Tuesday, June 3, 2025

Graph connectivity as constraints

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I was generating, for an example model, a random, sparse, directed graph. Unfortunately, when sparse enough, this is likely to yield a graph...
1 comment:
Thursday, April 24, 2025

Revisiting a continuous facility location problem

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I am revisiting here a problem from [1]: We have \(n\) demand points and their locations. How many facilities do we need to service these cu...
4 comments:
Wednesday, April 16, 2025

Nonconvex problem: local vs multistart vs global

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In [1] a somewhat abstract non-convex problem is given: \[\begin{align}\min_x & - x_1^2 - x_2^2 - x_3^2 - x_4^2\\ & Ax \le b \end{al...
Tuesday, April 1, 2025

Towers of Hanoi: inventory and network formulation

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The towers of Hanoi problem [1] is a famous puzzle demonstrating recursion. The task is to move a stack of disks from one peg to another. We...
1 comment:
Friday, March 21, 2025

Wolf, goat and cabbage problem: MIP and network model

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The Wolf, goat, and cabbage problem can be stated as [1]: A farmer with a wolf, a goat, and a cabbage must cross a river by boat. The boat ...
Tuesday, February 25, 2025

Small MIP, proving optimality is difficult

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This is a simple, smallish MIP model that is difficult to solve to proven optimality. The problem is stated as [1]: I have grid of dimension...
6 comments:
Monday, February 24, 2025

Programming vs Modeling

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I found another interesting GAMS model. Here, I wanted to demonstrate the difference between programming (implementing algorithms in a progr...
Saturday, February 15, 2025

Network models with node capacities

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Min-cost flow network model A standard min-cost flow network model, formulated as a linear programming model, can look like: Model ...
Monday, November 4, 2024

Sorting using a MIP model

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This is not, per se, very useful, but sorting a parameter inside a MIP model is not very easy for MIP solvers. Obviously, if you need a sort...
6 comments:
Saturday, October 26, 2024

PuLP surprises

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Formulating optimization models inside traditional programming languages such as Python is very popular. The main tool the developers use to...