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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Does OptaPlanner give equally good results when comparing with commercially available MIP solvers?
I want to solve a Mixed Integer problem with several constraints. Gurobi or Google OR tools solve such problems. Though I am not sure, I think they use an exact method such as branch and bound or ...
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union of constraints
How to solve problems like $\min_x f(x) \\ g(x) < 0 \ or \ h(x)<0$?
I think we can solve $\min_x f(x) \\ g(x) < 0 $ and $\min_x f(x) \\ h(x) < 0 $, then we compare the solutions from these ...
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$\min\{f(x_1),\dots,f(x_n)\}$ with other constraints
I have an optimization problem which goes:
\begin{align*}
\text{Minimize:}
\\
& \sqrt{x} + \sqrt{y} \tag{NL-objective}
\\
\text{Subject to:}
\\
&3x + 2y \geq 2 &...
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Find the minimum number of equipment required for a service period
I'm starting to learn operations research and trying to get my head around this problem that I have.
Problem statement: Find the minimum number of equipment needed to run a service schedule.
There are ...
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Is there a comprehensive list of problems in OR?
I was trying to search for different types of problems in OR and couldn't find a exhaustive list of problems. So far I have,
Travelling salesman problem
Cutting Stock problem
Shortest path problem
...
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Mixed Integer Programming - How to model a term in objective function with a constant multiplied by (1-Decision Variable)
I am solving an optimization problem, where I want to minimize the objective function
$$Z = \sum_q \left(D_q \text{fare}_q - \sum_{p \ne q} \Delta D^p_q \text{fare}_q \right) (1-Z_q)$$
Each $q$ is an ...
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What are some good references of OR techniques applied to revenue management?
For teaching purposes, I am looking for some nice examples of revenue management problems which are tackled with optimization techniques, ideally linear programming (including MIPs).
For example, this ...
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Using PULP to model machines in a factory
Complete revision:
I have all 4 machines that can run in positive and negative directions which results in 2 outputs:
$ P_1 = \begin{cases}
-390 \le P_1 \le -300 & \text{for neg mode}\\
0 &...
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What are some important real life examples of multi objective optimization problem with box constraints to work on?
In the search of some of the important cutting edge many objective optimization problems to be solved using non-dominated sorting genetic algorithm (NSGA) and its variants.
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constrained optimization with decreasing constraint thresholds -Literature tips
consider a constrained optimization problem (typically c=0), with f highly nonlinear:
\begin{equation}
\text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c
\end{equation}
I experimented a bit and found ...
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Is there a name for this variation of the generalized assignment problem?
All the input variables are positive float (x > 0). We have $M$ agents with limited amount of time $t_1,\dots,t_M$, $N$ tasks $task_1,\dots,task_N$ associated with duration $d_1,\dots, d_N$. Cost ...
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it is possible to have a constraint that does not contain any decision variables
I had formulated an optimization model, and along the way I had to change a variable into a parameter. In doing so, one of my constraints that contained the variable I changed no longer contained a ...
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How to formulate the minimum and maximum range of possible values?
In Store $X$, shelf 1 accounted for $\frac{1}{4}$ of Bakery $C$ 's average weekly sales and shelf 2 accounted for $\frac{2}{3}$ as much as shelf 1 . If shelves 3 and 4 each accounted for less than ...
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OR applications in medicine
Read this article on potential application of Markov Decision Process in decision making process of patient evaluation schedule.
Does anyone know or have experience in application of such OR ...
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Plant Network model
I am looking for some help in Plant Network Optimization- as an example scenario would be to optimize the Plant network based on the below inputs and figure out best possible plants to use to service ...
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Sign of the reduced cost in LP
I'm new to operation research. I'm confusing about the sign of reduced cost and I have a few questions that I'd like to ask. Suppose that I solve a maximization problem, considering a variable x with ...
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Optimize least squares penalized by curvature of log pdf
I have probability values $p \in \mathbb{R}^n$. Given $A \in \mathbb{R}^{m\times n}$, $b \in \mathbb{R}^m$, I want to minimize the following objective function. $||Ap - b||_2^2 + \sum_{i=1}^{n-2} (\...
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How to identify which node is serving each customer?
I have a linear programming problem. There are two questions:
Consider 2 centers (1,2) that should serve clients [s,b,c,t], What it the minimum distance cost. The formulation is straight forward.
The ...
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Potential methods for solving quadratic optmization problem
I am trying to solve a non-convex optimization problem with the help of sequential quadratic programming.
I need to develop an algorithm inside SQP to solve this subproblem. What potential methods (...
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How to embed an arbitrary graph into (k,d)-kautz space (like multidimensional scaling of non-normed space)
How to embed an arbitrary graph into (k,d)-kautz space (like multidimensional scaling of non-normed space)? See details in the following.
Given a graph $G = \{V,E\}$,
we have a distance matrix (the ...
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Linear Programming aggregate planning
I'm having trouble with the formulation of a linear program constraint, for an aggregate planning problem for 30 months.
Company XYZ wants to maximize profit, and wants to know how many workers the ...
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Understanding mathematical concept behind an objective function
I'm trying to understand the following expression (which can be called an objective function as well):
${b_t}\left( {\omega ,\rho } \right) = \arg \mathop {\max }\limits_{b \in {\Delta _m}} \quad\prod\...
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Solving a Global Optimization problem using Differential Evolutionary Algorithm using R
I need to determine the global optimum results of this objective function. I define the problem by minimizing the squared difference as represented in function $f(q_1,q_2,\alpha_1,\alpha_2)$
The ...
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PuLP ensure first and last choice
I have an assignment problem where I have $N$ locations and $M$ dates for each location, and the goal is to choose $K$ location-date pairs that maximize revenue. There are a number of constraints, for ...
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Quadratic optimization with non-constant coefficients
I have a series of functions (very similar to convex quadratic equations, see the first comment below) $f_1(x), f_2(x), \dots, f_n(x)$. Each of these functions touches the $x$-axis at $a_i$, which can ...
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Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$
Let $\mathbf{A} \in \mathbb{R}^{n \times n}$. I'm working in a problem where I have a black-box algorithmic solution to compute the products $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T \mathbf{x}$ given ...
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Auxiliary parameters for two uncertain parameters Robust Optimization
I have the following constraint for robust counterpart formulation, where two uncertain parameters appear at the same time;
$\sum{QG_{ij}}$*${\theta}$+$\sum_{}\sum{QD_{ij}}*p $ * ${\theta}$
where;
${...
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Finding the minima of a multivariable function with constraints
I have a multivariable function (9 variables), and I want to find where the function records a minimum value. The function is as follows:
It also has a few constraints:
I tried a brute force ...
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Number of scenarios in non-deterministic optimization methods
I am investigating an optimization problem under uncertainty and am using scenario-based robust optimization to deal with uncertainties. I have developed a heuristic approach in which I can set the ...
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About Mathematical Programs
I am dealing with the following problem as follows.
$$\min \sum_{i,j}( x_{i}+y_{j}+q_{ij}+w_{i})$$
$$\text{s.t.} x_{i}+y_{j}+q_{ij}+w_{i} \geq b_{ij}, \forall i,j$$
Is it possible to handle this ...
user5245
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Smallest graph coloring in Gurobi
I am trying to design an algorithm to label a graph’s nodes with as few colors as possible
such that all pairs of nodes joined by an edge do not have the same color.
This is the code I have written so ...
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How to Set Up an Optimization Problem Like the 0/1 Knapsack
I'd like some help in understanding and setting up (what may be) an optimization problem that has some similarities to the 0/1 knapsack problem. In this problem the items are a given number of words (...
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Quantifying a measure of standard deviation in MILP
I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
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use Forecast distribution width in inventory optimization
I have a demand forecast that gives me a distribution for future demand, for each time period in percentiles (e.g. demand for period 1 will be between 6 and 25 (zero and 100th percentiles, and i know ...
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Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )
While working on optimization issues I encountered the following problem:
$$\left\{\begin{array}{ll}
{\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
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How to implement tiered pricing based on weight or cube volume or order amount total into objective function with Guro i py
I am working on an optimization project here and my objective is to come out with the optimal amount of each item to buy at certain vendors that can minimize the cost while meeting the demand(already ...
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Array of string in OPL
how to make 2d array of strings in Cplex
//indics
{string} cluster=...;
setof(string) darkstore =...;
setof(string)demandpoint =...;
//data
cluster={chav,sree};
demandpoint=[{tsnami,adholokam,...
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Fixing binary variables in an Binary Integer Program
I have a Binary Integer Program with two binary decision variables and additionally have an expected solution. At the time of execution of this program I expect the parameters to change slightly. I am ...
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What's the suitable optimization model for solving the given model?
Given the following model, what's the suitable optimization model for it?
$X_{i,j}^N$ is a Matrix. (is known, and $N$ stands for Normalized. It means, $X_{i,j}^N$ is normalized version of $X_{i,j}$; ...
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Reformulate this constraint optimization problem such that I do not have to divide 2 variables?
I have a constraint optimization problem as follows:
I need to assign $m$ tasks to $n$ days, with $n \geq m$.
Each day can host 0 to $m$ tasks.
Each task either belongs to type $A$ or $B$.
I want to ...
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How to perform clustering of a large number of nodes?
I have a clustering problem with around 400-500 nodes. The edge between any two nodes has a weight (between 0 and 1, 0: can be considered as there is no edge/connection between these two nodes) as ...
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Optimization solver that satisfies variable values within set membership
Is there a solver that can handle an AMPL model of this sort:
...
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Gurobi-Python, unmet demand of customers
I would like to capture the unmet demand by modeling the following constraint with two decision variables. where $QU_{wc}$ is the unmet demand and $QW_{wc}$ the shipped amount of products. I model the ...
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Converting a piecewise function to a linear equation as a constraint
The value of one of the variable of my model (alpha_1) is given by a piecewise function. Each element of the piecewise depends on the value of some other binary decision variables (X1, x2, x3).
I'd ...
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Modelling with Gurobi-Python a Supply Chain Problem
I would like to write the following simple model in GurobiPy, which is part of many terms that's belongs to the objective function, I assumed that I have three suppliers are selected and three ...
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Multi-Scenario Gurobi Python Output
I have an lp and am trying to solve multiple scenarios at once. One of my scenarios is infeasible though this is not the issue.
For some reason, when I print m.status, both solutions have a status of ...
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GUI Optimization tool for business users
We are looking for a tool that can be used by business users where they can do the followings:
use a simple data modeler to create the classes of data and populate the data instances
simple option to ...
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Distributed optimization with coupled inequality constraints
Consider the optimization problem:
\begin{equation}
\begin{array}{l}
\min_{(x,y)\in \mathbb{R}^2_{+}} \quad x_{1}a_{1} + x_2a_{2}
\\ \text {subject to } \quad\;
y_{2} \ge \frac{1}{{x}_2},
\\ \quad \...
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How to find the maximizing number of expected delivered units of a probabilistic minimum cost flow problem?
I am a Bitcoin / Lightning Network open source developer and researcher and new here but very active on the sister site. In the context of my research I discovered the field of operations research ...
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