Abstract Univariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting trees are significantly smaller and more accurate than their univariate counterparts due to their ability of adapting better to the underlying data and capturing interactions of attribute pairs. Moreover, our evaluation shows that our algorithm even outperforms algorithms based on heuristically obtained multivariate oblique splits despite the fact that we are focusing on two attributes only.

Platooning – vehicles travelling close together behaving as a unit – aims to improve network throughput both on highways and in urban traffic. We study the problem of platoon formation in an urban environment using the scenario of logistic service providers equipped with fleets of autonomously driving pods to carry out same-day delivery tasks by creating cross-provider platoons. The novelty of our work is that we investigate the problem of cross-provider platoons, i.e., platoons with members from different self-interested logistic service providers. Our aim is to study platoon formation mechanisms and possible benefits of cross-provider platooning using simulation. We formulate optimal platoon formation as an integer linear optimisation problem (ILP), aiming to find the longest sub-routes to be shared between vehicles by platooning. The proposed method was implemented and tested on a mesoscopic model to simulate platoon formation and operation, on real network data with realistic background traffic models. Comparing our method to a simpler route matching algorithm reveals comparable system level performance; however, our method performs better with respect to local participant utility, i.e.appears more suited to take vehicle/provider preferences into account.

The Traveling Tournament Problem (TTP) is a complex problem in sports scheduling whose solution is a schedule of home and away games meeting specific feasibility requirements, while minimizing the total distance traveled by all the teams. A recently-developed "hybrid" algorithm, combining local search and integer programming, has resulted in best-known solutions for many TTP instances. In this paper, we tackle the TTP from a graph-theoretic perspective, by generating a new "canonical" schedule in which each team's three-game road trips match up with the underlying graph's minimum-weight P_3-packing. By using this new schedule as the initial input for the hybrid algorithm, we develop tournament schedules for five benchmark TTP instances that beat all previously-known solutions.

Abstract We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which may depend on the arc. This problem has recently been shown to be weakly NP ‐complete even on series–parallel graphs. In this article, we provide further complexity and approximability results for MFPMQ and several special cases. We first show that it is strongly NP ‐hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor. On series–parallel graphs, however, we present a pseudo‐polynomial time dynamic programming algorithm for the problem. We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still weakly NP ‐complete on general graphs, but can be solved in strongly polynomial time on series–parallel graphs. On general graphs, we present a \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}(2-\frac{1}{\lambda})\end{align*}\end{document} ‐approximation algorithm for this case, where λ denotes the common minimum quantity of all arcs. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013