Questions tagged [mixed-integer-programming]

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

70 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
10
votes
0answers
171 views

Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
8
votes
0answers
91 views

Automatic detection of SOS variables and constraints

We've been working on a new feature for Octeract Engine, namely to automatically extract SOS structure from a model and then exploit it. While the literature is quite rich on what to do with SOS once ...
8
votes
0answers
92 views

For subset selection regression as a mixed integer program, how tightly should the bounding box be set?

When solving best subset regression as a mixed integer program, how do you decide how tightly to bound the range of values of the $X$ values? When the box is tight, the solver finds a solution ...
7
votes
0answers
92 views

Network design problem with rounded capacity constraints

I have a network design problem with complicating capacity constraints which I'm trying to model through a Mixed Integer Programming formulation. The problem is defined on a directed, incomplete graph ...
7
votes
0answers
82 views

Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
7
votes
0answers
76 views

Modelling a simple ordering problem to have balanced delivery days

Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
6
votes
0answers
120 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 ...
6
votes
0answers
50 views

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 ...
6
votes
0answers
89 views

Benefits of removing slack variables during presolve

I was reading Tobias Achterberg's thesis, and on page 138 he mentions the following presolving technique for linear equations (I'm slightly paraphrasing Example 10.2): Consider the equation $4x_1+...
6
votes
0answers
75 views

Data Formulation for Mixed-Integer-Programming Models

Until now, I have used the Gurobi, CPLEX and OR-Tools (GCO) interface to formulate mixed-integer-programming models. Recently, I have discovered MiniZinc and want to utilize it to formulate big ...
6
votes
0answers
363 views

Cplex is stuck after root node relaxation solution

I am solving an MIP through Benders decomposition (coded both generic and legacy callback versions), by employing Java with Cplex 12.9. For some of the instances, Cplex is stuck for two hours (time ...
5
votes
0answers
55 views

Reference request — fishery yield optimization

I'm looking for references to do a review of research on managing fisheries in industry. I've seen adaptions of population growth models which include some harvesting constant or function and was ...
5
votes
0answers
97 views

Are there any good models for min-max vehicle routing problem?

I am trying to model a min-max VRP problem with multiple delivery vehicles and I have come up with a model using branch and cut but I do not think it is strong enough as it takes lot of time to ...
5
votes
0answers
472 views

What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
5
votes
0answers
79 views

Complexity of determining whether a LP or MIP is infeasible

What is the best complexity for the worst case scenario and the algorithm associated with it to determine if a linear programming (LP) is infeasible ? Further, what if we consider a mixed integer ...
5
votes
0answers
266 views

Solver for Go Programming Laguage

Has anyone used MIP solvers (open source or commercial) with Go language https://golang.org/? I am looking for a solver for simple linear MIPs for network flows and set cover types of problems.
4
votes
0answers
64 views

Modeling question on continuous variable that dependens on binary variables

Given a model with a binary variable $b_s$ that describes whether taking an item $s$ from a set $S$ or not. Consider that some other constraint in the model depends upon whether all items of the set ...
4
votes
0answers
196 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 ...
4
votes
0answers
74 views

Adding redundant inequality to a model

The following relationship is part of my optimization model ($W_k$ denotes a binary variable) $$W_{1} \le \cdots \le W_{k-1} \le W_{k} \le W_{k+1} \le \cdots \le W_{k^{\max}}$$ My question is, do ...
4
votes
0answers
67 views

Continue on "Is there a known MILP to schedule routes after routes are made"

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
4
votes
0answers
884 views

cvxpy: Code that works for default solver doesn't work for cp.GLPK_MI

The following code works: ...
4
votes
0answers
166 views

Publishing paper that uses LP solver to solve equation

I was reading this paper by Cerna et al. (2018)1. In the paper there are only CPLEX-solvable equations given by the authors and the results. How valuable is this paper, and what is its quality? Can ...
3
votes
0answers
59 views

Is there any open source solver for MILP that can output the top N best results instead of the global best?

I am working on an MILP problem, and the project needs to output the top N best results rather than the global best. I am looking for an open source solver which has a callback function. Can anyone ...
3
votes
0answers
53 views

Polynomial Time Solution For a Mixed-Integer Linear Programming Specific Case

Consider the following mixed-integer linear programming (MILP): \begin{equation*} \begin{array}{ll@{}ll} \text{maximize} & 1 & \\ \text{subject to}& x_{i} \geq 0, &i=1 ,\dots, m\\ ...
3
votes
0answers
76 views

Extract/Inject Solutions (orig problem-space) during Search in MILP -> CoinOR Cbc

Task / Goal I'm considering adding some customized problem-specific local-search component on top of a general-purpose MILP solver (= improvement heuristic). The basic idea is the following: All new ...
3
votes
0answers
105 views

Harvest planning problem

I need to model the following problem: For a planning horizon of $P$ equal periods, one has $N$ harvesting locations and $K$ contractors who can harvest at those locations ($K < N$). Each ...
3
votes
0answers
103 views

In binary linear programming, what's the relationship between the dual solution and the lagrangian multipliers?

In my optimization problem the objective function and all the constraints are linear. The decision variables are binary. [so, it's BLP] Some of the hard constraints are very time-consuming to be ...
3
votes
0answers
64 views

Resource scheduling problem with synchronization constraints: Weak LP relaxation

I have a resource assignment/scheduling problem which involves assigning jobs to $m$ workers. There are 2 sets of different jobs, $J^1$ and $J^2$, and a set of periods $T$. Let $d_{jt}$ be the number ...
3
votes
0answers
62 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 ...
3
votes
0answers
47 views

How to formulate a storage component?

Let’s say I have a drink for several customers, and I know their demand. Besides, I also have a storage tank for the drink during times when demand exceeds supply. The storage tank's size is not yet ...
3
votes
0answers
69 views

Solving a nonlinear model with constraints of exponential functions and continuous variable multiplications

I have a nonlinearly-constrained model and wonder if a nonlinear solver like Ipopt or Knitro can solve the problem. Briefly, my objective function is linear. I have the following variables with their ...
3
votes
0answers
50 views

PuLP Python: How to linearize an inequality involving an integer variable

I am working on a Copper payables problem where the objective function is to maximise the sum of copper payable over a time period, T. The total amount of payable tonnes i.e. what the customer will ...
3
votes
0answers
87 views

Linearization of the shifted copy of a function

Suppose in a model I have the expression $y_{1}(x) = 10 + 5 x^2$ where $x \in [0,20]$ is a continuous variable. In order to be able to use an MILP solver, I piecewise linearise $z_{1} = x^2$, by ...
3
votes
0answers
49 views

Linearisation using SOS2

I am trying to linearise the following expresssion. $C(k) = B(k) e^{-d(k)}, B(k) \ge 0 , d(k) \ge 0 $ I am trying to do this by using SOS2 sets. I set $X(k) = e^{-d(k)}$ and I get $C(k) = B(k) X(...
3
votes
0answers
58 views

What are the efficient ways to model this scheduling problem and ways to improve running time

There are $N - \{1 \ldots N\}$ jobs, each with processing time $p_j$, to be scheduled on $M - \{1 \ldots M\}$ machines over span of $D - \{1 \ldots D\}$ days and while working $T - \{1 \ldots E \ldots ...
3
votes
0answers
66 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
3
votes
0answers
57 views

Discrete optimization in transport economics

I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ ...
2
votes
0answers
29 views

How to construct a restriction for a blending problem that has 2 inputs that are blended, and as result we get 2 outputs?

THE PROBLEM A refinery has 10 million barrels of type A crude and 6 million barrels of Type B crude oil. The refinery has 3 plants to produce Gasoline (it makes a profit of 2 USD / barrel) and Naphtha ...
2
votes
0answers
64 views

Minimizing the number of machine starts

Please, if somebody has another approach to a similar MIP problem... Assume we have some machines $m$ and their activity could be interpreted by the boolean decision variable $x_{i,j} \ i \in m, j \in ...
2
votes
0answers
39 views

Indeterminacy Reduction for MINLP

I am considering a Mixed Interger NonLinear Program (MINLP), and using a solver to obtain admissible solutions. Is there a general method to reduce indeterminacy of solutions (e.g. by adding ...
2
votes
0answers
59 views

How to make a constraint for consecutive zeros in the mixed integer programming problems

I intend to generate a binary sequence with a size of N = 10, for example, [1, 0, 0, 0, 0, 1, 1, 1, 0, 0]. The constraint is that when 0 appears, it must appear for at least two consecutive times, ...
2
votes
0answers
54 views

Designing Multi Floor Architectural Layouts

Architectural layouts define the position and shape of rooms in 3D space, where windows and water pipes are and as well as how humans travel between rooms (among other things). There is a lot of ...
2
votes
0answers
94 views

Problem with Piecewise constraint in Gurobi

I am facing a problem in my model with piecewise constraints that is making my one of the decision variables equal to zero for every value. My objective function is: \begin{equation} \min \sum_{t=...
2
votes
0answers
61 views

Mathematical model complexity Vs Time Complexity of the model

As far as I know, when we talk about the term of complexity, it referred to the time complexity of the model in which how long does it take to solve a specific mathematical program by a specific ...
2
votes
0answers
101 views

About combinatorial Benders Cuts

I am solving an OR scheduling problem where I assign the patient to (day,OR) tuple in Master Problem. Once the assignment is made, a subproblem can be solved for each (day,OR) tuple independently ...
2
votes
0answers
121 views

Why is exact TDTSP solving much harder to do than TSP solving?

I was thinking about exact methods for solving the Time Dependent TSP (TDTSP). Clearly, it is at least as complex as TSP because it extends TSP, but why is it for exact approaches that difficult to ...
2
votes
0answers
75 views

What if anything do linear relaxations of "nearby" MILP nodes tell us about other MILP nodes

Assume we are given MILP where $y \in (\mathbb{R}^+)^n$, $x_1, x_2 \in \{0, 1\}$ are the integer variables. It is obvious that this problem when solved via branch and bound has a 2 deep b&b-tree. ...
2
votes
0answers
89 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}\\ \...
2
votes
0answers
89 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
0answers
91 views

Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$ COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0) $$ Here, $a_i, b_j \in \mathbb{R}_+$ ...