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LGO Software Development

1. The Relevance of Global Optimization

A large variety of quantitative decision problems in the applied sciences, engineering and economics can be described by constrained optimization models. In these models, the best decision is sought that satisfies all stated feasibility constraints and minimizes (or maximizes) the value of a given objective function.

While man-made objects and (manufacturing, transportation, distribution, etc.) systems often manifest strong linearity, natural - physical, chemical, biological, geological, environmental - systems are typically described by nonlinear relations. The corresponding nonlinear decision models frequently possess multiple optima of very different quality. In such cases, the 'traditional' numerical repertoire of (continuous convex) optimization does not guarantee the correct approximation of the global solution.

The objective of global optimization (GO) is to find the 'very best' solution of nonlinear decision models, in the possible presence of multiple locally optimal solutions. For thorough discussions of the most prominent GO models and solution strategies, consult, e.g., the Handbook edited by Horst and Pardalos (1995). There exist a few dozen other academic research level books, several informative www sites, and literally thousands of scholarly articles devoted to the subject. For a WWW-enabled review of GO models, solution approaches, test problems and real-world applications, please consult Pintér (1999c).

Illustres Beispiel

2. LGO Solver Suite Overview

The LGO - abbreviated from Lipschitz(-Continuous) Global Optimizer - solver system integrates algorithms of global and local scope. It serves to analyze and solve complex nonlinear models, under minimal analytical assumptions. In order to use LGO, only computable function values are required, without a need for gradient or higher order information. (See the general model form stated above.) LGO can be used in several search modes, providing a robust, effective, and flexible solver suite approach to a broad range of nonlinear models. The solver suite approach increases the reliability of the overall solution process.

LGO solver components
* branch-and-bound based global search
* global adaptive random search
* multistart global search
* exact penalty function based search
* constrained local optimization

Current standard implementations can handle up to thousands of decision variables and constraints. Note that the corresponding runtimes may vary significantly, since global optimization problem instances can be extremely difficult. For smaller scale, yet non-trivial models LGO, typically provides the (numerical) global solution in a matter of seconds, on today's personal computers.

For over two decades, LGO has been successfully applied to highly complex, 'black box' system models. Please see a list of illustrative application areas below at Applications. See also the illustrative list of References at the end of the product description.

The LGO solver suite is developed and supported by Pintér Consulting Services, Inc. (János D. Pintér, PhD, DSc, and developer partners).

3. Hardware and OS Platforms, LGO Versions

LGO has been primarily developed on PC platforms, with portablity in mind also to other environments such as workstations and mainframes.

A command line style version of LGO (called here LGO/CL) and various other customized implementations are available for personal computers, workstation platforms and mainframes. LGO/CL has a simple, but functional screen interface, for the necessary (minimized) communication with the user, to maintain some interactive features. The detailed results are directly written to designated text files, and all numerical functionality is identical to that of the other implementations.

A fully Windows-compatible implementation (called here LGO IDE)) is also available, for MS Windows. In this version, LGO is embedded under a menu-driven graphical user interface mentioned above, thus providing a fully integrated development environment.

4. Connectivity to Application Development Platforms

LGO can be directly connected to user applications by using sample (template) files provided with the software. Among other direct connectivity options, LGO can also be called from any application which enables external calls. Conversely, LGO can call external numerical procedures to evaluate functions which are components of the GO problem analysed.

5. LGO Applications

LGO, MathOptimizer und MathOptimizer Professional wurden zur Lösung einer großen Anzahl unterschiedlicher global-konexer Optimierungsprobleme eingesetzt. Zu den Einsatzbereichen gehören zum Beispiel folgende Einsatzfelder:

For over two decades, these products have been applied to solve global optimization problems. The corresponding runtimes may vary significantly, since GO problem instances can be extremely difficult. For smaller scale, yet non-trivial models LGO typically provides the global solution in a matter of seconds, on today's personal computers.

The list of LGO application areas includes, for instance, the following broad problem-classes:

* advanced engineering design (acoustics, electrical, electronic, mechanical, engineering and other areas)
* aggregation of negotiated expert opinions
* calibration and operation of laboratory or medical instruments
* combination of deterministic or statistical forecasts and estimates
* data classification (cluster analysis)
* data visualization (e.g., multidimensional scaling and state space reduction)
* econometrics and finance
* extremal energy (potential function) models in physical, chemical, and biological modelling
* facility location and service allocation (distribution) problems
* general nonlinear approximation, including e.g., shape design
* model fitting to empirical data: identification, calibration and verification
* object arrangement designs
* optimized design and operation of 'black box' (confidential or other closed) systems
* risk analysis and management, and other (potentially nonconvex) stochastic decision problems
* robust product or mixture design e.g., in chemical and processing industries
* solution of systems of nonlinear equations and inequalities.

For additional information on these applications, please see the illustrative list of references provided below. In particular, please consult the research monograph

Global Optimization in Action , Kluwer Academic Publishers, Dordrecht Boston London (Published: 1996, 508 pp. hardbound, ISBN 0-7923-3757-3.)

This work presents a detailed exposition of the theoretical background of LGO. It also discusses various implementation aspects, selected case studies and applications, and provides an extensive list of references.

Peer reviews of this book appeared in: Optima 51 (1996) 13-14. (written by Prof. H. Ratschek) and Journal of Global Optimization 12 (1998) 319-321. (written by Prof. A. Neumaier)

The book is now distributed by Springer Science. Please visit www.pinterconsulting.com for links also to other books by Dr. Pinter.

6. LGO Distribution

LGO is available in professional, non-profit research and educational versions. Registered users receive the LGO User's Guide together with the software.

As of today, LGO and its various implementations are used around the world, at hundreds of universities, research institutes, and private companies.

Demonstration (executable) programs, a detailed list of relevant professional references, and additional information are available upon request. Please consult the illustrative list of references below.

Potential LGO users are encouraged to send - preferably Fortran or C coded - test problems, following standard user file templates which will be provided upon request. We are also interested in joint research and application development projects.

LGO is developed and supported by Pintér Consulting Services, Inc.

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