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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Setting up a community Server for OR-enthusiasts [migrated]

It is more a suggestion than a question. I am thinking it would be a great idea to set up a OR-Discord-Server for people who are studying or working with the methods for operations research. I myself ...
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How to interpret this problem of multicriteria decision

I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in ...
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1answer
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Circular reference in states of the Bellman equation

I want to formulate a game of darts as a dynamic program. The goal is to minimize the number of darts thrown while reaching checkout. A dart player has a score s. If his score is s = ...
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1answer
70 views

Mosek Fusion APIs

Does anyone know if there is a list of available function APIs for Mosek Fusion APIs? Namely, what functions are available, their arguments list and meaning, what they do. Something similar to UNIX ...
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87 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 ...
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2answers
136 views

How to get professional help in OR

I would like to hire a consultant at OR to do a formulation of a mathematical optimization problem. Which website is reliable for it?
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1answer
78 views

Resource Optimization For Cargo Handling

I have to work on some real world data and come up with an optimization technique to handle cargo. To make thing simpler let's assume that there are 2 types of resources Manpower (150 ton / 8 hour) ...
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3answers
765 views

From a performance/speed perspective, does the programming language matter if the solver used is the same?

Perhaps a silly question, I know... But just wondering if the programming language has an impact here if the solver used is the same? For instance, the same model formulation being solved using Gurobi ...
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1answer
142 views

Are short-sell allowed in conic formulation of Markowitz optimization?

Sorry to ask a question about the basic Markowitz portfolio optimization. The example is from Mosek's example book. The basic Markowitz portfolio optimization is formulated as: The book mentioned we ...
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1answer
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Optimization Problem: Recommending Service Providers to Clients

I am new to optimization, not sure if the problem described below is trivial. Any guidance on solution or nudge in the right direction would be very helpful. Problem: There are two groups – clients ...
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1answer
123 views

Tuning the coefficients of an objective function of LP

I want to solve a problem that results in this general objective function which I want to maximize: $$a\cdot x_1+b\cdot x_2-c\cdot x_3-d\cdot x_4+e\cdot x_5$$ When I write out in full this objective ...
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How to calculate the complexity order of an optimisation model?

In some optimisation problem it is stated that the complexity is ${\cal O}(n)$ or ${\cal O}(n^2)$. How is this calculated? Any example will be very helpful.
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Convex Optimization Problem with norm inequality constraint

Consider the following optimization problem: \begin{align} \inf_{x,y}&\quad(x-x_0)^\top A(x-x_0) + (y-y_0)^\top B(y-y_0) \\\text{s.t.}&\quad x^\top a\geq0,\\ & \quad y^\top b\geq0, \\& ...
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1answer
87 views

Advanced Transportation optimization problem

I'm trying to explore OR problems and wanted to know what algorithm fits here. Consider fuel stations with lithium ion battery that service replacing battery at each refuel ( you replace your batters ...
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1answer
137 views

Bin Packing with CP Solver

[ [0,5], [0,4], [1,6], [2,4], [3,6], [3,2], [4,5], [5,5], [6,4], [7,3], [8,2], [8,3], [9,5], [10,3]] ...
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1answer
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Constraintlist with two Options Pyomo

I recently started with Pyomo and I have the following Problem: I want to construct a ConstraintList with an if statement. I already learned, that it's not possible. But the problem still exists... My ...
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1answer
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Maximizing sum of step functions under single linear constraint

I am trying to efficiently solve the following optimization problem: \begin{align}\max_{b \in \mathbb{R}_+^D}&\quad\sum_{n=1}^{N}\operatorname H(b^T w^{(n)} - c^{(n)}) \\\text{s.t.}&\quad\sum_{...
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1answer
87 views

Continuous minimax with linear objective and constraints

How to solve the following minimax problem quickly? The variables are all continuous. $$\max_{x_{1}, x_{4}, x_{5}} \min_{x_2,x_3} \vec{c}^{\intercal} \vec{x}$$ subject to the following constraints: $$...
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2answers
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Optimizing a capacitated clustering problem with Greedy search algorithm

So, I am trying to implement a greedy search algorithm to cluster a number of points. Each point has a specific demand and each cluster shouldn't exceed that demand. Now, when I run it for a smaller ...
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4answers
440 views

What is the best open source solver for large scale LP optimization in pyomo?

I have used Gurobi and cplex for solving large scale LP problems with Pyomo. However, I do need to use open source solver. Any advise? glpk and cbc seems to be very slow in solving the problem (with ...
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1answer
183 views

The optimum is achieved only by forced "solution polishing"

I have the behavior of CPLEX during a MIP search, when it finds the optimal solution in a reasonable time during a forced "solution polishing" phase only. Otherwise, if you do not switch the ...
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1answer
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Questions on Mosek Fusion Power Cone example

Just trying to understand the example given in Mosek Fusion handbook as shown I'm not exactly sure how to convert 7.3 to 7.4 in terms of objective function. I understand the power cone $P_{3}^{0.2, 0....
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How to approach this Truck Utilisation problem?

The problem statement currently I have is very broad (or you can say very vague at the same time): I have a number of dropping locations (Customer locations) I have the location of the HUB I have a ...
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Has anyone ever worked on a OR problem like this before?

Here is the situation (it's a silly example just to illustrate the point): A computer repair company is primarily focused on repairing computers. However, the company has recently become interested in ...
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MLE application with gekko in python

I want to implement MLE (Maximum likelihood estimation) with gekko package in python. Suppose that we have a DataFrame that ...
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2answers
187 views

Multi-product distribution modeling : too many constraints

I have received many helps to model the problem, thank's for that ! I just edited the post to make clear what my actuel problem is. The following model is giving me amazing results with few products (...
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1answer
79 views

Is there any solver intended specifically for integer and binary variables alone on the optimization model other than solvers for MIP, MILP?

Any solvers which can be integrated in python where we can quickly solve if we have integer and binary variables alone in our model other than normal solvers for MIP, MILP?
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2answers
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How to linearize specific range constraints?

I would like to know about the linearization of the $(If, Then)$ constraints as follows: $$\begin{array}{l} \text { If: } \\ 15 \leqslant x \leqslant 25 \\ \text { then: } \quad y=\color{blue}{a} x+\...
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Minimising average holding cost per unit time is equivalent to minimising average delay per customer in queue

This question was originally asked on Math Stack Exchange. It is probably better suited here. Introduction When one thinks about a queue, it is natural to want to find a policy that minimises the ...
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Lower bound very bad. How to improve?

I have the following MILP: \begin{alignat}{2} \nonumber \mbox{minimize } \quad & \phi = \sum_{i=1}^{m-1} \sum_{f=1}^{F} \sum_{\underset{\bar{f} \neq f}{\bar{f}=1}}^F \sum_{h \in H} \left( D_{f \...
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1answer
116 views

How to compute the minimum number of vehicles required

I am trying to solve the following problem: I have a set of $N$ requests that must be processed by vehicles. I do not know the locations of these requests. Requests can be processed by a same vehicle, ...
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Optimization When True Costs Are Unknown

here is a problem I thought of: Suppose there is a car repair shop and 5 mechanics work there. Everyday, new cars arrive at the shop and each mechanic has to choose 3 cars to work on. In short, the ...
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Multiple Depot/Crew Office Bus Driver Scheduling Modelling

I'm working on Bus Driver Schedule with multiple add-on constraints that are complex and hence trying to figure out how this can be achieved. Reference of Bus Driver Scheduling using OR-Tools:- https:/...
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1answer
90 views

How to exponentiate binary variables in QUBO-type problems?

Ising Model In an Ising model, the Hamiltonian of one configuration of spins $\vec{s}$ is: $$ H(\vec{s}, \mathcal{J}, \mathcal{h}) = \sum_{i} h_{i} s_{i} + \sum_{i \ne j}J_{ij} s_{i}s_{j} $$ where ...
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1answer
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Violation of specific constraint in Pulp

I have successfully implemented a program where I allocate N truck drivers to M gathering hubs for each one of the days of the ...
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2answers
177 views

Inverse Ising problem

Inverse Ising Problem The inverse ising problem means fitting the coupling $J_{ij}$ and field $h_{i}$ parameters given a sample of configurations of spins. Each spin $s_{i}$ is either +1 or -1. The ...
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1answer
178 views

Scheduling minimization Integer Programming problem formulation

I am working with integer optimization. I have a problem with $t$ tasks and every task $i$ needs $w_i$ weeks to be completed and $p_{il}$ workers on a specific week $l$. There is a total time in weeks ...
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3answers
219 views

What industries and applications are chronically underoptimized?

What are examples of industries or applications, which would greatly benefit from using OR, but it is not standard or common to use these technologies there?
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Optimisation Multiple Constraints

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is \...
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3answers
180 views

Prove NP Hardness for non-convex multi-objective optimization

The multi-objective optimization problem in my case is non-linear as it consists of three objective function of which two are nonlinear function and the third is a linear function. Lets say objective ...
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1answer
137 views
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1answer
68 views

Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program

I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function: \begin{equation} x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
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1answer
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Excel Solver is not performing as desired

I have a simple optimization problem and would like to solve it using Microsoft Solver. However, the solver does not do what it is supposed to. Briefly to the background: In the problem the gross ...
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1answer
88 views

How do I arrive at the form given in this paper, for the QUBO version of the number partitioning problem?

In this article A new modeling and solution approach for the number partitioning problem1, it transforms the number partition problem into a QUBO form like equation (2.1) on page 2. $$\text{diff}=\...
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Which multi-objective optimization algorithm should one select?

The multi-objective optimization problem in my case is defined below: Objective 1: Minimize $f_1(X_1,X_2)=C_1X_1+C_2X_2+C_3X_1^2+C_4X_2^2+C_5X_1^2X_2^2$ Objective 2: Minimize $f_2(X_1,X_2)=D_1X_1+...
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1answer
275 views

Non-symmetric Positive Definite/Semidefinite Matrix in Quadratic Program

A necessary condition in any quadratic programming to be convex is the matrix $\mathbf{Q}$ in the formulation $x^\intercal \mathbf{Q}x$ to be positive definite or positive semidefinite. Positive ...
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Solver issue? Xpress (slp) - Nonlinear - Python - Pyomo

I tried solving my model with xpress: pip install xpress And then in the model: ...
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1answer
112 views

Is that Ok to exclude fixed components from an objective function?

Suppose we have the following objective function with one decision variable $x_i$ where $p_i$ is a fixed parameter for each $i$ and also, $a$ is a constant for the problem \begin{align} \label{eq} \...
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1answer
256 views

Solving Quadratically Constrained Quadratic Program with Cross Product Terms Only

I'm totally new to the world of optimization and I have an optimization problem that I think it can be formulated as Mixed Integer Quadratically Constrained Quadratic Program (QCQP) but I'm not sure ...
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102 views

Existence of a transformation to convex optimization

Question Does a transformation of the following problem to convex optimization exist? \begin{aligned} \label{1} \min_{\vec{x}, \vec{y}} \quad & F(\vec{x}, \vec{y}) \\ \textrm{s.t.} \quad ...

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