Statistics and Computation
1. R Project
Replaces: SAS, SPSS
R is a free and open source statistical computing environment that holds its own against some of the most established proprietary statistical environments. R is available on all operating systems and is free for download. R also has a community driven library of add-on packages that are also freely available and cover almost any statistical, mathematical, or optimization need.
Also a great reference manual for those switching from SAS to R is SAS and R: Data Management, Statistical Analysis, and Graphics
RapidMiner is a data mining software with a graphical front-end. RapidMiner is suitable for most data mining and data transformation needs.
Mathematical Programming and Optimization
GLPK is a GNU/free software linear programming software kit. GLPK is intended for large-scale linear programming, mixed integer programming. GLPK is based on GNU MathProg (or GMPL) which is considered a subset of the AMPL syntax. GLPK also has its own solver.
Replaces: CPLEX, Gurobi
Symphony is a mixed integer linear programming solver developed under COIN-OR. Symphony is a flexible framework that offers many methods to customize solver capabilities given problem sets.
Replaces: Excel Solver
OpenSolver is a linear an integer optimizer alternative to the Excel Solver in Microsoft Excel. OpenSolver is based on the COIN-OR CBC engine. Unlike the Excel Solver there is no software limits to the size of the problem that can be solved.