function that receives the number of people working on a project and returns the time to finish it. The number of employees in a ...
2
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1answer
63 views

Examples of LP problems in irrigate engineering

I need examples of linear programming problems applied to irrigation system. My idea is to give students many examples of LP applications in the irrigation engineering.
6
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1answer
175 views

Guides for strong MILP Formulations

When developing MILPs, often there are different alternatives possible to express a constraint. The question then arises, which of the alternatives is better, meaning, which alternative is expected to ...
5
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1answer
468 views

MILP - stronger models

Let $y, x_1, x_2, x_3$ be binary variables. The following holds: $y=1 \implies x_1=1, x_2=1, x_3=1$ I can model this by requiring (1) \begin{align}x_1 &\ge y\\x_2 &\ge y\\x_3 &\ge y\end{...
5
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3answers
1k views

How to represent an integer variable via binary variables?

Suppose we have a model with $N$ integer variables, i.e. $x \in \mathbb{Z}^{N}$ with $L \leq x \leq U$. How can we represent the integer variables via binary variables? Or in other words: how can we ...
1
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0answers
73 views

Minimax problem with a large high dimensional feasible region

How to solve minimax mixed integer problem with a large high dimensional feasible region? \begin{aligned} \max_{\vec{x}}\min_{\vec{y}} \quad & \vec{r} \cdot \vec{x} + \vec{s} \cdot \vec{y}\\ \...
5
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1answer
108 views

Is that Ok to exclude fixed components from an objective function?

Suppose we have the following objective function with one decision variable $x_i$ where $p_i$ is a fixed parameter for each $i$ and also, $a$ is a constant for the problem \begin{align} \label{eq} \...
5
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1answer
248 views

Solving Quadratically Constrained Quadratic Program with Cross Product Terms Only

I'm totally new to the world of optimization and I have an optimization problem that I think it can be formulated as Mixed Integer Quadratically Constrained Quadratic Program (QCQP) but I'm not sure ...
3
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0answers
56 views

Linearization of a quadratic model, what is the difference while using gurobi?

I have a quadratic model of parking $N$ cars in $S$ separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ...
4
votes
1answer
228 views

CPLEX log always the same after hours (“Gap” and “Best Integer” always blanks)

I'm using the Java API of CPLEX 12.6.1 (with license) to solve a MILP (Mixed-Integer Linear Programming) maximization problem. The point is that, after 21 hours, CPLEX has consumed 32 GB of RAM and ...
5
votes
1answer
109 views

Solver Recommendation : Discrete Variables and Quadratic Constraints

I would like some solver recommendations to solve a problem with boolean/integer variables, mostly linear constraints but also some quadratic constraints. I also have an objective to minimize which is ...
4
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0answers
190 views

Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
3
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1answer
58 views

Benders Decomposition for deterministic MILP

When I think of Benders Decomposition, I typically think of two-stage stochastic programs. However, I was wondering if there is any application to decomposing a large scale deterministic MILP with ...
4
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1answer
34 views

behaviour of CPXsetincumbentcallbackfunc

I am using the incumbent callback CPXsetincumbentcallbackfunc to identify integral solutions that do not satisfy nonlinear constraints that are not explicitly part of the constraint set. When such a ...
0
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0answers
82 views

Problems with a MILP

I need some advice, any hints will be appreciated. I have a MILP and I am using Gurobi to solve it. I have a feasible integer solution. When I use mipstart, after ...
2
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1answer
67 views

CPLEX Indicator Constraints in Java API

I'm using the Java API of CPLEX (12.6.1 version) to solve a MILP problem. This is how I create 'normal' constraints: ...
2
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1answer
67 views

The precision of the decimal number of the Cplex

I have faced a little weird problem when I use Cplex to solve my test problem. Basically, some of my data are float numbers up to three decimal numbers (For instance, 0.627). But, when I print out the ...
6
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0answers
118 views

Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
5
votes
1answer
240 views

What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I ...
2
votes
2answers
81 views

Docplex, CPLEX Warning 1036 :

I am trying to solve a large-scale MIP problem. I have the following errors, I know, it's about the data, but I can't change the data. Is there a method to deal with it? ...
1
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0answers
118 views

CPLEX ignores a feasible solution given as start one

Assume we have 100% feasible solution for the model with decision variable a[i]. Then we are changing the objective function on something similar to ...
4
votes
1answer
89 views

Approximately evenly-spaced subsequence

Suppose you have $n$ time series data where the times are in arithmetic series with difference $d$, and suppose further that some of the data are missing at random (say, $p=.30$). Now suppose you want ...
6
votes
2answers
233 views

Forbid transformation of max(x,y) into MILP

The function $\max(x,y)$ can be linearized by making use of additional binary variables. I suppose global optimisers are implemented to perform this transformation automatically. Is there a global ...
1
vote
2answers
85 views

Combinatorial Optimization Problem using IBM ILOG CPLEX

Consider the combinatorial optimization problem described as below. Let $D=(V,A)$ be a directed graph with $V$ the set of vertices and $A$ the set of arcs, i.e., $A=\{(i,j)\mid i,j\in V\}$. On each ...
-4
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1answer
94 views

Multiple If else constraints in Mixed integer programming

How to formulate the following as constraints in MILP? a[0][0] = y, if x[0]= 0, a[0][0] = 0, if x[0] != 0, . . . . a[i][j] = b[i][j-1] + y, if x[j]=i, a[i][j] = a[i][j-1], if x[j] != i, ... . . . b[0]...
5
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1answer
156 views

How to model this multi-commodity flow problem with a twist?

Problem description I am working on a variation of the multicommodity flow problem on a graph $G=(V,E)$. I have requests $r_{uv}$ for pairs of nodes $(u,v), u\in V, v\in V$, which means that $r_{uv}$ ...
-1
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1answer
74 views

For docplex, it's possible to set the number of iterations without improvement?

When running the cplex model, I noticed that the CPLEX repeats the same gap value several times. I ask if there is a parameter in docplex that limits the number of iterations without improvements or ...
2
votes
2answers
75 views

Graph partitioning/cutting problem

Let $G = (V,E)$ be an undirected graph, with $e \in E$ has positive weight $w_e$. Given a set of integers $I = \{i_1,\dots,i_n\}$ such that $\sum_{k=1}^n i_k = |V|$. I want to find a partition $P$ of $...
4
votes
2answers
152 views

Setting up Branching Priority for GUROBI in Pyomo

I am currently experimenting with GUROBI and would appreciate some kind advice on the following: In Pyomo: Setting variable branching priorities, there was a response to doing so for CPLEX, hence I ...
2
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0answers
52 views

Pyomo Trouble - Number of Constraints in Output is 0 When It Should Be > 5000

I have an MILP program written in Pyomo and I am using CBC as a solver. Below is a description of my problem: The model works fine when it is run on my local computer The output is the following in ...
2
votes
1answer
63 views

Finding the minimum of a group of timings

I would like to seek some modeling advice on the following: Say for instance I have 5 nodes representing workstations of the operation of 5 jobs, and that I have less than 5 vehicles. Say I have two ...
0
votes
1answer
74 views

How to solve this clustering problem with heuristic or meta-heuristic approach?

I have clustering problem with servers and users. This is different to the one posted in https://math.stackexchange.com/questions/4088441/what-will-be-an-efficient-joint-clustering-solution-to-this-...
1
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1answer
155 views

References to publications on representation of any boolean function as a system of linear inequalities

It is known that any boolean function may be represented, in some sense, as a system of linear inequalities. But my rather intensive literature search brought a little references. I will appreciate ...
5
votes
4answers
429 views

How to visit a subset of network nodes in a single trip?

I have a connected network where I want to visit a set of destinations which may require visiting intermediate nodes as well because there may be no direct edge between source and destination nodes. I ...
3
votes
2answers
80 views

MILP modelling on minimal disturbance of right-hand-side to make a linear system infeasible

I try to model the following problem: given $z\in\{0,1\}^m$ and a linear system $Ax\le b(z), x\in\Bbb R^n, A\in\Bbb R^{d\times n}, b(z)\in\Bbb R^{d}$, where $b(z)$ means that some entries of $b$ are ...
3
votes
1answer
99 views

Electricity market clearing price using fixed-MIP formulation?

Dual information of electricity markets clearing problem is required to calculate the marginal clearing price. As most electricity market problems are based on MIP (and dual information of MIP is not ...
7
votes
1answer
140 views

How can I strengthen a family of constraints in the presence of a clique constraint?

Suppose $x_i$ are binary variables, $y_j$ are arbitrary variables, $a_j$ and $b$ are constants, and I have the following linear constraints: \begin{align} x_i + \sum_j a_j y_j &\le b &&\...
4
votes
1answer
59 views

Name for subclass of ILP without any inequality constraints (including constraints on x)

In "Myths and Counterexamples of Mathematical Programming" myth "IP Myth 21" says: The problem of finding $x\in \mathbb{Z}$ such that $Ax=b$, where $A\in\mathbb{Z}^{m\times n}$ ...
3
votes
1answer
95 views

How to deal with log0 in optimization problem

I am adding some constraints to my model described in my previous post, where a discontinuous piecewise-quadratic functions is the objective to be minimized in cvx. Here I have an additional terms, ...
3
votes
2answers
149 views

How to reformulate a discontinuous piecewise-quadratic functions

I am trying to develop a model, solving an optimization problem which has the following objective function: variable p(i); minimize sum(cost) subject to p>=0 ...

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