We study the notion of robustness in stable matching problems. We first define robustness by introducing (a, b)-supermatches. An (a, b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1, b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1, b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.
One of the challenges of deploying machine learning (ML) systems is fairness. Datasets often include sensitive features, which ML algorithms may unwittingly use to create models that exhibit unfairness. Past work on fairness offers no formal guarantees in their results. This paper proposes to exploit formal reasoning methods to tackle fairness. Starting from an intuitive criterion for fairness of an ML model, the paper formalises it, and shows how fairness can be represented as a decision problem, given some logic representation of an ML model. The same criterion can also be applied to assessing bias in training data. Moreover, we propose a reasonable set of axiomatic properties which no other definition of dataset bias can satisfy. The paper also investigates the relationship between fairness and explainability, and shows that approaches for computing explanations can serve to assess fairness of particular predictions. Finally, the paper proposes SAT-based approaches for learning fair ML models, even when the training data exhibits bias, and reports experimental trials. This work was partially funded by ANITI, funded by the French program "Investing for the Future -PIA3" under Grant agreement n o ANR-19-PI3A-0004.
International audienceIn the car-sequencing problem, a number of cars has to be sequenced on an assembly line respecting several constraints. This problem was addressed by both Operations Research (OR) and Constraint Programming (CP) com-munities, either as a decision problem or as an optimization problem. In this paper, we consider the decision variant of the car sequencing problem and we propose a systematic way to classify heuristics for solving it. This classification is based on a set of four criteria, and we consider all relevant combinations for these criteria. Some combinations correspond to common heuristics used in the past, whereas many others are novel. Not surprisingly, our empirical evaluation confirms earlier findings that specific heuristics are very important for efficiently solving the car-sequencing problem (see for in-stance [17]), in fact, often as important or more than the propagation method. Moreover, through a criteria analysis, we are able to get several new insights into what makes a good heuristic for this problem. In particular, we show that the criterion used to select the most constrained option is critical, and the best choice is fairly reliably the "load" of an option. Similarly, branching on the type of vehicle is more efficient than branching on the use of an option. Overall, we can therefore indicate with a relatively high confidence which is the most robust strategy, or at least outline a small set of potentially best strategies. Last, following a remark in [14] stating that the notion of slack used in heuristics induces a pruning rule, we propose an algorithm for this method and experimentally evaluate it, showing that, although computationally cheap and easy to implement, this is in practice a very efficient way to solve car-sequencing benchmarks
Abstract. The weighted degree heuristic is among the state of the art generic variable ordering strategies in constraint programming. However, it was often observed that when using large arity constraints, its efficiency deteriorates significantly since it loses its ability to discriminate variables. A possible answer to this drawback is to weight a conflict set rather than the entire scope of a failed constraint. We implemented this method for three common global constraints (AllDifferent, Linear Inequality and Element) and evaluate it on instances from the MiniZinc Challenge. We observe that even with simple explanations, this method outperforms the standard Weighted Degree heuristic.
The Robust Stable Marriage problem (RSM) is a variant of the classic Stable Marriage problem in which the robustness of a given stable matching is measured by the number of modifications required to find an alternative stable matching should some pairings break due to an unforeseen event. We focus on the complexity of finding an (a, b)-supermatch. An (a, b)-supermatch is defined as a stable matching in which if any a (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those a men/women and the partners of at most b others. We first discuss a model based on independent sets for finding (1, 1)-supermatches. Secondly, in order to show that deciding whether or not there exists a (1, b)-supermatch is N P-complete, we first introduce a SAT formulation for which the decision problem is N P-complete by using Schaefer's Dichotomy Theorem. We then show the equivalence between this SAT formulation and finding a (1, 1)supermatch on a specific family of instances. We also focus on studying the threshold between the cases in P and N P-complete for this problem.
FairCORELS is an open-source Python module for building fair rule lists. It is a multi-objective variant of CORELS, a branch-and-bound algorithm to learn certifiably optimal rule lists. FairCORELS supports six statistical fairness metrics, proposes several exploration parameters and leverages on the fairness constraints to prune the search space efficiently. It can easily generate sets of accuracyfairness trade-offs. The models learnt are interpretable by design and a sparsity parameter can be used to control their length. CCS CONCEPTS• Software and its engineering → Software libraries and repositories; • Computing methodologies → Rule learning; Supervised learning; Machine learning algorithms.
Abstract. The ATMOSTSEQCARD constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints ATMOST u on each subsequence of size q. This constraint is useful in car-sequencing and crew-rostering problems. In [18], two algorithms designed for the AMONGSEQ constraint were adapted to this constraint with a O(2 q n) and O(n 3 ) worst case time complexity, respectively. In [10], another algorithm with a O(n 2 log n) worst case time complexity and similarly adaptable to filter ATMOSTSEQCARD in O(n log n) was proposed. In this paper, we introduce an algorithm for achieving Arc Consistency on the ATMOSTSEQCARD constraint with a O(n) (hence optimal) worst case time complexity. We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems.
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