Polylithic modeling and solution approaches using algebraic modeling systems

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. Tailormade 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.

Near optimal minimal convex hulls of disks

“…The term polylithic has been coined by [13,14] to refer to tailor-made modeling and solution approaches to solve optimization problems exploiting several models where output of one is input to another. Hence, polylithic methods consist of a set of models which are linked to each other with regard to their inputs and outputs, i.e., model i+1 can use the results of the first i models.…”

Analysis of TBA‐Based ETBE Production by Means of an Optimization‐Based Process‐Synthesis Approach

“…The direct access to the databases and property calculation routines of Aspen Properties® enables an easy adaptability and reusability of the approach for different chemical systems and case studies. Furthermore, ACM allows for a polylithic model formulation that enables a successive initialization and optimization of the resulting problem in several subsequent steps. This is of specific importance for the considered synthesis problem, which on the one hand involves a large number of complex nonlinear and non‐convex equations based on the thermodynamic models, while on the other hand no specific structure is to be assumed that would facilitate the use of tailored initialization modes as proposed by Skiborowski et al , .…”

Operations research in BASF's supply chain operations

“…Back in 1997, the problem could not be solved by formulating a single (monolithic) model; instead, several models (“polylithic approach”; cf. Kallrath, ) were developed that interact with each other to find a solution; the solution of one model is the starting point of another. The result of the polylithic model were good proposals for network design.…”