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Solving Sparse Systems of Equations with an optimizer: a basis trick
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View ArticleFun with a quadratic model
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Singular system of nonlinear equations
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Van der Waerden Puzzle
In [1] a puzzle is mentioned:Find a binary sequence \(x_1, \dots , x_8\) that has no three equally spaced \(0\)s and no three equally spaced \(1\)sI.e. we want to forbid patterns like...
View ArticleModeling vs Programming, Python vs GAMS
In [1] a question is posed about formulating an LP model dealing with a shortest path problem. The suggested solution is programmed in Python. This is a good example where coding even in a high-level...
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On the scheduling of reading book chapters
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View ArticleRAS, Entropy and Exponential Cones
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View ArticleMatlab: Problem Based Optimization
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Brain Storm Optimization
I have seen the name of this heuristic before. There is also a Hypo-Variance Brain Storm Optimization. Reading the abstract in [1] made me laugh again.Of course a human is smarter than an ant or a bee,...
View ArticleSquare system solver: Barzilai-Borwein spectral method in R
I was playing with some large sparse square systems of non-linear equations (actually resulting from some spreadsheets). R has a package called BB [1] which is based on [2,3]. Technically: this is...
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Regular Constraints
Here is an interesting problem (1) that can be stated in terms of regular expressions.ProblemPuzzle description: The player is given an empty game board (varying size) that they must fill with...
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production scheduling: Minimum up-time
In [1] a minimum up-time question is posted:Assume we have \(T=12\) periods. If we produce in period \(t\) we have a profit of \(c_t\). Some \(c_t\)'s are negative.If we turn production on, it should...
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Piecewise linear regression
In [1] a data set is presented, where a piecewise or segmented linear regression approach can help. A linear fit looks like:There are two issues we can see from the plot: we can expect a better fit if...
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MIP Gap Artifacts
For large integer programming models we may not be always willing to wait for a global, proven optimal solution. A straightforward way to deal with this is to set a time limit. A different way is to...
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Excel and L1-norms
In an Excel spreadsheet I am studying (actually generating an optimization model from the formulas in the spreadsheet) I see the following construct: =SUMIF(X,">0")-SUMIF(X,"<0")where X is a...
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Geometry Lesson: find point closest to set of lines
In [1] a simple optimization problem is posted:Find a single point \(q\) in 3d space that is closest to a number of given lines. Each line \(L_j\) is defined by two points \(p_{j,a}\) and...
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SOCP reformulations of a min distance problem
In [1] I discussed a geometric problem: find a point (in 2d or 3d space) as close as possible to a number of given lines. In the comments it was suggested to write this as a Second Order Cone...
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Speed Dating Scheduling
Speed Networking [source]In [1] a question is posed about a speed dating like problem. Here is my version of this:There are 140 people. Each of them has stated some preference (or dis-preference) to...
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Python constraint solver
In [1] a small problem is stated:We need to assign 7 devices to 3 locationsThe maximum number of devices assigned to a location is: loc1:3, loc2:4, loc3:2Not all assignments are allowed. The allowed...
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K best solutions for an assignment problem
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