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Questions tagged [mixed-integer-programming]

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

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which method has been used to automatically reformulate logical constraints in a standard MIP solver?

There are many of the formulations to linearize logical constraints by introducing new auxiliary binary or any appropriate variables and adding the corresponding constraints to the model. It can be ...
A.Omidi's user avatar
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9 votes
0 answers
226 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 ...
S_Scouse's user avatar
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8 votes
1 answer
100 views

Is there any way to use Lazy constraints in Pyomo?

I would like to know if there is any way to implement a Lazy constraint in the Pyomo package. (As far as I know, the only way to implement such a constraint is by ...
A.Omidi's user avatar
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8 votes
0 answers
112 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 ...
Charles Fox's user avatar
7 votes
0 answers
102 views

MIP formulation for graph planarity test

In this question, it was asked wether a MIP formulation exists to test for a graph's planarity. The inputs are the graph's nodes and edges, and the output would be a certificate which guarantees that ...
Kuifje's user avatar
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7 votes
0 answers
92 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 ...
dassouki's user avatar
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7 votes
0 answers
81 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 ...
Sean's user avatar
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6 votes
0 answers
210 views

Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
Enthusiast's user avatar
6 votes
0 answers
89 views

Issue of Dense columns in the formulation

I'm working on a price-selection model where we need to identify price point for each time-period (could be day/week). Objective of the model is to figure out optimal price-point for each time-point ...
anjikum's user avatar
  • 984
6 votes
0 answers
126 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 ...
Nisith Singh's user avatar
6 votes
0 answers
53 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 ...
user3680510's user avatar
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6 votes
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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+...
Nikos Kazazakis's user avatar
6 votes
0 answers
91 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 ...
Georgios's user avatar
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6 votes
0 answers
629 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 ...
Vedat BAYRAM's user avatar
5 votes
1 answer
154 views

Numerically stable way to optimize a lexicographical preference between two objective functions?

I am solving a mixed-integer program whose decision variables are $x \in \{0, 1\}^n$ and $y \in \mathbb{R}^m$, where $0 \leq y_j \leq u_j$ for constant upper bounds. My primary objective function is ...
Max's user avatar
  • 544
5 votes
0 answers
120 views

Reduce overhead Gurobi Python getting and setting attributes

I am using Gurobi 9.5.1 in Python 3.10. In the context of column generation I request the duals of the master problem and set them in the objective of the subproblem. This is done repeated times. <...
rllb's user avatar
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5 votes
0 answers
62 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 ...
Ryan Howe's user avatar
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5 votes
0 answers
179 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 ...
Morpheus's user avatar
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5 votes
0 answers
1k 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 ...
A.Omidi's user avatar
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5 votes
0 answers
116 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 ...
G Oliveira's user avatar
5 votes
0 answers
739 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.
Alexey Sorokin's user avatar
4 votes
0 answers
164 views

Stochastic optimization for inventory management

The deterministic problem is to minimize operational cost subject to constraints in demand, supply and capacity. The ordering policy is periodic review, order-up-to. The stochastic version of the ...
anerjee's user avatar
  • 119
4 votes
0 answers
122 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 ...
Andreas's user avatar
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4 votes
0 answers
247 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 ...
Qurious Cube's user avatar
4 votes
0 answers
77 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 ...
Clement's user avatar
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4 votes
0 answers
71 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 ...
dimboukosis's user avatar
4 votes
0 answers
1k views

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

The following code works: ...
Rohit Pandey's user avatar
4 votes
0 answers
171 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 ...
ooo's user avatar
  • 1,589
3 votes
0 answers
43 views

Gurobi - Is finding a feasible solution when optimizing a lot harder than finding a feasible solution?

The code is working fine but I feel as my intuition could be wrong. I first set up my problem as: $$\min_{f(x)\leq F} g(x) $$ and gurobi was unable to find a feasible solution. I then relaxed ...
John's user avatar
  • 31
3 votes
0 answers
124 views

Continuous optimization with a Euclidean TSP objective

I am trying to solve a problem of the form $$\min_{x_1,\dots,x_n} f(x_1,\dots,x_n)$$ subject to a constraint that $\mathrm{length}(\mathrm{TSP}(x_1,\dots,x_n))\leq c$, where $x_1,\dots,x_n$ are all ...
Tom Solberg's user avatar
3 votes
0 answers
120 views

From Quadratic to MILP?

I am playing around with some Quadratic Programs (QPs), and I want to check if my reasoning is right concerning a re-modeling from QP to MILP. So, let's consider the below QP: (QP) $\min c^T x + x^T Q ...
Matheus Diógenes Andrade's user avatar
3 votes
0 answers
132 views

Creating Disjunctions for MIP Model. Code taking too long to execute

I am currently following this guide in the hopes of building a linear programming model in python and solving using gurobi. https://towardsdatascience.com/schedule-optimisation-using-linear-...
SevenArmy's user avatar
3 votes
0 answers
56 views

Separating two LP solutions at the same time

In a cutting plane algorithm for integer linear programming problems you would usually use an LP solver to get an extreme point of the polyhedron corresponding to the LP relaxation. Let's call that ...
Sune's user avatar
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3 votes
0 answers
135 views

When and where the cutting plane method should be applied?

As the cutting plan algorithm is a method to strengthen the feasible space of the linear programming, specifically in the MILP problems to invoke the integer solutions, it may be a problem-based ...
A.Omidi's user avatar
  • 8,950
3 votes
0 answers
54 views

PWL constraints efficiency

So, I'm trying to optimize MILP, which has PWL constraints. I use gurobi, and when I'm optimizing model without those constraints, gurobi finds solution in a matter ...
Aisec Nory's user avatar
3 votes
0 answers
56 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 ...
Meth's user avatar
  • 424
3 votes
0 answers
109 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\\ ...
Samuel Bismuth's user avatar
3 votes
0 answers
124 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 ...
A.Omidi's user avatar
  • 8,950
3 votes
0 answers
97 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 ...
sascha's user avatar
  • 527
3 votes
0 answers
139 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 ...
Víctor Fing's user avatar
3 votes
0 answers
450 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 ...
Antonio Piemontese's user avatar
3 votes
0 answers
96 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 ...
Joris Kinable's user avatar
3 votes
0 answers
76 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 ...
OR Junior's user avatar
  • 521
3 votes
0 answers
53 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 ...
Snowflake's user avatar
  • 517
3 votes
0 answers
228 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 ...
tcokyasar's user avatar
  • 1,249
3 votes
0 answers
89 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 ...
cmp's user avatar
  • 327
3 votes
0 answers
90 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 ...
Clement's user avatar
  • 2,252
3 votes
0 answers
62 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(...
Clement's user avatar
  • 2,252
3 votes
0 answers
72 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
S_Scouse's user avatar
  • 803
3 votes
0 answers
68 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 $c$ ...
Ishan Kashyap Hazarika's user avatar