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
11
votes
0answers
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 ...
10
votes
0answers
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
votes
0answers
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\...
8
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
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
votes
0answers
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 ...
5
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
0answers
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
votes
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
votes
0answers
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:
$$
\small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F
$$
...
4
votes
0answers
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 ...
4
votes
0answers
769 views
4
votes
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\...
3
votes
0answers
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, \\& ...
3
votes
0answers
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
votes
0answers
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
...
3
votes
0answers
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
votes
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
votes
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
votes
0answers
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
0answers
62 views
Integer variable optimization - decreasing execution time
I have a variable declared as follows in AMPL:
...
3
votes
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
votes
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 ...
2
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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:
...
