Questions tagged [optimization]

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

86 questions with no upvoted or accepted answers
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11
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118 views

Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
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166 views

Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
8
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159 views

Relationship between two minimization problems

Let $\mathbf{A}$ be a ${n\times J}$ matrix with $A_{ij}\geq0$ (and $A_{ij}>0$ for most $ij$, there cannot be any rows or columns that consist only of $0$s), $Q=\left\{\mathbf{q}\mid \mathbf{q}\in\...
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87 views

Calculating robustness of layout plans

We have tried to design a manufacturing cell which will produce specific families of products. We figure out three layout plans for implementation. For practical reasons, we need to calculate the ...
7
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59 views

KKT conditions validation- one dual variable equating to two values

I have the following optimization problem: \begin{alignat}2\min &\quad A(t)\cdot x(t)-B(t)\cdot y(t)+C(t)\cdot z(t)-D(t)\cdot k(t)\\\text{s.t.}&\quad z(t)+z_1(t)-y(t)-y_1(t)+x(t) = k(t);&...
7
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538 views

Having trouble with objective function in Python: "GurobiError: Variable not in model". What else could I try?

I am trying to figure out how I can write this objective function into python using Gurobi. I have to minimize the sum of the product of three dictionary's values. The reason I am confused is that ...
6
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120 views

Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
6
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0answers
52 views

Semi-definite Programming, non standard notation

The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is: $$ \begin{array}{cl} \min & c^\top x \\ \mathrm{s.t.} & 0 \succeq ...
6
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258 views

How to make constraints satisfy disciplined convex programming guidelines?

How do I turn my convex constraints (described below) into constraints that are DCP so that I can solve them in CVXPy? Is there some ``cheat sheet'' of standard tricks? I'm trying to implement the ...
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55 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 ...
5
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226 views

Substituting inequality by equality constraints

Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row or column has all its entries equal to zero. Let also $\mathbf{k}=\left(k_j\right)$ be a ...
5
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45 views

Mixing time exponent above threshold temperature for Glauber dynamics or annealing

It is well-known that the Glauber dynamics will converge in polynomial time to the Gibbs distribution for, say, the Ising model on a d-regular graph at high enough temperatures $T>T_c$. There are ...
5
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374 views

What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
5
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124 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 ...
5
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34 views

In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
4
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193 views

Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
4
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86 views

Fast solvers for LASSO-type non-convex optimization problems

Given $y \in \mathbb{R}^{n \times 1}, X \in \mathbb{R}^{n \times p}$, $p > n$, assume a LASSO-type optimization problem in the form of $$ \hat\beta=\underset{\beta}{\operatorname{argmin}}\frac{1}{2}...
4
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56 views

Identifying saddle point in constrained optimization

Suppose we are minimizing $f(x)$. The first order necessary condition of $x^*$ being local minmum is: $$\nabla f(x^*)= \mathbf{0}.$$ For sufficiency, we check if also $\nabla^2f(x^*) \succ 0$, i.e., ...
4
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56 views

Confused in how to insert a slack variable in a constraint inequality

According to my understanding, we should put a slack variable to equate an inequality constraint by inserting the slack variable in the side that is less than the other side. For example, if we have $...
4
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0answers
52 views

Instructors optimized schedule task

I'm trying to solve one interesting math task. Let’s imagine we have a number of instructors with different timespans during the day in which they work or they are available. We need to display to ...
4
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45 views

Help with constrained or regularized optimization problem involving variable matrices and powers of matrices (or perhaps matrix logarithms)

I am attempting to solve the following optimization problem: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
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65 views

Continue on "Is there a known MILP to schedule routes after routes are made"

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
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769 views

cvxpy: Code that works for default solver doesn't work for cp.GLPK_MI

The following code works: ...
4
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0answers
194 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\max\...
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47 views

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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139 views

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 ...
3
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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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64 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 ...
3
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0answers
101 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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0answers
40 views

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 ...
3
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53 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 ...
3
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0answers
41 views

R ompr MILPModel array multiplication?

In R, I regularly ompr::MILPModel for optimization. I adapt the below snippet to enable multiplication of a decision variable with two dimensions (e.g., x[i,j] ) ...
3
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0answers
54 views

Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a simulated annealing algorithm to ...
3
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0answers
64 views

Density Optimization by Fitting an Circle to a Field - Monte Carlo Method

Given: I have 2D non-parametric formula that provides instantaneous intensity at certain (x,y) location. Required: I want to en-circle a region where the density is high via optimization. In other ...
3
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0answers
54 views

What are the efficient ways to model this scheduling problem and ways to improve running time

There are $N - \{1 \ldots N\}$ jobs, each with processing time $p_j$, to be scheduled on $M - \{1 \ldots M\}$ machines over span of $D - \{1 \ldots D\}$ days and while working $T - \{1 \ldots E \ldots ...
3
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0answers
40 views

Constraint equivalence in PuLP

I'm working on an optimization problem in PuLP and I have to enforce a daily minimum of shifts and a daily maximum of assigned shifts. I have the following constraints to ensure each day has a minimum ...
3
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0answers
41 views

Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
3
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0answers
62 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
3
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0answers
51 views

Discrete optimization in transport economics

I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ ...
3
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0answers
72 views

How can I do this in GAMS?

I am mimicking a GAMS model that was introduced in Soler et al. (2013)1 to compare my new model with its results. In a nutshell, assume we have a variable $t$ that is supposed to only take certain ...
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0answers
30 views

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 ...
2
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0answers
91 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 ...
2
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0answers
58 views

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 ...
2
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0answers
99 views

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:/...
2
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0answers
42 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
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0answers
81 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
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0answers
38 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 ...
2
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0answers
131 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=...
2
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0answers
94 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) $$ \...
2
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0answers
57 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: ...