ABSTRACT In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard problem, which justifies heuristics methods for its resolution in larger instances. The main feature of our heuristic is based on the selection of the next circle to be placed inside the container according to the position of the system's center of mass. Our approach has been tested on a series of instances up to 55 circles and compared with the literature. Computational results show good performance in terms of solution quality and computational time for the proposed algorithm.

ABSTRACT In this paper we study a particular aspect of the urban community policing: routine patrol route planning. We seek routes that guarantee visibility, as this has a sizable impact on the community perceived safety, allowing quick emergency responses and providing surveillance of selected sites (e.g., hospitals, schools). The planning is restricted to the availability of vehicles and strives to achieve balanced routes. We study an adaptation of the model for the multi-vehicle covering tour problem, in which a set of locations must be visited, whereas another subset must be close enough to the planned routes. It constitutes an NP-complete integer programming problem. Suboptimal solutions are obtained with several heuristics, some adapted from the literature and others developed by us. We solve some adapted instances from TSPLIB and an instance with real data, the former being compared with results from literature, and latter being compared with empirical data.