Pieter Leyman

Jorik Jooken, Pieter Leyman, Patrick De Causmaecker

Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators for this class. In the current paper, we formulate several new computationally challenging problems related to the IMSs of arbitrary 0-1 knapsack problem instances. Based on generalizations of previous work and new structural results about IMSs, we formulate polynomial and pseudopolynomial time algorithms for solving these problems. From this we derive a set of 14 computationally expensive features, which we calculate for two large datasets on a supercomputer in approximately 540 CPU-hours. We show that the proposed features contain important information related to the empirical hardness of a problem instance that was missing in earlier features from the literature by training machine learning models that can accurately predict the empirical hardness of a wide variety of 0-1 knapsack problem instances. Using the instance space analysis methodology, we also show that hard 0-1 knapsack problem instances are clustered together around a relatively dense region of the instance space and several features behave differently in the easy and hard parts of the instance space.

Theresa Eimer, Lennart Schäpermeier, André Biedenkapp et al.

Empirical research on meta-algorithmics, such as algorithm selection, configuration, and scheduling, often relies on extensive and thus computationally expensive experiments. With the large degree of freedom we have over our experimental setup and design comes a plethora of possible error sources that threaten the scalability and validity of our scientific insights. Best practices for meta-algorithmic research exist, but they are scattered between different publications and fields, and continue to evolve separately from each other. In this report, we collect good practices for empirical meta-algorithmic research across the subfields of the COSEAL community, encompassing the entire experimental cycle: from formulating research questions and selecting an experimental design, to executing experiments, and ultimately, analyzing and presenting results impartially. It establishes the current state-of-the-art practices within meta-algorithmic research and serves as a guideline to both new researchers and practitioners in meta-algorithmic fields.

Dieter Brughmans, Pieter Leyman, David Martens

In this paper we suggest NICE: a new algorithm to generate counterfactual explanations for heterogeneous tabular data. The design of our algorithm specifically takes into account algorithmic requirements that often emerge in real-life deployments: (1) the ability to provide an explanation for all predictions, (2) being able to handle any classification model (also non-differentiable ones), and (3) being efficient in run time. More specifically, our approach exploits information from a nearest unlike neighbour to speed up the search process, by iteratively introducing feature values from this neighbour in the instance to be explained. We propose four versions of NICE, one without optimization and, three which optimize the explanations for one of the following properties: sparsity, proximity or plausibility. An extensive empirical comparison on 40 datasets shows that our algorithm outperforms the current state-of-the-art in terms of these criteria. Our analyses show a trade-off between on the one hand plausibility and on the other hand proximity or sparsity, with our different optimization methods offering users the choice to select the types of counterfactuals that they prefer. An open-source implementation of NICE can be found at https://github.com/ADMAntwerp/NICE.

Jorik Jooken, Pieter Leyman, Tony Wauters et al.

In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is used to explore game trees and represents the state-of-the-art algorithm for a number of games. Several enhancements to Monte Carlo tree search are proposed that make the algorithm more suitable in a combinatorial optimization context. These enhancements exploit the combinatorial structure of the problem and aim to efficiently explore the search space tree by pruning subtrees, using a heuristic simulation policy, reducing the domains of variables by eliminating dominated value assignments and using a beam width. The algorithm was implemented with its components specifically tailored to two combinatorial optimization problems: the quay crane scheduling problem with non-crossing constraints and the 0-1 knapsack problem. For the first problem our algorithm surpasses the state-of-the-art results and several new best solutions are found for a benchmark set of instances. For the second problem our algorithm typically produces near-optimal solutions that are slightly worse than the state-of-the-art results, but it needs only a small fraction of the time to do so. These results indicate that the algorithm is competitive with the state-of-the-art for two entirely different combinatorial optimization problems.