Set Variables and Local Search

Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This modelling device has been around for quite some time in the constraint programming area, and proved its usefulness in many applications. This paper introduces set variables and set constraints also in the local search area. It presents a way of representing set variables in the local search context, where we deal with concepts like transition functions, neighbourhoods, and penalty costs. Furthermore, some common set constraints and their penalty costs are defined. These constraints are later used to model three problems and some initial experimental results are reported.Updated May 200

Set variables and local search

Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This was already known to the constraint programming community, and solvers based on constructive search for set variables have been around for a long time. In this paper, set variables and set constraints are put into a local-search framework, where concepts such as configurations, penalties, and neighbourhood functions are dealt with generically. This scheme is then used to define the penalty functions for five (global) set constraints, and to model and solve two well-known applications

Set variables and local search

Abstract. Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This was already known to the constraint programming community, and solvers based on constructive search for set variables have been around for a long time. In this paper, set variables and set constraints are put into a local-search framework, where concepts such as configurations, penalties, and neighbourhood functions are dealt with generically. This scheme is then used to define the penalty functions for five (global) set constraints, and to model and solve two well-known applications.