CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Bound-consistent deviation constraint
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Operations research and constraint programming at google
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Neuron constraints to model complex real-world problems
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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Weighted average expressions frequently appear in the context of allocation problems with balancing based constraints. In combinatorial optimization they are typically avoided by exploiting problems specificities or by operating on the search process. This approach fails to apply when the weights are decision variables and when the average value is part of a more complex expression. In this paper, we introduce a novel average constraint to provide a convenient model and efficient propagation for weighted average expressions appearing in a combinatorial model. This result is especially useful for Empirical Models extracted via Machine Learning (see [2]), which frequently count average expressions among their inputs. We provide basic and incremental filtering algorithms. The approach is tested on classical benchmarks from the OR literature and on a workload dispatching problem featuring an Empirical Model. In our experimentation the novel constraint, in particular with incremental filtering, proved to be even more efficient than traditional techniques to tackle weighted average expressions.