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Optimization Letters

, Volume 5, Issue 3, pp 453–466 | Cite as

Polylithic modeling and solution approaches using algebraic modeling systems

  • Josef KallrathEmail author
Original Paper

Abstract

Based on the Greek term monolithos (stone consisting of one single block) Kallrath (Comput Chem Eng 33:1983–1993, 2009) introduced the term polylithic for modeling and solution approaches in which mixed integer or non-convex nonlinear optimization problems are solved by tailor-made methods involving several models and/or algorithmic components, in which the solution of one model is input to another one. This can be exploited to initialize certain variables, or to provide bounds on them (problem-specific preprocessing). Mathematical examples of polylithic approaches are decomposition techniques, or hybrid methods in which constructive heuristics and local search improvement methods are coupled with exact MIP algorithms. Tailor-made polylithic solution approaches with thousands or millions of solve statements are challenges on algebraic modeling languages. Local objects and procedural structures are almost necessary. Warm-start and hot-start techniques can be essential. The effort of developing complex tailor-made polylithic solutions is awarded by enabling us to solve real-world problems far beyond the limits of monolithic approaches and general purpose solvers.

Keywords

Algebraic modeling languages Branch and price Column generation Decomposition Hybrid methods Monolithic Primal methods Polylithic Problem-specific preprocessing 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of AstronomyUniversity of FloridaGainesvilleUSA

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