Combinatorial Testing (CT) tools are essential to test properly a wide range of systems (train systems, Graphical User Interfaces (GUIs), autonomous driving systems, etc). While there is an active research community working on developing CT tools, paradoxically little attention has been paid to making available enough resources to test the CT tools themselves. In particular, the set of available benchmarks to asses their correctness, effectiveness and efficiency is rather limited. In this paper, we introduce a new generator of CT benchmarks that essentially borrows the structure contained in the plethora of available Combinatorial Problems from other research communities in order to create meaningful benchmarks. We additionally perform an extensive evaluation of CT tools with these new benchmarks. Thanks to this study we provide some insights on under which circumstances a particular CT tool should be used.

Recently, there has been a growing interest in creating synergies between Combinatorial Optimization (CO) and Machine Learning (ML), and vice-versa. This is a natural connection since ML algorithms can be seen in essence as optimization algorithms that try to minimize prediction error. In this paper, we focus on how CO techniques can be applied to improve decision tree classifiers in ML. A decision tree classifier is a supervised ML technique that builds a tree-structured classifier, where internal nodes represent the features of a dataset, branches represent the decision rules and each leaf node represents the outcome. In essence, every path from the root to a leaf is a classification rule that determines to which class belongs the input query.

We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of parallel trials. This is a typical scenario when optimizing variable settings that are very costly to evaluate, for example in the context of simulation-based optimization or machine learning hyperparameterization. We propose an original method that uses established approaches to propose a set of points for each batch and then down-selects from these candidate points to the number of trials that can be run in parallel. The key novelty of our approach lies in the introduction of a hyperparameterized method for down-selecting the number of candidates to the allowed batch-size, which is optimized offline using automated algorithm configuration. We tune this method for black box optimization and then evaluate on classical black box optimization benchmarks. Our results show that it is possible to learn how to combine evaluation points suggested by highly diverse black box optimization methods conditioned on the progress of the optimization. Compared with the state of the art in black box minimization and various other methods specifically geared towards few-shot minimization, we achieve an average reduction of 50\% of normalized cost, which is a highly significant improvement in performance.

We show how both techniques can be combined MaxSAT is the optimization version of the Satisfiability and empirically demonstrate on SAT that our improved (SAT) problem. It can be used effectively to model problems method works notably better than the original method and in several domains, such as scheduling, timetabling, other instance-specific algorithm tuners. We then apply the FPGA routing, design and circuit debugging, software package new technique to MaxSAT. Finally, in extensive experiments installation, bioinformatics, probabilistic reasoning, etc. we show that the developed solvers significantly outperform From the research perspective, MaxSAT is also of particular the current state-of-the-art in every MaxSAT domain.

We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver. We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.