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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1answer
66 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 ...
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2answers
102 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\...
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0answers
68 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 ...
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1answer
416 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 ...
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0answers
69 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) $$ \...
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0answers
47 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 ...
3
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1answer
58 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 ...
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1answer
84 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 ...
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2answers
96 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:}...
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0answers
31 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 ...
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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 (...
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1answer
64 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 $Y$ ...
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52 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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0answers
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PuLP Python: How to linearize an inequality involving an integer variable

I am working on a Copper payables problem where the objective function is to maximise the sum of copper payable over a time period, T. The total amount of payable tonnes i.e. what the customer will ...
4
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1answer
68 views

Assignment Problem With Weighted Bipartite Graph

I have the following problem: Given $n$ workers and $n$ tasks I have to assign a worker to each task where each worker has a time to get to the task, and each task has a preparation time. for example, ...
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0answers
79 views

Solving systems of equations with simple implicit functional relations

I am attempting to solve five variables from a system of equations. Let the variables be $x_1,x_2,x_3,x_4,x_5$. Let the problem have the form: $\exp(x_1)+x_1^6=x_3+x_4+x_5 \tag{1}$ $\exp(x_2)+x_2^6=...
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2answers
144 views

Interpretability Vs Accuracy in Operations Research and Management Science Community

This question might be somewhat general and not completely relevant to this forum but I think here is the most relevant place to ask the question. Currently, deep learning, RL and generally black-...
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1answer
50 views

Handy way to index set of tuples in AMPL

I am dealing with a discrete math optimization problem on a complete graph. My variables are the arcs but I want to delete the arcs that "cost too much". I have $n$ nodes which means I have $...
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1answer
105 views

How can I have minimum amount of resources wasted in this resource allocation problem?

I have a demand, $d$ I also have supply from 1000 sources. The supplies from those $N$ (for example, $N=1000$) sources are given by $s_1,s_2,s_3,\cdots,s_N$. So,the total supply is : $s_1+s_2+\cdots+...
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2answers
169 views

Two-Objective Optimization in CPLEX

Until now, I used CPLEX to solve single-objective optimization problems only, but now I need to solve a two-objective mixed-integer linear optimization problem and I noticed that CPLEX 12.6.9 (unlike ...
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0answers
122 views

A good memoryless elevator strategy?

Could you OR whizkids please help me out with this one: https://stackoverflow.com/questions/61854621/a-good-memoryless-elevator-strategy Surely somebody has solved this before. How do you classify ...
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1answer
145 views

ILP Constraint to ensure exactly one constraint from a set of constraints is satisfied

Consider several Integer (0/1) ILP variables, i.e., Boolean variables, $x_i$'s. Consider an ILP constraint $x_1 + x_2 + x_3 \geq 1$ and another constraint $x_4 + x_5 + x_6 \geq 1$. I would like to ...
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0answers
64 views

Decomposition of Polyhedra

There is no doubt that clear examples consolidate the understanding of concepts being learnt. I am new to finding the structure and decomposition of a polyhedra. Suppose that we have the system $$ \...
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1answer
96 views

Do I need to use a stochastic optimisation approach

I have used deterministic optimisation approaches before but never ventured into stochastic optimisation. In my problem there are a number of decision variables that the optimiser must choose from in ...
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1answer
81 views

Converting evolutionary optimization problem from Excel to Python

I've set up and successfully executed an evolutionary optimization in Excel, and now have a need to convert the problem to Python. differential_evolution() in the ...
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1answer
65 views

How to convert static variables into arrays for use with PuLP

I have the following code in Python and PuLP which uses static variables. I want to know how to solve the problem by converting all of the LpVariable parts into an array, as well as the constraints. ...
2
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1answer
40 views

Logical equivalencies to modeling an indicator decision variable in transportation problem

I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
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1answer
44 views

What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?

Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
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10answers
10k views

MATLAB vs. Python in industry

I am a beginning PhD student in math, and I would like to focus on optimization. I am learning programming for the first time, and I have written out some rudimentary optimization algorithms in both ...
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0answers
50 views

Where I can study some job shop scheduling by course (video )?

I am seeking the help to know where I can study the job shop scheduling Heuristics or using solver by some course/video as I see some of books and papers hard to understand . It is hoped that the ...
2
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1answer
74 views

Formulating “more complicated” objectives in Python Gurobi

I am currently learning how to use Gurobi for Python using their official tutorial found here. In this example, they appear to formulate the objective by simply specifying a cost dictionary to the <...
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0answers
61 views

How to start the Dantzig-Wolfe decomposition?

I have the following problem: \begin{align}\min&\quad3x_1+5x_2+3x_3-2x_4+3x_5\\\text{s.t.}&\quad x_1+x_2+x_3+x_4\geq3\\&\quad3x_1+x_2+5x_3+x_4-2x_5\geq6\\&\quad x_1+2x_3-x_4\geq2\\&...
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1answer
98 views

Linear objective function with power term in constraint

Given $n$ variables $x_{i}$ where $i\in [0,n)$, denoted as a vector $x$, given a linear objective function that we want to minimize $c^\top x$ with 2 constraints: $\sum x_{i}^{2} < n+1$ $\sum\log(...
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1answer
41 views

Adding slack nodes to min cost network flows

I have the following question. I want to clarify couple of points. As you can see, total demand and total supply does not match, we do not have enough demand. What I want to ask is: Do we need to ...
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2answers
387 views

Can I use 'SCIP' solver for PYOMO?

I have an MINLP problem to solve where I was initially using 'ipopt' solver but the solution was not sticking to 'binary/boolean/integer' domain type for a variable. I am not sure which free solver ...
2
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2answers
230 views

Hard to soft constraint

What are all necessary changes to the below model so that constraint set $(2)$ becomes soft? Give the new full model. $\alpha_{ij}$ are parameters. Eqn. $(1)$ refers to an already existing function of ...
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2answers
400 views

How to maximize “contrast” between nodes on a graph?

I have an undirected graph such as the one shown below. I can make up to 3 choices about the color of each node. The edge weights are equal to the difference between the nodes, given by the "...
1
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1answer
61 views

KKT for second order approximation of $f(x)$

Let $f: \mathbb{R}^n \rightarrow \mathbb{R}.$ Consider second order approximation $f(x) \approx f_0(x)$ where $$f_0(x) = f(x_0) + \nabla f(x_0)^T (x-x_0) + (\mathrm{H}f(x_0)(x - x_0))^T(x - x_0)$$ ...
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2answers
85 views

Solve nonlinear programming problems practically

In an exam, I studied Theoretical approaches to converting constrained minimum problems into unconstrained minimum problems. Specifically: KKT conditions Projection Gradient Descent Penalty and ...
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1answer
104 views

Find a particular optimal solution

After writing an integer linear program in AMPL, I solved it using CPLEX. Now, I have some variables that must necessarily be 1, others that must necessarily be 0 and finally it is possible that some ...
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15answers
2k views

Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
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1answer
46 views

Greedy algorithms for assignment problems — prediction doesn't match simulation

I'm considering the following basic assignment problem: a group of $n$ people is to be assigned, in one-to-one fashion, a set of $n$ jobs. Write $C_{ij}$ for the cost incurred when person $i$ gets ...
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2answers
679 views

Fast algorithm for Transportation Problem in Python?

The Transportation Problem can be solved with a simplex algorithm, but it's time-consuming. I'm wondering if there exists a specific Python-implemented algorithm with low complexity.
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0answers
52 views

CPU time on Linux with Gurobi

I am solving a MILP model in C++ using Gurobi 10.1. I retrieve the CPU time of my C++ program under Linux via the following commands: ...
3
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1answer
181 views

How to optimize a utility function that contains step function?

I have an optimization problem with an uncommon utility: to find a $\beta$ that maximizes $$ r^{T}\cdot H(X\cdot\beta) $$ where $H()$ is a Heaviside step function as in wiki $r$ is a vector of size ...
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1answer
570 views

Deep Reinforcement Learning for General Purpose Optimization

Recently, I attended a very nice talk given by someone at the place I work about applying Deep Reinforcement Learning (DRL) for a design optimization problem. It was particularly interesting to me ...
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3answers
340 views

Gurobi and CPLEX cannot exploit more than 32 cores of machine

I have some attempts to solve a scheduling problem using the Gurobi and doCPLEX API in python and .NET on Ubuntu-server installed on a hyper-computing cluster with 64 physical cores. Unfortunately, ...
5
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1answer
80 views

Prove that $x^*$ is an optimal solution where $f_0$ is $C^1$ and convex and $f_i$ are $C^1$ and strictly convex functions

Let $x^*$ be a feasible solution of the following convex optimization problem \begin{align}\min&\quad f_0(x)\\\text{s.t.}&\quad f_i(x)\leq0,i=1,\ldots,m\end{align} where $f_0$ is $C^1$ and ...
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0answers
91 views

Prove Non-Homogeneous Farkas' Lemma

Let $A\in\mathbb{R}^{m \times n}, c\in\mathbb{R}^{n}, b\in\mathbb{R}^{m}, d\in\mathbb{R}$. Suppose that there exists $y\geq0$ such that $A^Ty=c$. Question: prove that exactly one of the following is ...
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2answers
1k views

Linear programming: objective function with “buckets”

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. This problem was ...

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