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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2
votes
1answer
14 views

warmstarting simplex algorithm- how much can problems differ from each other?

I'm working on an implementation of the simplex algorithm. I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem. I couldn't really say ...
3
votes
1answer
40 views

Control & Experimental Group Selection Methodology using STDEV and T-Test?

I would like to know if my methodology was 'correct': I am trying to conduct an experiment on my stores. I would like to find out the effect of a marketing campaign on the number of transactions. Only ...
1
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1answer
111 views

fpl and constraints about centers

Does anybody know how we could optimise fpl problems with additional constraints?
3
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3answers
641 views

Model if-else statement

I need to build a if-else constraint for this statement, where $x_P$ and $x_I$ are decision variables, and $C$ is a constant: if $x_P \ge C$ then $x_I = x_P - C$ else $x_I = 0$. Any help is greatly ...
1
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0answers
96 views

Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
2
votes
1answer
148 views

How to convexify log(convex) function?

I have the following optimization problem: \begin{align}\max_x&\quad\log_2(1+|a+bx|^2+cx^2)\\\text{s.t.}&\quad0\le x\le1\\&\quad(1-x^2)\ge\text{constant}\end{align} where $a$ and $b$ are ...
4
votes
1answer
82 views

Optimization of strongly convex functions with approximate evaluations of gradient and Hessian

Suppose I want to find the minimum of a differentiable, strongly convex function $f:\mathbb{R}^n\to\mathbb{R}$ with constant $\mu>0$. That is, for all $x,y\in\mathbb{R}^n$, I have that: $$f(y) \geq ...
1
vote
1answer
47 views

Find an upper bound for an objective function

My objective function is $\log_2(1+{x^2y^2})$ and I found two upper bounds for $x^2$ and $y^2$. For example, assumed that we have the following upper bounds: $x^2\leq\text{constant}_1^2$ and $y^2\leq\...
3
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0answers
99 views

Two binding constraints - Linear Programming

I'm having some troubles to continue solving my system, I'm used to solve such systems but with "one" binding constraint, if someone could give me some helpful hints so I can solve it I will ...
0
votes
1answer
106 views

Invalid solutions to Piecewise Mccormick Envelope Implementation

I am currently trying to implement a piecewise McCormick envelope in Drake (c++). The current issue I am having is that the solution produced by the optimization does not produce a valid $x$ and $y$ ...
3
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1answer
145 views

Oscillations with (online) mixed-integer optimization problem

I have the following mixed-integer optimization problem: \begin{aligned} \max_{x,y} \quad & \sum_i x_i - \|wx\|_2 \\ \text{s.t.} \quad & \sum_i x_i \leq A \\ \quad & x \leq x_{\max} y \\ ...
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0answers
40 views

What will be an efficient heuristic approach for this optimization problem

I am looking for a heuristic approach to this optimization problem. How to mathematically formulate the optimization problem? RobPratt suggested an mathematical formulation for this problem which is ...
4
votes
2answers
182 views

Mixed-integer optimization with bilinear constraint

So I have an optimization problem of the following form: \begin{aligned} \max_{x,y} \quad & \sum_i x_i \\ \text{s.t.} \quad & \sum_i x_iy_i \leq a \\ \quad & x_{\min} \leq x \leq x_{\max} ...
2
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3answers
115 views

Linearizing a Max Function in the constraint - not working

I have a minimization function which is in its simplest form looks like below. I am including the index of the variables. ...
5
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2answers
85 views

Is $\min \ x^3 \ \mathrm{s.t.}\ x \geq 0$ a convex problem?

The problem $$\min \ x^3 \ \mathrm{s.t.} \ x \geq 0$$ is sometimes said to be a convex optimization problem. $f(x) = x^3$ is not a convex function. However, in the domain of $x\geq 0$ it is convex. So ...
2
votes
1answer
63 views

Impose binary constraint on integer matrix with CVXPY

So I have the following matrix: \begin{equation} P_{i,j}= \begin{bmatrix} x_0 & x_1 & x_2 \\ y_0 & y_1 & y_2 \\ z_0 & z_1 & z_2 \end{bmatrix} \end{equation} where ...
1
vote
1answer
73 views

Relation between order quantity and average cycle stock

Annual demand: $1000$ units Unit cost: $5$ dollars Company replenishes the inventory two times per year. Average Cycle Stock: $300$ I am asked to compare average cycle stock with number of ...
3
votes
1answer
61 views

Clustering problem involving multidepots and customers requiring commodities located exclusively in an specific depot

I'm trying to solve a clustering problem that's similiar to a VRP Pickup and Delivery problem with multiple depots and customers. Each customer demands a commodity that is exclusively found on one ...
6
votes
2answers
157 views

Index of element in MILP vector decision variable that equals 1

Consider a decision variable in a MILP constrained: $$\sum_i p_i = 1$$ $$p_i\ \in \{0, 1\}$$ Obviously one element in $p$ is 1 and all others are 0. How can I set a decision variable to the index i of ...
0
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0answers
74 views

Mixed Integer Programming - Model Formulation for A Resource Allocation Problem

There are a number of orders, which needs to be shipped. For each order, there may be 1 to 3 route options. The problem here is to find out the best allocation (combination) of orders among these ...
2
votes
1answer
43 views

How to define a stationary point of the MINLP problem?

As we all know, KKT point and stationary point are well defined when the optimization variables are continuous in the problem. Now, I want to know whether there exist some special points except for ...
2
votes
0answers
29 views

How to use NEOS without using Pyomo

I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
2
votes
0answers
51 views

How to model non-zero minimum constraint?

I found following way to model a minimum constraint but in my case I need a non-zero minimum value. So in this figure, if any value of x_i is 0 then answer is 0 (assume x_i >=0) but I need non-zero ...
9
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4answers
553 views

Recommendations for OM blogs

Could someone suggest good blogs to follow for researchers in Operations Management/ Supply Chain Management /Operations Research?
1
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1answer
88 views

complexity order of the interior point method

I was wondering why the complexity order of the interior point method is O()^3 or O()^3.5? Much appreciate your time and consideration.
5
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1answer
110 views

Maximize number of backups that fit on backup drive

This is an intrinsically "practical" question, but it leads to a well-defined mathematical problem. Let me start with the practical part: I regularly back up my data. My backup strategy are ...
1
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0answers
147 views

Is there any Operations Research group in Clubhouse?

Since the introduction of the Clubhouse app, there are several groups on different topics and people can talk about specific topics in different fields. Is there any group related to "Operations ...
0
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0answers
74 views

MILP formulation for “if (a>=b) then c=1, 0 otherwise”

I need to build a MILP (Mixed integer linear programming) constraint form this if-else statement. In my formulation a and b are two continuous variables and c is boolean. if (a >= b) then c = 1, 0 ...
4
votes
1answer
143 views

how to implement an optimization function with polynomial in Gurobi (Java)

I have the following problem: I have an objective function with the optimization variable $x$, which looks simplified like this: $ZF = (a+b)*(x+1)$ Here $a$ is simply a constant value. However, behind ...
8
votes
5answers
632 views

Paper suggestions on local search algorithms

I am looking for papers (or any resources) that go deep into the details of implementing local search algorithms. I don't want an introductory paper on the subject. Rather, I would prefer a survey ...
0
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0answers
40 views

Linear equation from pairs of values with conditions in Gurobi (Java)

How can I create a linear equation in Gurobi (Java) from values (x-y value pairs) that also has the following properties: $\forall x \leq 0 \Longrightarrow y = 0$ The linear line/equation should have ...
9
votes
3answers
304 views

To which area does constraint programming belong?

The problem I solved is a flow-shop scheduling problem with parallel machines. I solved it with the IBM ILOG CPLEX Optimization framework. There I used the constraint programming (CP). The question ...
0
votes
1answer
121 views

if-else query depending on optimization variable in Gurobi (Java)

I am looking for the most elegant solution to the following problem: I have an if-else query that depends on my optimization variable $x_i$. If $a \leq b_i + x_i$, the parameter $c$ should take the ...
2
votes
1answer
60 views

Constraining flow into a node and out of a node using Min Cost Flow input

Let's say I have a graph $G=(V,E)$ where each vertex has an edge going both into and out of it (i.e. cyclic, akin to the kidney donor pair problem). Now suppose we have a capacity $u_{ij} = 1 \forall(...
2
votes
3answers
74 views

Link a binary variable to continuous variable in Java Gurobi

I have the following problem: Depending on my continuous optimization variable $S_m$, I would like to introduce a binary variable $x_m$, which, depending on the value of $S_m$ (greater or less than 0) ...
3
votes
1answer
105 views

Min Cost Flow with lower bound reduction to MCF algorithm

We define the Min Cost Flow Problem with Lower Bounds (MCFPLB) as a generalization of the usual Min Cost Flow. The input consists of: a directed graph $G=(V,E)$ capacities $u_{ij} \geq 0$ for each ...
5
votes
3answers
1k views

How does a solver generally know whether a solution is optimal?

I was wondering how does the solver for a MILP determine whether a solution is optimal. I am having a hard time to believe that the solver actually tries all solutions, since in some cases I have over ...
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 ...
1
vote
1answer
75 views

Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
4
votes
2answers
124 views

Continuous water-filling optimization problem

Disclaimer: this question has been previously posted on Math StackExchange. I reposted it here since I did not receive any satisfactory answer there and a user suggested to re-post it here. Let $x\in\...
1
vote
0answers
75 views

PYOMO - Optimization for the daily production of a products demand minimizing the production cost

I am trying to build an optimization model using PYOMO for the daily production of a product demand, minimizing the production cost. I have demand, production capacity (by machine by day), production ...
2
votes
1answer
436 views

How to learn Optimization?

I am a 2nd year PhD student in a (mostly) pure Mathematics department. I do not have any prior experience in applied mathematics, but I've recently had a change of heart and decided to study ...
2
votes
0answers
72 views

Solving transportation problem by the Network Simplex

I am trying to solve the following problem using Network Simplex method. But I have questions. My attempt: Basis Matrix$(B)$ Rows: 1, 2, 3, 4, 5 Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) $$ \...
3
votes
1answer
84 views

How to assign values to array in CPLEX with C++?

I am new to CPLEX. I am using CPLEX with Xcode in macOS. I have three arrays (known parameters used in optimisation) which I define as ...
1
vote
1answer
93 views

Solving general minimum cost flow problems using only one demand and one supply node

This is a practice in using reduction. Suppose I have a solver that only allows input to a MCF that specifies only one demand and one supply node. How could I use this solver to solve general MCF ...
1
vote
2answers
98 views

Should I process the data or add a new constraint to achieve the target?

I have an MILP as below $\begin{equation} \begin{array}{*{35}{l}} \underset{d_{u,c}}{\max}\hspace{1mm}\hspace{1mm}\sum_{u=1}^{U}\sum_{c=1}^{C}d_{u,c}\omega_{u,c}\\ \text{}\text{subject to }\text{ C1:}...
2
votes
0answers
35 views

Hardness Reduction for assigning Users to Servers

Suppose there are $x$ servers, and $y$ users. The $y$ users are to be assigned to the $x$ servers similar to classic scheduling problems. The cost of using servers is given by $c(|x|)$ which is an ...
5
votes
1answer
58 views

Discontinued function optimization

I am struggling with transport optimization problem, that simplified might stated as: Minimize the number of bananas transports to the shop in the following 5 days (...
2
votes
1answer
73 views

Which is better to minimize w.r.t a lower bound or an upper bound of an objective function?

Suppose there is a optimization problem that aims at minimizing an objective function $X$ but we can't develop a mathematical model for minimizing $X$. However, there are two objective functions $Y$ ...
5
votes
0answers
54 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 ...

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