In this short note, we recall the developments prior to the publication of A Cost-Regular Based Hybrid Column Generation Approach. Constraints 11, 315-333 (2006), and discuss some of the related work on mathematical/constraint programming hybrids.
The Zinc modelling language was developed as part of the G12 project, which aimed to generate a new approach to constraint programming. A key feature of Zinc was its solver-independence, deliberately designed to separate the modelling of a discrete optimisation problem from how it is solved. This viewpoint was critical for the later design and uptake of the modelling language MiniZinc, created as a potential standard for constraint programming modelling, by cutting features from the existing Zinc language. MiniZinc has subsequently gone on to grow to encompass most of the Zinc features that were cut, and is widely used.
As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.
Essence is a constraint language for specifying combinatorial problems. It is designed to be significantly more abstract than constraint modelling languages currently in use. The first full description of the language and its design rationale was published in Constraints in 2008. This paper, written to mark the 30th anniversary of the journal, describes the history of the development of Essence, summarises developments since publication and provides some afterthoughts.
