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Polylithic modeling and solution approaches using algebraic modeling systems

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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.

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  1. Department of Astronomy, University of Florida, Gainesville, FL, 32611, USA

    Josef Kallrath

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  1. Josef Kallrath
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Kallrath, J. Polylithic modeling and solution approaches using algebraic modeling systems. Optim Lett 5, 453–466 (2011). https://doi.org/10.1007/s11590-011-0320-4

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