Questions tagged [constraint-programming]
Constraint programming is a particular form of optimization modeling that tends to be well-suited for combinatorial models like scheduling and planning.
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How to extend the $p \Rightarrow q$ constraint with logical AND within the $p$ statement for Big-M method?
I am a network engineer who is currently doing some network optimization problem. In my application, there is a requirement for the network delay to be bounded in some interval once some boolean flag ...
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Single Machine Job Scheduling With Release Dates and No Idling Constraint
I'm trying to model a linear job scheduling optimisation problem. There is a single machine and N jobs $J_1, J_2, ..., J_N$. Each job consists of one step with processing time $p_1, p_2, ..., p_N$. ...
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A Mathematical Approach to Solving a Sudoku Puzzle
I've been trying to develop the most efficient algorithm to solve a Sudoku puzzle. The one that I've developed isn't able to solve certain kinds of puzzles without having to use backtracking. One such ...
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Optimization/Constraint Solving on Graphs
I play video games, and it sounded like a fun exercise to try to find the optimal order in which to complete quests:
There exist multiple quest trees
There are some quests with inter-dependencies ...
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Weighted Least Square with infinite weights
I am considering a weighted least square problem with data $X \in \mathbb{R}^{n \times p}$, (diagonal) weight matrix $W \in \mathbb{R}^{n \times n}$ and responses $y \in \mathbb{R}^n$, i.e. finding $$\...
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Constraint optimisation of an objective function
I have below objective function
$S = \lvert 18 - a - b \rvert + \lvert 15 - a - 2b \rvert + \lvert 11.1 - a - 3b \rvert + \lvert 7 - a - 4b \rvert + \lvert 3.4 - a - 5b \rvert + \lvert -1.5 - a - 6b \...
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A function optimization problem with constraints
Let a, b, c be three real number constants satisfying $a^2 + b^2 + c^2 \leq 1$. Define the function $f(x, y, z) = \frac{x^2 + y^2}{2(1+z)}$ under the constraints $(x-a)^2 + (y-b)^2 + (z-c)^2 \leq \mu^...
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Constraint forcing maximum parameter value to constant
I have an optimisation problem that I thought should be in the form,
\begin{align}
\mathrm{maximise}_{x\in\mathbb{R}^p} & f(x) + \lambda\|x\|_1 \\
\mathrm{subject~to~~~~~~~} ...
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Summations and constraints over sets in ILP problem
In a simplified version of the ILP problem I am trying to formulate, I have the following:
A set of elements $A_{i,j} \in \mathcal{A}$.
Each element $A_{i,j} \in \mathcal{A}$ has an associated ...
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Relaxing a binary variable in a Mix Integer Programming problem
I am quite new to the field of optimization and currently having a problem of formulating a constraint with binary variable.
For each value of $b$, if there exists one value of k such that $z_1[b, k]$ ...
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Demonstrating Piecewise Linearity in a Parametrized Optimization Solution
Let $\mathbf{B}$ be a definite positive square matrix of size $n \times n$, and $\mathbf{b}$ an $n$-sized vector. It can be shown that the solution of $\arg\min_x \left(\mathbf{x}^T \mathbf{B} \mathbf{...
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Placing numbers of 1-9 so that the six equations hold
Place the numbers 1 to 9 into the nine positions in such a way that, the 6 equations are valid. Each position must have a distinct value. Multiplication and division have priority over addition and ...
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Discrete point inside a polygon formed by set of vertices
I am working on a problem where I have a set of 2D vertices and a test point. I want to check whether the test point lies inside the polygon formed by the set of given vertices. I am trying to model ...
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Polynomial constraints for restricting: $a=0$ if and only if $b\neq 0$
For this discussion, I will be considering polynomials over multiple complex variables, and a system of polynomial constraints, where the constraints on the variables can be written as a set of ...
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Social golfer problem with additional requirement
I need to write a program that sorts people into groups.
To give a little context: The aim of the program is to create an equitable distribution of tasks and people for a school trip. Every day the ...
