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Holt Double Exponential Smoothing
Given a time series $x_t,\, t=1,2,\dots,$ presumed to contain linear trend, Holt's double exponential smoothing method computes estimates $s_t$ of the level (mean) at time $t$ and $b_t$ of the...
View ArticleA Bicriterion IP Model for a Game Strategy
A question on Mathematics Stack Exchange asks how to solve an optimization problem related to a game apparently called "speedrunner". The problem boils down to selecting integer values for variables...
View ArticleScheduling a Round-Robin Tournament
Once in a while I come across a scheduling problem, and of course my first reaction is to think "integer program". A while back, for example, I used an IP model to work out a schedule for a rotating...
View ArticleSelecting Dispersed Points
Fellow blogger Erwin Kalvelagen posted a comparison of two binary programming models, one quadratically constrained and one linearly constrained, for the problem of selecting a maximal number of points...
View ArticleFinding All Simple Cycles (I)
This is the first of a sequence of posts related to the question of finding all simple cycles in an undirected graph. Motivation for the posts comes from a question on OR Stack Exchange. A simple cycle...
View ArticleFinding All Simple Cycles (II)
Yesterday's post described my introduction (by way of a question on OR Stack Exchange) to the problem of how to find all simple cycles in a graph. In that post I described a simple, efficient iterative...
View ArticleFinding All Simple Cycles (III)
This is the third and (hopefully) final post about finding all simple cycles in an undirected graph. In the first post, I discussed the problem briefly and described a simple, efficient iterative...
View ArticleWeird Caja Bug
In the past day or so I've tripped over a rather annoying bug in Caja, the file manager for the MATE desktop (which I use with Linux Mint, and which is also used by many Ubuntu users). Theoretically,...
View ArticleA Random Tree Generator
For a problem I was noodling with in R, I needed to generate random trees (meaning connected, acyclic, layered, undirected graphs, not classification trees or anything statistical). There are a bunch...
View ArticleAnother GA for Clustering
Someone asked on OR Stack Exchange about clustering nodes, a subject that comes up from time to time. The premise is that you have $N$ points (nodes), and for each pair $i \neq j$ there is (or may be)...
View ArticleAnnoying Message with R GA Package
This is a small technical note (mainly a reminder to myself) about using the GA package for genetic algorithms in R, specifically within an R Markdown document (such as an R notebook). The GA::ga()...
View ArticleThe rJava Curse Strikes Again
Apparently I have not needed the rJava R package in a while, because when I wanted to install an R package today that has rJava as a dependency, it was not there. So I tried to install it (this is on...
View ArticleNode Coloring
Someone posted a question on OR Stack Exchange about coloring nodes in a sensor network. The underlying problem has something to do with placing sensors, but in mathematical terms the poster wanted to...
View ArticleA Matrix Puzzle
A question on Mathematics Stack Exchange, "Placing number blocks so that the resulting matrix is symmetric", revolves around a square matrix whose entries are partitioned into blocks (submatrices). The...
View ArticleFinding a Connected Subgraph
A recent question on Mathematics Stack Exchange asked about using a mixed integer linear program (MILP) to find a connected subgraph of a specified size (vertex count) within a given graph....
View ArticleAn Unbounded Bounded Feasible Region (I)
If you find the title of this post confusing, join the club! A question on Operations Research Stack Exchange, "Randomly constructing a bounded ellipsoid", sent me down a rabbit hole, eventually...
View ArticleAn Unbounded Bounded Feasible Region (II)
In my previous post, I cited a question on Operations Research Stack Exchange about an allegedly unbounded feasible region defined by a randomly generated quadratic constraint. In that post, I...
View ArticleVisiting All Nodes
A question on Operations Research Stack Exchange asks about finding a shortest route through a connected graph that visits every node. This is distinct from the well-known traveling salesman problem...
View ArticleThe "Set" Card Game
Someone asked a question (actually a pair of questions) about the "Set" card game on OR Stack Exchange. This was the first I had heard of the game. For purposes of this post, the game play is...
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