Many real-world problems can be effectively solved by means of combinatorial optimization. However, appropriate models to give to a solver are not always available, and sometimes must be learned from historical data. Although some research has been done in this area, the task of learning (weighted partial) MAX-SAT models has not received much attention thus far, even though such models can be used in many real-world applications. Furthermore, most existing work is limited to learning models from non-contextual data, where instances are labeled as solutions and non-solutions, but without any specification of the contexts in which those labels apply. A recent approach named hassle-sls has addressed these limitations: it can jointly learn hard constraints and weighted soft constraints from labeled contextual examples. However, it is hindered by long runtimes, as evaluating even a single candidate MAX-SAT model requires solving as many models as there are contexts in the training data, which quickly becomes highly expensive when the size of the model increases. In this work, we address these runtime issues. To this end, we make two contributions. First, we propose a faster model evaluation procedure that makes use of knowledge compilation. Second, we propose a genetic algorithm named hassle-gen that decreases the number of evaluations needed to find good models. We experimentally show that both contributions improve on the state of the art by speeding up learning, which in turn allows higher-quality MAX-SAT models to be found within a given learning time budget.

Constraint satisfaction problems (CSPs) are used widely, especially in the field of operations research, to model various real world problems like scheduling or planning. However,modelling a problem as a CSP is not trivial, it is labour intensive and requires both modelling and domain expertise. The emerging field of constraint learning deals with this problem by automatically learning constraints from a given dataset. While there are several interesting approaches for constraint learning, these works are hard to access for a non-expert user. Furthermore, different approaches have different underlying formalism and require different setups before they can be used. This demo paper combines these researches and brings it to non-expert users in the form of an interactive Excel plugin. To do this, we translate different formalism for specifying CSPs into a common language, which allows multiple constraint learners to coexist, making this plugin more powerful than individual constraint learners. Moreover, we integrate learning of CSPs from data with solving them, making it a self sufficient plugin. For the developers of different constraint learners, we provide an API that can be used to integrate their work with this plugin by implementing a handful of functions.

Combinatorial optimization problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with a preference function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism. We provide learnability results within the realizable and agnostic settings, as well as hassle, an implementation based on syntax-guided synthesis and showcase its promise on recovering synthetic and benchmark instances from examples.

Many problems in operations research require that constraints be specified in the model. Determining right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and machine learning principles. We focus on personnel rostering and scheduling problems in which there are often past schedules available and show that it is possible to automatically learn constraints from such examples. To realize this, we adapted some techniques from the constraint programming community and extended them in order to cope with multidimensional examples. The method uses a tensor representation of the example, which helps in capturing the dimensionality as well as the structure of the example, and applies tensor operations to find the constraints that are satisfied by the example. The algorithm also identifies inherent clusters in the data and uses it as background knowledge to learn more detailed constraints. To evaluate the proposed algorithm, we used constraints from the Nurse Rostering Competition and generated solutions that satisfy these constraints; these solutions were then used as examples to learn constraints. Experiments demonstrate that the proposed algorithm is capable of producing human readable constraints that capture the underlying characteristics of the examples.

Integer programming (IP) is widely used within operations research to model and solve complex combinatorial problems such as personnel rostering and assignment problems. Modelling such problems is difficult for non-experts and expensive when hiring domain experts to perform the modelling. For many tasks, however, examples of working solutions are readily available. We propose ARNOLD, an approach that partially automates the modelling step by learning an integer program from example solutions. Contrary to existing alternatives, ARNOLD natively handles multi-dimensional quantities and non-linear operations, which are at the core of IP problems, and it only requires examples of feasible solution. The main challenge is to efficiently explore the space of possible programs. Our approach pairs a general-to-specific traversal strategy with a nested lexicographic ordering in order to prune large portions of the space of candidate constraints while avoiding visiting the same candidate multiple times. Our empirical evaluation shows that ARNOLD can acquire models for a number of realistic benchmark problems

We tackle the problem of constructive preference elicitation, that is the problem of learning user preferences over verylarge decision problems, involving a combinatorial space of possible outcomes. In this setting, the suggested configuration is synthesized on-the-fly by solving a constrained optimization problem, while the preferences are learned iteratively by interacting with the user. Previous work has shown that Coactive Learning is a suitable method for learning userpreferences in constructive scenarios. In Coactive Learning the user provides feedback to the algorithm in the form of an improvement to a suggested configuration. When the problem involves many decision variables and constraints, this type of interaction poses a significant cognitive burden on the user. We propose a decomposition technique for large preference-based decision problems relying exclusively on inference and feedback over partial configurations. This has the clear advantage of drastically reducing the user cognitive load. Additionally, part-wise inference can be (up to exponentially) less computationally demanding than inference over full configurations. We discuss the theoretical implications of working with parts and present promising empirical results on one synthetic and two realistic constructive problems.