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This paper presents Multi-Step A^\ast (MSA ^\ast), a search algorithm based on A ^\ast for multi-objective 4-D vehicle motion planning (three spatial and one time dimensions). The research is principally motivated by the need for offline and online motion planning for autonomous unmanned aerial vehicles (UAVs). For UAVs operating in large dynamic uncertain 4-D environments, the motion plan consists of a sequence of connected linear tracks (or trajectory segments). The track angle and velocity are important parameters that are often restricted by assumptions and a grid geometry in conventional motion planners. Many existing planners also fail to incorporate multiple decision criteria and constraints such as wind, fuel, dynamic obstacles, and the rules of the air. It is shown that MSA ^\ast finds a cost optimal solution using variable length, angle, and velocity trajectory segments. These segments are approximated with a grid-based cell sequence that provides an inherent tolerance to uncertainty. The computational efficiency is achieved by using variable successor operators to create a multiresolution memory-efficient lattice sampling structure. The simulation studies on the UAV flight planning problem show that MSA^\ast meets the time constraints of online replanning and finds paths of equivalent cost but in a quarter of the time (on average) of a vector neighborhood-based A^\ast. [ABSTRACT FROM AUTHOR]

Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible with business constraints such as size and stability considerations. Additionally, statistical peer groups are constructed from many different variables, and can be difficult to understand, especially for non-statistical audiences. We developed methodology to apply business constraints to clustering solutions and allow the decision-maker to choose the balance between statistical goodness-of-fit and conformity to business constraints. Several tools were utilised to identify complex distinguishing features in peer groups, and a number of visualisations are developed to explain high-dimensional clusters for non-statistical audiences. In a case study where peer group size was required to be small (≤ 100 members), we applied constrained clustering to a noisy high-dimensional data-set over two subsequent years, ensuring that the clusters were sufficiently stable between years. Our approach not only satisfied clustering constraints on the test data, but maintained an almost monotonic negative relationship between goodness-of-fit and stability between subsequent years. We demonstrated in the context of the case study how distinguishing features between clusters can be communicated clearly to different stakeholders with substantial and limited statistical knowledge. [ABSTRACT FROM AUTHOR]