Integrating network optimization capabilities into a high-level modeling language

Reviewer: Donald Harris Kraft

The author offers an interesting study of adding optimization capability in a high-level modeling language for network optimization. The paper shows how the modeler can consider a graphical representation, an algebraic representation, and a computer-readable representation such as one from a modeling language such as GAMS. It then describes a general case, where one can see if a network model can be extracted from the problem statement posed in a standard format. The general data structures and procedures for this extraction process are described in some detail. The author goes into special detail to describe how the gradients and second-order Hessian matrix are derived for the nonlinear objective function. The optimization capabilities are from the GENOS system developed by the author and others. Zenios describes the organization of the integrated system and gives examples of problems, such as a transportation model and social accounting matrices. This latter example gives rise to the GAMS/SAMBAL system. The author also allows one to use the MINOS system for nonlinear optimization within his framework. Times are given for an example transportation problem, and comparisons are provided for GAMS/GENOS, GAMS/SAMBAL, and GAMS/MINOS. The effects of an attached array processor are mentioned. Finally, the author discusses network decompositions. The purpose of this paper is to present the research work that went into the development of an integrated optimization system, bringing together a modeling language and network optimization capabilities. The paper is long and occasionally uses terminology without defining it for the novice reader (for example, MPS format). This well-written paper shows what is being done in this important area of software development for optimization.