Abstract Scalarization is a common technique to transform a multiobjective optimization problem into a scalar-valued optimization problem. This article deals with the weighted Tchebycheff scalarization applied to multiobjective discrete optimization problems. This scalarization consists of minimizing the weighted maximum distance of the image of a feasible solution to some desirable reference point. By choosing a suitable weight, any Pareto optimal image can be obtained. In this article, we provide a comprehensive theory of this set of eligible weights. In particular, we analyze the polyhedral and combinatorial structure of the set of all weights yielding the same Pareto optimal solution as well as the decomposition of the weight set as a whole. The structural insights are linked to properties of the set of Pareto optimal solutions, thus providing a profound understanding of the weighted Tchebycheff scalarization method and, as a consequence, also of all methods for multiobjective optimization problems using this scalarization as a building block.

Despite recent interest in multiobjective integer programming, few algorithms exist for solving biobjective mixed integer programs. We present such an algorithm: the boxed line method. For one of its variants, we prove that the number of single-objective integer programs solved is bounded by a linear function of the number of nondominated line segments in the nondominated frontier. This is the first such complexity result. An extensive computational study demonstrates that the box line method is also efficient in practice and that it outperforms existing algorithms on a diverse set of instances.

Summary We describe a sustainable strategy to support a large number of researchers with widely varying scientific software needs, which is a common problem for most centralized Research Computing Centers on university campuses. Changes in systems and hardware, coupled with aging software, often necessitates re‐compilation of existing software. The naive approach of re‐compiling all of the existing packages is not only counterproductive but may also become unrealistic, especially for small support teams such as Georgia Tech's PACE Team. Instead, we analyze job scheduling data to identify actively used software, then rank, and distribute them in three support tiers, which define the level of support we provide. The distribution of software into multiple tiers is a non‐trivial problem. We use a heuristic ranking algorithm that uses four metrics, namely the number of users, groups, jobs, and their collective runtimes. The results revealed a surprisingly small subset of software that is sufficient to support a very large portion of the overall research computing activity on campus. This approach allows us to make data‐driven strategic technical and policy decisions to provide high‐quality support for the software that really matters and sustain these services with a relatively small team in the long term.