Licentiate thesis 2005-003

High-Level Modelling and Local Search

Magnus Ågren

September 2005


Combinatorial optimisation problems are ubiquitous in our society and appear in such varied guises as DNA sequencing, scheduling, configuration, airline-crew and nurse rostering, combinatorial auctions, vehicle routing, and financial portfolio design. Their efficient solution is crucial to many people and has been the target for much research during the last decades. One successful area of research for solving such problems is constraint programming. Yet, current-generation constraint programming languages are considered by many, especially in industry, to be too low-level, difficult, and large. In this thesis, we argue that solver-independent, high-level relational constraint modelling leads to a simpler and smaller language, to more concise, intuitive, and analysable models, as well as to more efficient and effective model formulation, maintenance, reformulation, and verification. All this can be achieved without sacrificing the possibility of efficient solving, so that even time-pressed modellers can be well assisted. Towards this, we propose the ESRA relational constraint modelling language, showcase its elegance on some real-life problems, and outline a compilation philosophy for such languages.

In order to compile high-level languages such as ESRA to current generation constraint programming languages, it is essential that as much support as possible is available in these languages. This is already the case in the constructive search area of constraint programming where, e.g., different kinds of domain variables, such as integer variables and set variables, and expressive global constraints are readily available. However, in the local search area of constraint programming, this is not yet the case and, until now, set variables were for example not available. This thesis introduces set variables and set constraints in the local search area of constraint programming and, by doing this, considerably improves the possibilities for using local search. This is true both for modelling and solving problems using constraint-based local search, as well as for using it as a possible target for the compilation of ESRA models. Indeed, many combinatorial optimisation problems have natural models based on set variables and set constraints, three of which are successfully solved in this thesis.

When a new set constraint is introduced in local search, much effort must be spent on the design and implementation of an appropriate incremental penalty function for the constraint. This thesis introduces a scheme that, from a high-level description of a set constraint in existential second-order logic with counting, automatically synthesises an incremental penalty function for that constraint. The performance of this scheme is demonstrated by solving real-life instances of a financial portfolio design problem that seem unsolvable in reasonable time by constructive search.

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