Sunday, April 04, 2010

MultiDimensional Scaling (MDS) with Solver

This file creates the Solver model for multidimensional scaling (see a previous post on MDS in Excel/VBA). The application calculates MDS for the matrix from McCormick’s BEA article (see the previous post on BEA in Excel/VBA).

PROXIMUS with Solver

This file creates an approximation of a matrix (using PROXIMUS – see a previous post on Koyutürk’s PROXIMUS) using Solver.

McCormick’s Bond Energy Algorithm (BEA) in Excel/VBA

This file contains an implementation of a classic seriation algorithm by McCormick, Schweitzer and White (Problem Decomposition and Data Reorganization by a Clustering Technique) – bond energy algorithm – in Excel/VBA. This implementation is very similar to the fortran code on the S-Plus/R page of Fionn Murtagh’s. Additionally, an article by Arabie, Schleutermann, Daws and Hubert (Marketing Applications of Sequencing and Partitioning of Nonsymmetric and/or Two-Mode Matrices), that uses multiple iterations, is examined. Some modifications to this algorithm are considered.

Approximating matrices with PROXIMUS in Java

This file is an application of Mehmet Koyutürk’s algorithm PROXIMUS – an efficient framework for error-bounded compression of high-dimensional discrete attributed datasets. As sources for information on PROXIMUS, on the internet, seem to be limited, the best is perhaps the C source code of the R PROXIMUS package.

Sometimes, it would just be better to switch to VBA :)

This file contains vehicle routing paths (a solution to the two truck problem a few posts back), as a Trendline’s Microsoft Excel Solver optimization result. The problem (in the two left red columns) is that the two paths have become mixed. One path would have to take us: Tallinn-Märjamaa-Riidaku-Tallinn and the other: Tallinn-Pärnu-Valgerand-Tallinn, as determined by the ones and zeros in the solution. But the six ones determining the paths reside in the same column and have to be separated.
The set of Excel relationships is visualized by the formula auditing tool. The final result is in the right side of the spreadsheet, where the two red columns have three ones each.

A Solver model for a transportation problem that finds a location for an additional factory – using 625 changing cells :(

In this file a location for an additional factory has to be determined. It cannot be built on an existing location, goods can only be moved in vertical/horizontal directions, the distance between adjacent cells being 1. Total distance has to be minimized.

A transportation model with two trucks in Solver

This model uses flow balance constraints as well as Boolean variables.