In numerous fields, from science and engineering to economics, quantitative decision-making often involves solving constrained optimization problems. These problems aim to find the best solution, represented as a real vector, that satisfies all feasibility constraints while minimizing or maximizing an objective function. Classical techniques like linear and nonlinear (convex) programming have been extensively used to formulate and solve such constrained optimization models.
However, when dealing with difficult nonlinear decision models that exhibit multiple local solutions, global optimization (GO) becomes crucial. In these cases, local solutions often represent mere ‘pseudo-optima’ that are surpassed in quality by the ‘true’ globally optimal solution. The number of these local (pseudo)solutions is frequently unknown and can be quite large, with significant differences in quality among the various local and global solutions. As a result, global optimization problems can be highly challenging, and most ‘classical’ numerical approaches with a local search scope are generally not directly applicable.
The LGO Program System: A Powerful Solution
The LGO program system is designed to analyze and solve problems under very general structural assumptions, such as continuity or Lipschitz conditions. It is particularly well-suited for handling GO problems related to ‘black box’ system models or models supported by limited, difficult-to-use analytical information. This feature makes LGO directly and easily applicable to numerous scientific, engineering, and economic decision problems.
LGO integrates several robust and efficient derivative-free global and local scope solvers, which can be applied in both automatic and interactive operational modes. It can be embedded under a menu-driven user interface, and its unique visualization capabilities assist in the application development process.
With a consistent Windows interface, LGO can be run in ‘pure’ DOS sessions or within a DOS ‘box’ of any Windows version. It has been developed using the Fortran 90 implementation provided by Lahey Computer Systems, Inc. (LF90), and supports DLL connectivity with various development environments, including Borland C/C++ and Delphi, as well as Microsoft Visual C/C++ and Visual Basic. Generic Windows API connectivity is also possible, and LGO can be called from an executable ‘box’ of any application that supports external (system) calls to executable programs.
LGO is also available for workstation platforms, although currently without the graphics capabilities mentioned above.
Applications of LGO
GO problems are prevalent in applications described by nonlinear system models, and LGO has been routinely applied to problems with several tens of variables, with the largest problems solved so far having a few hundred variables.
Some of the numerous existing areas of LGO applications include:
- Data classification (cluster analysis)
- Extremal energy problems in physical/chemical/biological modeling
- Generic ‘black box’ (‘oracle’) system design and operation (e.g., the optimization of a complete wastewater treatment system)
- Inverse model fitting (calibration) to observation data
- Nonlinear approximation (including curve/surface fitting, etc.)
- Optimized tuning of equipment and instruments
- Resource allocation related problems (cutting, loading, scheduling, sequencing, etc.)
- Risk analysis and management
- Robust product/mixture design
- Systems of nonlinear equations and inequalities
LGO Availability, Support, and Services
LGO is sold to university departments (providing a department license) and research organizations at a reduced price, and is also available for commercial use. Prices depend on the actual LGO configuration (problem size and platforms requested) and whether it is for commercial or educational/research use. On-site installation and consulting, as well as off-site consulting services related to LGO and other nonlinear decision support system development and application services, are also offered.
The LGO software is accompanied by a User’s Guide, and registered users have access to technical support and can obtain future development upgrades at a significant discount. Minor revisions are provided for a nominal fee or can be electronically transferred.
Demo programs and additional information about LGO are available upon request. All demo programs illustrate the complete functionality of the LGO program system, with some solving GO problems up to 50 variables in minutes on Pentium class PCs (as of January 1998).
For more information related to LGO application areas, please consult the Selected List of Publications, Research Reports, and Presentations.