Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain variables as well as constraints over these variables and their propagators. These constraints are subdivided into kernel constraints and additional constraints formulated as networks of kernel constraints. For some of these constraints a dedicated global constraint and its associated propagator are sketched. CP(Graph) is integrated with finite domain and finite sets computation domains, allowing the combining of constraints of these domains with graph constraints. A prototype of CP(Graph) built over finite domains and finite sets in Oz is presented. And we show that a problem of biochemical network analysis can be very simply described and solved within CP(Graph). 1

This paper presents a Large Neighborhood Search (LNS) approach based on constraint programming to solve cumulative scheduling problems. It extends earlier work on constraint-based randomized LNS for disjunctive scheduling as reported in (Nuijten & Le Pape 1998). A breakthrough development in generalizing that approach toward cumulative scheduling lies in the presented way of calculating a partial-order schedule from a fixed start time schedule. The approach is applied and tested on the Cumulative Job Shop Scheduling Problem (CJSSP). An empirical performance analysis is performed using a well-known set of benchmark instances. The described approach obtains the best known performance reported to date on the CJSSP. It not only finds better solutions than ever reported before for 33 out of 36 open instances, it also proves to be very robust on the complete set of test instances. Furthermore, among these 36 open instances, one is now closed. As the approach is generic, it can be applied to other types of scheduling problems, for example problems including resource types like reservoirs and state resources, and objectives like earliness/tardiness costs and resource allocation costs.

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.

Cumulative scheduling is a generalization of jobshop scheduling, where machines have discrete capacities and activities may require several capacity units. This paper considers iterative flattening, a heuristic procedure aiming at producing high-quality solutions to large cumulative problems in reasonable time. On standard benchmarks (with as much as 900 activities), iterative flattening quickly delivers solutions that are within 10% of the best upper bounds in average. This paper analyzes iterative flattening and identifies a pathological behaviour which explains why it may result in solutions where resources are under-utilized in early parts of the schedules. It proposes a simple extension of the algorithm which has dramatic effect on the quality of the solutions, while preserving its computational efficiency. The new algorithm found 21 new best upper bounds to the same benchmarks and quickly delivers solutions that are within 1% of the best available upper bounds in the average.

Comet is an object-oriented language supporting a constraint-based architecture for local search. This paper presents a collection of abstractions, inspired by constraint-based schedulers, to simplify scheduling algorithms by local search in Comet. The main innovation is the computational model underlying the abstractions. Its core is a precedence graph which incrementally maintains a candidate schedule at every computation step. Organized around this precedence graph are differentiable objects, e.g., resources and objective functions, which support queries to define and evaluate local moves. The abstractions enable Comet programs to feature declarative components strikingly similar to those of constraint-based schedulers and search components expressed with high-level modeling objects and control structures. Their benefits and performance are illustrated on two applications: minimizing total weighted tardiness in a job-shop and cumulative scheduling.