Large Combinatorial Optimization Problems: a Methodology for Hybrid Models and Solutions

Large Scale Combinatorial Optimization problems (LSCO) appear in numerous types of industrial applications (e.g. production scheduling, routing problems , nancial applications). They are NP-complete problems characterized by large sets of data, constraints and variables, and often have an impure structure. Tackling such problems successfully requires both experience and skill. The current trend in the Constraint Programming (CP) community is to enhance the features of CP languages to ease the modelling and solving of LSCO problems by providing 1) natural modelling, 2) built-in constraints facilities (global constraints), and 3) integration of diierent constraint solvers (from mathematical programming, constraint programming , stochastic search methods). The common aspect is the growing awareness that we need to hybridize diierent models and methods and go beyond the constraint programming framework, essentially for eeciency and scaling reasons. This sets strong requirements upstream the programming phase to reduce the increasing level of expertise that is required to model the problem and map the model to adequate methods. This talk aims at lling a gap in this direction. We present the ongoing work within the CHIC2 Esprit project and at IC-Parc, in terms of providing a thinking process and a methodology for modelling LSCO problems with a hybrid perspective. We address the aspects of problem modelling, algorithm characterization, and mapping of the model to hybrid algorithms. 1 From constraint programming to hybrid methods... The Constraint Programming (CP) framework has emerged in the wide eld of Artiicial Intelligence to extend the application domain of logic based programming languages to deal with combinatorial search problems modelled as CSPssMac77]. This has been achieved by embedding and integrating the CSP