Eoin O'Mahony

Constraint programming and combinatorial optimisation in numberjack

Numberjack is a modelling package written in Python for embedding constraint programming and combinatorial optimisation into larger applications. It has been designed to seamlessly and efficiently support a number of underlying combinatorial solvers. This paper illustrates many of the features of Numberjack through the use of several combinatorial optimisation problems.

A Shortest Path-Based Approach to the Multileaf Collimator Sequencing Problem

The multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-Hard, even for a matrix restricted to a single row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one line problem is fixed-parameter tractable in the maximum intensity. This result was obtained recently by [9] with a complex construction. We develop new linear and constraint programming models exploiting this idea. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of complete methods.

Embedding system dynamics in agent based models for complex adaptive systems

Complex adaptive systems (CAS) are composed of interacting agents, exhibit nonlinear properties such as positive and negative feedback, and tend to produce emergent behavior that cannot be wholly explained by deconstructing the system into its constituent parts. Both system dynamics (equation-based) approaches and agent-based approaches have been used to model such systems, and each has its benefits and drawbacks. In this paper, we introduce a class of agent-based models with an embedded system dynamics model, and detail the semantics of a simulation framework for these models. This model definition, along with the simulation framework, combines agent-based and system dynamics approaches in a way that retains the strengths of both paradigms. We show the applicability of our model by instantiating it for two example complex adaptive systems in the field of Computational Sustainability, drawn from ecology and epidemiology. We then present a more detailed application in epidemiology, in which we compare a previously unstudied intervention strategy to established ones. Our experimental results, unattainable using previous methods, yield insight into the effectiveness of these intervention strategies.

Hybrid methods for the multileaf collimator sequencing problem

The multileaf collimator sequencing problem is an important component of the effective delivery of intensity modulated radiotherapy used in the treatment of cancer. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. In this paper we extend the state-of-the-art optimisation methods for this problem, which are based on constraint programming and decomposition. Specifically, we propose two alternative hybrid methods: one based on Lagrangian relaxation and the other on column generation. Empirical evaluation on both random and clinical problem instances shows that these approaches can out-perform the state-of-the-art by an order of magnitude in terms of time. Larger problem instances than those within the capability of other approaches can also be solved with the methods proposed.

A shortest path-based approach to the multileaf collimator sequencing problem

The multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms.

A complete multi-valued SAT solver

We present a new complete multi-valued SAT solver, based on current state-of-the-art SAT technology. It features watched literal propagation and conflict driven clause learning. We combine this technology with state-of-the-art CP methods for branching and introduce quantitative supports which augment the watched literal scheme with a watched domain size scheme. Most importantly, we adapt SAT nogood learning for the multi-valued case and demonstrate that exploiting the knowledge that each variable must take exactly one out of many values can lead to much stronger nogoods. Experimental results assess the benefits of these contributions and show that solving multi-valued SAT directly often works better than reducing multi-valued constraint problems to SAT.

Incorporating variance in impact-based search

We present a simple modification to the idea of impact-based search which has proven highly effective for several applications. Impacts measure the average reduction in search space due to propagation after a variable assignment has been committed. Rather than considering the mean reduction only, we consider the idea of incorporating the variance in reduction. Experimental results show that using variance can result in improved search performance.

Enhanced Inference for the Market Split Problem

Inference in constraint programming is usually based on the deductions generated by individual constraints which are then communicated to other constraints through domain filtering. Frequently we find that this is a too coarse-grained form of communication since constraints could exchange more powerful forms of deductions that could help reduce the search effort. In this paper we propose a particular technique for enhancing inference in constraint programming, by generating deductions that involve tighter interleaving of constraints. We apply our method to the Market Split Problem and obtain massive speed-ups which brings a new order of Market Split Problems into the realm of solvability by means of constraint programming.

Fast and scalable domino portrait generation

A domino portrait is an approximation of an image using a given number of sets of dominoes. This problem was first stated in 1981. Domino portraits have been generated most often using integer linear programming techniques that provide optimal solutions, but these can be slow and do not scale well to larger portraits. In this paper we propose a new approach that overcomes these limitations and provides high quality portraits. Our approach combines techniques from operations research, artificial intelligence, and computer vision. Starting from a randomly generated template of blank domino shapes, a subsequent optimal placement of dominoes can be achieved in constant time when the problem is viewed as a minimum cost flow. The domino portraits one obtains are good, but not as visually attractive as optimal ones. Combining techniques from computer vision and large neighborhood search we can quickly improve our portraits to be visually indistinguishable from those found optimally. Empirically, we show that we obtain many orders of magnitude reduction in search time.