Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

Filter by
Sorted by
Tagged with
8
votes
2answers
362 views

How can I transform this MILP into an LP problem?

I have a MILP problem with one of the constraints is given below. Sometimes, even for a small-sized problem, the solver takes a very long time to find a solution. What could be an efficient ...
8
votes
1answer
246 views

Speedup or Caching for a Multi-Iteration MIP problem

I'm solving an MIP: \begin{align}\mathrm{arg\,min}&\quad\sum\limits_{i}{x_i}\\\text{s.t.}&\quad A\,x\geq1,\end{align} where both the matrix $A$ and vector $x$ are boolean valued, and $A$ is ...
11
votes
1answer
315 views

Minimize number of pieces required to cover distances, with overlap

The specific optimization problem I'm trying to solve is this: Find the minimum integer number of $2$m pieces required to cover $2$ or $4$ distances of length $D$ given that adjacent pieces must have ...
12
votes
3answers
1k views

Does it make sense to use strict equality constraints in optimization?

Once I learned from some post that the strict equality constraint in an optimization problem does not make much sense. We should always use $\le$ constraint. How much truth is in this? If I must have ...
15
votes
2answers
254 views

Search approach to solve optimization problem with only a minimum where time series get scaled

Currently, I am working on a relatively simple optimization problem: There is a set of time series (red) that get summed up to a cumulated time series (blue). The red time series have different forms ...
12
votes
1answer
305 views

Linearization of the product of two real valued variables - Binary expansion approach

I want to minimize the following objective function: \begin{align}\min &\quad x\cdot y\\\text{s.t.}&\quad2 \le x \le 5\\&\quad5 \le y \le 10.\end{align} Since the objective function is ...
11
votes
0answers
118 views

Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
13
votes
2answers
391 views

Black-box optimization with linear programming?

In my research, I do a black-box optimization based on a simulation model with nonlinear properties. The simulation model gets an operation plan for a time period and then returns a time series, which ...
7
votes
0answers
59 views

KKT conditions validation- one dual variable equating to two values

I have the following optimization problem: \begin{alignat}2\min &\quad A(t)\cdot x(t)-B(t)\cdot y(t)+C(t)\cdot z(t)-D(t)\cdot k(t)\\\text{s.t.}&\quad z(t)+z_1(t)-y(t)-y_1(t)+x(t) = k(t);&...
11
votes
1answer
375 views

Suggested Resources for Non-Linear Optimization

I recently completed an undergraduate course in Linear Programming and Operations Research. I am willing to look into advanced concepts and Non-Linear Optimization algorithms and also, their method of ...
12
votes
3answers
2k views

YALMIP-like modeling environment in Python

What are the handiest optimization parsers out there? Is COIN-OR's PyPy being used actively? I am currently trying to do an optimization project in Python, but I am used to using MATLAB + YALMIP ...
8
votes
1answer
277 views

GLPK: meaning of the "marginal' column in the solution output

I'm using GLPK to solve an LP. I use it through its standalone solver, that I call with the glpsol command, and I get the solution detail written in a file using ...
13
votes
1answer
299 views

Categorization of optimization models

For many families of optimization problems there is some sort of classification scheme. I am thinking about the triple notation for machine scheduling introduced in "Optimization and approximation in ...
17
votes
3answers
1k views

TSP with revenue maximization

How to approach a travelling salesman problem with an aim to maximize revenue at each town visited in a certain number of days (total number of towns is greater than what can be visited in the given ...
8
votes
0answers
159 views

Relationship between two minimization problems

Let $\mathbf{A}$ be a ${n\times J}$ matrix with $A_{ij}\geq0$ (and $A_{ij}>0$ for most $ij$, there cannot be any rows or columns that consist only of $0$s), $Q=\left\{\mathbf{q}\mid \mathbf{q}\in\...
10
votes
4answers
1k views

Integer programming problem with simple quadratic objective function in Python

I have $n$ objects that need to be divided among $k$ groups. Each group must receive at least $5$ objects. In addition, the percentage of objects in group $i$ should be as close as possible to $p_i$ ...
6
votes
2answers
235 views

A heuristic approach to solve a MILP problem?

I have the following optimization problem which is a MILP. I can solve it with a MILP solver. This one I posted here Is there a heuristic approach to the MILP problem? Since I have an additional but ...
8
votes
1answer
116 views

Can I use an MDP for a stochastic inventory model when my demand distribution is non-stationary?

Most formulations of Markov Decision Processes for stochastic inventory models I've come across assume a fixed demand distribution. But in my case I have a time series forecast with a non stationary ...
9
votes
1answer
148 views

Finding Dual Objective

I have the following simplified optimization problem: \begin{align}\max &\quad ax+by\\\text{s.t.}&\quad0 \le x \le \overline X\\&\quad0 \le y \le\overline Y\\&\quad z = E-x+\beta\cdot ...
8
votes
2answers
437 views

Is there a greedy heuristic approach to the MILP problem?

I have the following optimization problem which is an MILP. I can solve it with an MILP solver. \begin{alignat}{1}\max_{x_n,t}\,&\quad t\quad\\\text{s.t.}&\quad\sum_{n=1}^{N} x_n \,&= M\\...
12
votes
2answers
375 views

How difficult is it to understand a Machine Learning method based on integer optimization?

I'm trying to understand a paper called "Supersparse Linear Integer Models for Predictive Scoring Systems" by Ustun, Tracà and Rudin, who introduce a really interesting method for generating an ...
6
votes
1answer
97 views

MPS file generation

I have a code in MATLAB which uses YALMIP to structure my optimization model and solve it via a solver. I would like to obtain a .mps file out of my model, apparently, YALMIP does not produce this if ...
10
votes
1answer
116 views

Wild oscillation of dual infeasibility in Gurobi mixed-integer solver

As the question says, I am wondering what happens "behind the scene" when the Dual Infeasibility column of the Gurobi runtime log oscillates wildly, before Gurobi eventually quits with infeasibility. ...
11
votes
1answer
210 views

Looking for books in the same style as Hans Kellerer 2004, Knapsack Problems

I really enjoyed reading Hans Kellerer, David Pisinger, Ulrich Pferschy 2004 book Knapsack Problems. Can anybody recommend books in a similar style, about some other classes of problems / optimisation?...
10
votes
2answers
694 views

How to use warm start to solve MIPs efficiently?

I'm working on the scheduling model which takes a long time to solve to optimality (even for a small instance), therefore I would like to use a warm start (MIP start) to solve the problem. I'm using ...
11
votes
2answers
142 views

Is a "multistep" or "multiphase" Newsvendor model possible?

I'm trying to address the question of how many times should I order a product from my supplier, assuming highly stochastic demand. In my mind there would be something like the Newsvendor model, but ...
9
votes
1answer
173 views

Solving convex programs defined by separation oracles?

General question: What software can solve convex programs defined by a separation oracle? The objective function is concave, and the feasible set is a polytope. By a separation oracle I mean that I ...
9
votes
2answers
137 views

Partial derivative of LP solution $(x_1 , \ldots, x_n)$ w.r.t. $x_i$ or $a_i$

Suppose I have an optimal solution and I want to know how the solution would (likely) change if one of the coefficients in the objective function changes, or if I add a constraint that forces $x_i$ ...
6
votes
0answers
258 views

How to make constraints satisfy disciplined convex programming guidelines?

How do I turn my convex constraints (described below) into constraints that are DCP so that I can solve them in CVXPy? Is there some ``cheat sheet'' of standard tricks? I'm trying to implement the ...
12
votes
1answer
2k views

If-then constraints in MIP programming

For continuous variables $x$ and $y$, the constraints are: ...
9
votes
2answers
229 views

How to formulate a MIP that can minimize the costs with a combination of subsets given a set?

I am trying to solve the following problem. I have a set $\{1,2,3\}$, which gives the following subsets with its costs: $\{1\}=8$, $\{2\}=9$, $\{3\}=7$, $\{1,2\}=9$, $\{1,3\}=18$, $\{2,3\}=15$ and $\{...
15
votes
1answer
226 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
16
votes
4answers
315 views

Tool/Editor to visualize optimization problem files and solutions

Is there a tool with a graphical user interface which helps to visualize optimization problem files (e.g. lp/mps) and solutions? Let's say you have an optimization problem and a solution and want to ...
9
votes
1answer
1k views

Graphical method in linear programming

This page describes the graphical method to solve a linear program. The formulation is as follows. $$\begin{alignat}{2} \max &\quad Z = 200W + 100B\\ \text{s.t.} &\quad 1W + 0.8B &&\...
10
votes
0answers
165 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 ...
7
votes
0answers
535 views

Having trouble with objective function in Python: "GurobiError: Variable not in model". What else could I try?

I am trying to figure out how I can write this objective function into python using Gurobi. I have to minimize the sum of the product of three dictionary's values. The reason I am confused is that ...
8
votes
2answers
3k views

How can I add this conditional constraint to my model in Python?

I am creating an optimization model with 2 sets of binary decision variables. The first, site, is regarding which of 380 cities to place manufacturing sites in, and ...
5
votes
0answers
34 views

In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
11
votes
2answers
83 views

In portfolio optimization, how do we estimate the variance of a new asset?

Say I want to do Portfolio Optimization using the mean-variance approach (i.e Markowitz model), but that some of my assets are new with no returns history. I can use a judgmental (expert knowledge, ...
7
votes
1answer
105 views

Count this to the family of Job Shop Problem?

I will explain the problem in a simplified version. Three Tasks: $T_1, T_2, T_3$ Four Machines: $M_1, M_2, M_3, M_4$ The machines $M_2$ and $M_3$ make the same processing, so they are parallel. ...
14
votes
4answers
292 views

Does this $0-1$ integer program have any speciality?

Given matrix $A \in \{0,1\}^{m \times n}$ and vector $b \in (\mathbb{Z^+})^m$, where $\mathbb{Z^+}$ is the set of positive integers, $$\begin{array}{ll} \text{maximize} & c^\top x\\ \text{subject ...
8
votes
1answer
243 views

Standard cumulative distribution function with optimization model variable

We all know that expressions in mathematical optimization models can't contain "black boxes" around a decision variable since everything has to be written using mathematical expressions. For example, "...
9
votes
2answers
1k views

Reading an LP/MPS file using Pyomo software

I would like to know is it possible to read an LP/MPS file into the Pyomo software and solve the problem? If so, how can I do that?
18
votes
4answers
965 views

PhD-level textbooks on linear programming

My graduate Linear Programming class uses Bertsimas & Tsitsiklis's Introduction to Linear Optimization. Are there any alternative texts that I could use to supplement this textbook (mainly the ...
9
votes
1answer
218 views

Should I factor in time as a parameter or a variable in a scheduling problem with MILP?

I am trying to formulate a problem that will spit out an optimal schedule for my tasks to be completed. To keep the information confidential, I will refer to my tasks as papers that need to be written....
8
votes
2answers
2k views

How to linearize a constraint with max

I would like to linearize a constraint with max. I have the following constraint: $$\max_{pcj}X_{pwcj}\leqslant L_{wk}.$$ With this constraint, I would like to ensure that for $\forall w \in W$, no ...
9
votes
1answer
616 views

A variant of the Shortest Path Problem

Consider a layerwise directed acyclic graph DAG, $G=(V,E)$ and two vertices $s$ and $t$. $s$ is connected to all vertices in $L_0$, $L_0$ is connected to all vertices in $L_1$ and so forth. Consider ...
9
votes
2answers
598 views

What is the difference between job shop scheduling and resource constrained project scheduling?

I read here https://slideplayer.com/slide/3353960/ that RCPS is a generalized version of job shop scheduling. I'm new to this area and I'm trying to classify a specific variation of these types of ...
6
votes
2answers
722 views

Solving a Certainty Equivalent (Decision Analysis) problem

I am solving a Certainty Equivalent (Decision Analysis) problem. The problem is a Risk-Averse Case - a deal of $60\%$ chance to win $\$100,\!000$ and $40\%$ chance to lose $\$10,\!000$. Suppose the ...
6
votes
1answer
93 views

How to decide the hiring headcount for a retail department

The job responsibility is exactly the same in the department. The department has a total number of working hours required. The total retention is about 50% a year, and the hiring cost is about $2000 ...