Applications of mathematical models: An expert system for selecting solution methods for solving nonlinear programming problems

This paper presents an expert system for selecting solution methods for solving nonlinear programming problems. No general method exists for solving nonlinear programming problems in the same manner as the Simplex algorithm solves linear programming problems. Hence to some extent nonlinear programming even today exists as an experimental field of research. It has advanced to this date through the proposal and programming of particular algorithms, examinations of the results of the implementation of the algorithms to problems of interest, and the construction of better algorithms based on the experience gained. Computational experiences of many numerical methods such as direct search methods, method of multipliers, and linear approximation methods have been widely reported in literature int he past two decades. However, there is no unified approach to solve a genral NLP problem.

A small scale expert system has been developed using the Texas Instruments Personal Consultant Plus (PCPLUS) software to provide an organised approach for solving NLP problems. A knowledge base has been constructed to represent the past computational experiences of different solution methods on different classes of NLP problems. The system can be effectively used in conjunction with OPTLIB (1), which is a optimization program library for solving NLP problems. The purpose of the system is to guide inexperienced engineers to choose a proper NLP solution method and to serve as teaching aid. In selecting the methods more stress has been laid on the sure-footedness of the method, than on computational time and storage space requirement to make it more reliable for users. This paper presents the knowledge organisation, rules and the testing results.