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Filling up a container with boxes
In this post the following problem was proposed:We have a rectangular container in which we pace some differently sized boxes (rectangles, this problem is 2D only). There is some space left, and we...
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More tennis scheduling
In this post another tennis-scheduling problem is posted. In this case we deal with 20 players doing doubles in 5 rounds. That means teams of 2 players, 4 players per game, and 5 games per round....
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Fantasy football
From this post:I have been working on a hobby project for a while that involves finding all possible team rosters given the constraints of a salary cap and player positions while trying to N teams with...
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Solving non-convex QP problems as a MIP
Non-convex Quadratic Programming problems are difficult to solve to optimality. Most QP solvers do not even accept non-convex problems, so how can we attack this?The easy way: global solversThe easiest...
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Non-convex QPs and Marginals
The Cplex global QP solver has some problems providing marginals (duals and reduced costs) for a non-convex QP. Here is a small model taken from (1): To solve this problem to optimality in GAMS we add...
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Non-convex QP as a MIP: performance
In this post I showed how a small non-convex QP could be reformulated as a MIP using KKT conditions plus a special (linear) objective. Will this work in practice? How does this compare performance-wise...
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Excel Pivot Table and large data sets: PowerPivot
In this post I described a simple way to export a large GAMS data set to a CSV file which can be used as an external data source by Pivot Tables. Basically this was needed as Excel has a limit of a...
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IBM Data Science Experience
http://www.ibm.com/analytics/us/en/technology/data-science/http://datascience.ibm.com/Not sure what it is, but worth keeping an eye on.
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Optimization in the Huffington Post
The Huffington Post is now even reporting on optimization models:http://www.huffingtonpost.com/entry/a-revolutionary-model-to-optimize-promotion-pricing_us_579638bee4b0e002a313c6da
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Convexity Checker
In this post a somewhat complex class of functions was incorrectly assumed to be convex:(From: http://www.sfu.ca/~ssurjano/boha.html, the plot is \(f_1(x)\)).Indeed the picture gives the impression...
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Egyptian Vultures, Leaping Frogs and General Relativity
Some more exotic meta-heuristics with intriguing names:See also: http://yetanothermathprogrammingconsultant.blogspot.com/2016/05/more-nature-inspired-heuristics.html
View ArticleDynamic programming vs MIP
Many problems solved by dynamic programming can also be formulated as a Mixed Integer Programming problem. Here is a very simple problem. The participant is asked to provide a Dynamic Programming...
View ArticleCplex bug or not?
I was present at a GAMS demonstration yesterday, and I saw a strange thing. The model is a very small transportation model (model 1 in the GAMS model...
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Simple Cutting Stock Example in R
In http://rpubs.com/KGFeMan/PM_IP an example of a cutting stock problem in solved in R using LpSolve. In this example all possible cutting patterns are generated in advance using some facilities of the...
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Wolfram Language
In http://blog.wolfram.com/2016/08/08/today-we-launch-version-11/ a new version of Mathematica is announced. More emphasis on the underlying language (Wolfram Language). I guess that makes sense: using...
View Article10+ Free Open Source Solvers
http://www.butleranalytics.com/free-open-source-solvers/I am pretty sure Gurobi and Mosek should not be in this list.Update: Gurobi has been removed (now the list is exactly 10).
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Portfolio Optimization: Maximize the Sharpe Ratio
The problem of finding the portfolio with the largest Sharpe Ratio can be written as: \[\boxed{\begin{align}\max\>&\frac{r^Tx-r_f}{\sqrt{x^TQx}}\\ & \sum_i x_i = 1\\ & x_i\ge...
View Articlegdxrrw and R 3.3.1
From this post:I have written a dispatch model in GAMS which optimizes by minimizing system costs. I want to loop runs of the model; Run the optimization, save the output, varying a single...
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Multi-objective optimization: an illustration
In http://yetanothermathprogrammingconsultant.blogspot.com/2015/09/linearizations.html an example of a 2-objective land allocation problem is discussed. There are two competing objectives:Cost: assign...
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Back to basics: a very simple scheduling problem
In this post an extremely simple scheduling problem is proposed. But as we shall see, there are still a few interesting things to say about this. There are \(n=9\) persons, two of which need to be...
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