Modeling and Optimization Systems

TOMLAB Extended Name A General Purpose MATLAB Environment for Optimization

Kenneth Holmström
Mälardalen University, Västerås, Sweden
Applied Optimization and Modelling (TOM)
Office: Högskoleplan room 2528, Västerås
Phone: +46 21 10 14 39, +46 21 80 47 60
Fax: +46 21 10 13 30


TOMLAB is a general purpose, open and integrated MATLAB environment for research and teaching in optimization on UNIX and PC systems, developed by the Applied Optimization and Modeling (TOM) research group at Mälardalen University, Sweden. The motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of MATLAB.
By using a simple, but general input format, combined with the ability in MATLAB to evaluate string expressions, there is direct possibility to run internal TOMLAB solvers, MathWorks Optimization Toolbox and commercial solvers written in FORTRAN and C using MEX interfaces. Currently MEX interfaces have been developed for MINOS, NPSOL, NPOPT, NLSSOL and QPOPT.
Problems defined in the CUTE and AMPL language may be solved.
TOMLAB may either be used totally parameter driven or menu driven. The menu system makes it suitable for teaching. Many standard test examples are included and further more are easily added. There are many example and demonstration files. Iteration steps including line search may be graphically displayed together with contour plots when running both unconstrained and constrained optimization.
TOMLAB is based on NLPLIB TB, a MATLAB toolbox for nonlinear programming and parameter estimation and OPERA TB, a MATLAB toolbox for operational research, with emphasis on linear and discrete optimization. About 65 different algorithms are implemented. See the descriptions of NLPLIB and OPERA.
Of special interest in TOMLAB are the algorithms for weighted general and separable nonlinear least squares. Our new implementation of the Fletcher-Xu hybrid method, the Al-Baali-Fletcher hybrid method and Huschens totally structured secant method (TSSM) give fast and robust convergence on ill conditioned parameter estimation problems.
TOMLAB now includes implementations of two algorithms for global optimization without derivatives, the DIRECT algorithm and the EGO algorithm, both by Jones et. al. The DIRECT algorithm is available as a standalone version gblSolve . For generally constrained problems we have implemented the new Filter-SQP method by Fletcher and Leyffer, as well as some other old SQP methods.

TOMLAB features
  • TOMLAB offers about 65 numerically robust algorithms for linear, discrete, nonlinear, global optimization and constrained nonlinear parameter estimation.
  • It includes an advanced graphical user interface (GUI), menus, graphics and a lot of predefined test problems.
  • New user-defined problems are easily added.
  • TOMLAB has interfaces to C, Fortran, MathWorks Optimization TB, CUTE and AMPL.
  • Automatic differentiation is easy using an interface to ADMAT/ADMIT TB and four types of numerical differentiation are included.
  • Currently, MEX-file interfaces have been developed for MINOS, NPSOL, NPOPT, NLSSOL and QPOPT.
  • A problem is solved either by direct call to a solver or a general multi-solver driver routine, or interactively, using the graphical user interface (GUI) or a menu system.
  • References A User's Guide to the Optimization Environment TOMLAB 1.0. (TOM - Technical reports 19, IMa-TOM-1998-09. Date Dec 10, 1998) )