Questions tagged [optimization]

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

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Is mathematical programming synonymous with algebraic modelling?

Based on my on-again-off-again internet search of optimization problems over the past few years, the two terms seem to cover largely the same way of representing problems, if not the identically. I'm ...
user2153235's user avatar
1 vote
2 answers
50 views

How to maximise black-box function defined on a subset of integers, with access to its derivative?

The basic form of my problem is as follows. Let $S = \{ 1, 2, ..., 30 \}$. I have an integer-valued function $f$, whose argument is an integer-valued vector $\vec{x} \in S^{200}$. I also know that ...
j x's user avatar
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0 answers
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How to Find Optimal Way to Allocate a Budget?

How can I find the optimal or close to optimal way to allocate a budget if I have revenue and spending data? I was thinking of using linear programming, but Im assuming it wouldnt work as the ...
user13229's user avatar
-1 votes
0 answers
22 views

how to implement the correlation coefficient in cvxpy and how to rewrite cp.diff(cp.cumsum(x)/(cp.cumsum(x)[-1])

suppose that I have 2 sets of data, x and y,where x can be ...
Allen Zhang's user avatar
1 vote
2 answers
2k views

I have found so many tools that can solve optimization problems, I want to know which workflow is the best or the most practical?

I have found so many tools that can solve optimization problems, I want to know which workflow is the best or $\color{blue}{\text{the most practical}}$? Any preference? Miscelleous Wolfram ...
138 Aspen's user avatar
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1 vote
1 answer
107 views

0-1 Knapsack optimization problem

Can anyone explain how the writer rewrite the objective function in (7) to be written as (8)?
AhmedHassan's user avatar
0 votes
2 answers
65 views

Sewing lines orders assignment

What are the algorithms used to assign orders to sewing lines based on order priority, line capacity, time taken to sew garments, due dates, specialization of lines etc.
Tharindu Kariyawasam's user avatar
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0 answers
46 views

monte carlo for a selection problem

What type of Monte Carlo simulation is suitable for solving this problem? Also, how can we select results after simulation to guarantee feasibility?
Mohammad Reza Salehizadeh's user avatar
1 vote
0 answers
77 views

CVXPY ECOS and SCS solver stuck in local optima for convex problem?

Consider the following optimization problem: \begin{equation*} \begin{aligned} & \underset{z_{k, t}}{\text{maximize}} & & \sum_{k} \sum_{t} \text{concave-function}(z_{k,t}) \\ & \text{...
rutkov's user avatar
  • 11
0 votes
2 answers
89 views

Are Metaheuristics Global Optimizer?

In recent years, we experience an explosion in the publication of metaheuristics. They claim finding the global optimum of the optimization problems they are applied on. Is that claim correct? Can ...
Clement's user avatar
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2 answers
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Problem 8.17 of Korte and Vygen

An airline wants to conduct a given set of scheduled flights with as few airplanes as possible. All available airplanes are of the same type. For each flight we know the departure time and the flight ...
Nico Konrad's user avatar
1 vote
1 answer
106 views

How to turn off tree search in fico xpress ? Couldn't see relevant documentation

trying to solve a very large problem , using heuremphasis as 3 , cutfreq=0 , scaling =4, run time reduced significantly however , solver spends 400 seconds in tree search , but couldn't see any ...
21vs's user avatar
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1 vote
0 answers
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satisfactory vs optimal decision making

In most classical game theoretic problems (situations in which more than one decision maker impacts the state of the environment), we assume that the decision-makers optimize their objective function. ...
Mohammad Reza Salehizadeh's user avatar
0 votes
1 answer
113 views

PuLP is ignoring constraints, and setting everything to 0 for minimization problem

I have a multi-objective optimization problem I am trying to solve with competing objectives. I am trying to model a network of industrial businesses which can share wastewater rather than sending it ...
Caleb O's user avatar
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3 votes
2 answers
183 views

Can an Operations Research model optimize on a vector's indexes?

Theoretical model Suppose that I have an input vector $E_{t}\in\mathbb R^n$ for $n\in \mathbb N$ Suppose that I want to optimize $\displaystyle\max_{t,x} E_tx$. That is, my decision variables are the ...
JKHA's user avatar
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2 votes
0 answers
155 views

Global optimizers handling minimization of an expression arising from the likelihood of a multivariate normal

I am interested in converting the following optimisation problem into a form that an exponential cone and/or SDP solver such as MOSEK can handle. This is a multivariate version of the question I ...
cfp's user avatar
  • 259
3 votes
1 answer
724 views

Scipy.optimize can't get correct answer when objective is Piecewise Linear Function and Equality Constraint

I'm encountering a puzzling issue with SciPy's minimize function in a constrained optimization problem. My objective is to optimize a piecewise linear function with ...
Yiyuan Chen's user avatar
2 votes
1 answer
78 views

Optimizing for an unknown conjugation matrix

I am trying to find the invertible matrix $M$ satisfying: $$v_t'= MA_tM^{-1}v_t$$ For a dataset of observed transformations $(v_t',A_t,v_t)_t$. Note, there is a different linear transformation $A_t$ ...
hamza keurti's user avatar
0 votes
1 answer
28 views

Grouping of a list of elements in fixed order to maximize the total return of all the groups

I'd like to ask about if there's an existing type of problems that fits to my question. (Searching it for a while but cannot get to the point) Basic Problem Description: Given a sequenced list (order ...
X.Arthur's user avatar
  • 103
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0 answers
41 views

Can ADMM be applied to "latently coupled" variables?

I've been studying a paper where the authors employ the ADMM in a way that has left me somewhat perplexed. The paper focuses on addressing a robust principal component analysis (RPCA) problem, ...
Piko Mone's user avatar
5 votes
2 answers
167 views

Global optimizers handling minimization of expressions like $\log{v}+\frac{1}{v}$

Consider the simple problem of maximum likelihood estimation of the variance of a mean zero normal distribution. The expression to be minimised is: $$N \log{v}+\frac{1}{v}\sum_{n=1}^N{b_n^2},$$ where $...
cfp's user avatar
  • 259
2 votes
2 answers
96 views

benders decomposition master problem scale large

I am dealing with a benders decomposition problem, in which there are 100 sub-problems that need to be solved. During each iteration, 100 new optimal cuts will be added to the master problem. I would ...
XXia's user avatar
  • 39
0 votes
0 answers
47 views

nonlinear least square

The following objective function is non-convex. How can we solve min$ \left|| A^{\dagger}A-I \right||_F $? Will adding an auxiliary matrix be helpful or not? I am trying to solve it using ADMM Any ...
Nnn A's user avatar
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2 answers
80 views

Turning K-Medoids into an optimization problem

I am studying a clustering problem. By reading the literature, I found that the clustering problem can be converted into an optimization problem, K-Medoids can be converted into an integer programming ...
XXia's user avatar
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1 vote
1 answer
258 views

Standby optimization in Aviation

I am looking for a heuristic/exact algorithm to model this problem related to airport standby. The goal here is to suggest different standby slots required to cover all the flights leaving an airport. ...
Shibaprasad's user avatar
0 votes
0 answers
70 views

Cost function value of relaxed ILP after rounding is less than or equal to the optimal one

I have a minimization problem for which I am having some misunderstandings and confusions with regard to some results I am getting for an ILP and its LP relaxation. In the ILP I have two decision ...
LyLa's user avatar
  • 1
5 votes
3 answers
616 views

Algorithm needed to find optimum area of 2-dimensional data set

The python script depicted below generates the following toy data set. I need to determine the values for $x_{min}$, $x_{max}$, $y_{min}$, $y_{max}$ describing a rectangular area where the sum over ...
7824238's user avatar
  • 151
2 votes
2 answers
92 views

Differentiability of solution of optimization problem with respect to constraint (properties, conditions etc)

Assume you have the following simple constrained optimization problem: $$ \begin{equation} \begin{split} &\min_x f(x) \\ & s.t \quad g(x) = c \end{split} \end{equation} $$ where $f,g$ are both ...
c zl's user avatar
  • 21
4 votes
0 answers
91 views

Any recommendations for learning about polyhedra and integer programming?

My knowledge on convex polyhedra and systems of linear inequalities (facets, edges, Farkas Lemma, projections, duality, etc.) is very scattered, and I'l like to go through a book to solidify it. I'm ...
user56202's user avatar
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1 vote
1 answer
99 views

Creating a decision variable that is the sum of other variables in PuLP

I'm trying to represent the following problem with PuLP: A car factory needs to maximize profit with an X amount of car models. Each car model has an individual profit and a manufacturing limit, and ...
user avatar
1 vote
1 answer
105 views

Column generation for solving minimum cost multicommodity flow problem with additional edge disjoint constraints

I'm working on an integer programming problem that's fundamentally a minimum cost multicommodity flow (MCMF) problem with additional constraints. I'm exploring the use of column generation to solve it,...
Sina_Alef's user avatar
0 votes
1 answer
123 views

Question on Column generation

I am implementing a Column Generation algorithm to solve a set partitioning problem. The master problem takes the form : $\min \sum_{i \in I} c_i \lambda_i$ s.t $\sum_{i \in I} a_{ji} \lambda_i = 1, \...
CHE's user avatar
  • 113
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0 answers
17 views

Online auction system design resources

I’m interested in understanding how one might design online auctions (think Google, Facebook, eBay, etc.) I’m curious how the price of a physical item, ad, NFT, etc might be a function of economic ...
jbuddy_13's user avatar
  • 519
6 votes
3 answers
671 views

Can determining the unique fixed point of a function be posed as an optimization problem?

Consider the function $f : \mathbb R \to \mathbb R$, which has a unique fixed point $x^* \in \mathbb R$, such that $x^* = f(x^*)$ and there does not exist another $x \in \mathbb R$ such that $x = f(x)$...
mhdadk's user avatar
  • 601
3 votes
1 answer
93 views

How to modify Benders decomposition to handle overlapping or shared variables among the subproblems

I have a problem that can be separated into a master problem and two subproblems, SP-A and SP-B. SP-B share some variables with SP-A, and the shared/overlapping variables from SP-A cannot be fixed for ...
user4444's user avatar
2 votes
0 answers
72 views

Superscript use in optimization formulations

What are common uses of superscripts in mathematical optimization formulations? None of my optimization books start at the level of "proper" variable labeling. When I ask ChatGPT, it ...
Bryan R's user avatar
  • 21
-1 votes
1 answer
105 views

Grocery Store Problem

I have an issue with my Excel function for a grocery store problem and I am not sure where I messed up the constraints. I have the value of the solution it should be (cost = 8,283). I need to make a ...
zoomonkey101's user avatar
1 vote
2 answers
96 views

Need help writing a metaheuristic problem

I have a matrix which contains compatibility scores between objects. I have 56 objects, thus, the matrix dimensions are 56*56. I need to group said objects in groups of 8 to 10 elements. I have tried ...
slow_learner's user avatar
-1 votes
2 answers
140 views

Need help with integer programming exercise

This is an exercise from Wolsey that I can't solve. Show how to go from Equivalence (1) to (2) and from Equivalence (2) to (3): $$ \begin{align} X &= \{ x \in \{0, 1\}^4~\mid~97x_1 + 32x_2 + ...
Tio Pikachu Lizardon's user avatar
1 vote
0 answers
108 views

Applications of Knapsack and Cutting Stock in Pure Math

I'm giving a seminar to PhD students in pure math, and one of the things I'd like to do is show that more applied optimization can also make its way into pure Mathematics. As for classical problems, I'...
J. Dionisio's user avatar
-1 votes
1 answer
67 views

MIP formulation for a lower semi-continuous function

How can I formulate in mixed linear programming (a set of constraints) the following issue. I have an objective function $\underset{x}{\max} g(x)$. I need to convert a continuous linear function $f(x)$...
Di Al's user avatar
  • 11
1 vote
0 answers
55 views

Resources about Busacker & Gowen algorithm

I have a relatively hard time understanding the Busacker & Gowen algorithm. I could not find any resources on it, contrary to Ford-Fulkerson method that is described in Comen's "Introduction ...
satk0's user avatar
  • 123
1 vote
1 answer
96 views

Maximizing sum of probabilities with variable distributions

Suppose $\\{X_i\\}$ are binary decision variables and $\\{A_j\\}$ are Skellam random variables with $(\mu_1, \mu_2) = (\sum_i b_{i} X_i, c_j)$. Here, $b_i, c_j \in \mathbb{R}^{\geq 0}$ are constants. ...
Jacob's user avatar
  • 111
1 vote
1 answer
153 views

Job Scheduling with Energy Consumption using Linear Programming

I'm looking for some advice for an optimization problem regarding scheduling jobs in a datacenter. So I have a list of jobs and each job has a required time for finishing and a number of cores it has ...
wind.leon's user avatar
0 votes
2 answers
159 views

Algorithms to use for an assignment problem

Here is my problem: There are five sewing lines. When sample orders arrive, we have to assign them to the available line which is more skilled on a particular garment. Each line is given a rank ...
Tharindu Kariyawasam's user avatar
0 votes
2 answers
90 views

How to design a constraint to control flow in a non-network optimization model

I'm working on a production scheduling problem with a MIP model somebody left to me. This is a discrete-time model in which the constraints used to control the production and consumption of product p ...
CangWangu's user avatar
1 vote
0 answers
56 views

transform minimize weighted sum of absolute value into a linear optimization

For example, we have an optimization problem $$ \min \sum_{i=1}^{n} |w_{i} - a_{i}| b_{i} \quad \text{s.t.} \quad \sum_{i=1}^{n} c_i w_i = 0 $$ and $a_i, b_i, c_i$ are given. How to convert it into a ...
Pique's user avatar
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1 vote
0 answers
39 views

How would the Contextual Stochastic Optimization framework be applied to a bilevel problem whose uncertain parameters lie in the inner problem?

Although I only heard about Contextual Stochastic Optimization (CSO) a few months ago, I know now the excitement has been going on for a while. I'm not sure if the idea of CSO has been around for long,...
Jxson99's user avatar
  • 141
0 votes
0 answers
79 views

Validity of a VRP formulation

A delivery company is operating in Virginia and has a fleet of trucks that are used to deliver groceries from supermarkets to consumers. The company delivers orders and operates its fleet for one ...
talkandtalkers's user avatar
1 vote
1 answer
92 views

Optimization algorithm for space debris

I'm currently working on a research project to optimize the recovery of space debris. We have to recover 50 pieces of space debris with the minimum number of missions possible. The missions are sent ...
HunKhle's user avatar
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