Interactive, Semi-Automated, Lagrangean Relaxation and Decomposition Modeling System for Linear and Mixed Integer Programming

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This project addresses the need of the applications specialist for advanced mathematical programming methods without the heavy investment of time which is normally required. It aims to provide advanced modeling aids for setting up Lagrangean Techniques which are usually indispensable when dealing with large complex problems. This will be accomplished by imbedding Lagrangean Modeling into an interactive environment under state-of-the-art systems such as GAMS and MPSX/370. The user will be guided in setting up models and associated Lagrangean Techniques without having to code the details. He will be led by the system and will be able to try out various options before committing to a final set of decisions (how to decompose, how to set the various parameters, how to select from a set of specialized solvers, how to guide the Lagrangean Dual solution procedures, etc.) Various algorithmic devices will be provided as needed, including: solving the Lagrangean Dual by subgradient optimization or dual ascent; providing an overall Branch and Bound shell; making available special purpose algorithms; modifying GAMS to take advantage of the decomposition; introducing advanced integer programming (logical processing, probing) and heuristics.