The automated real time control of an electrical network is achieved through the estimation of its state using phasor measurement units. Given an undirected graph representing the network, we study the problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed. This problem is also known as the Power Edge Set problem, a variant of the Power Dominating Set problem. It is naturally modeled using an iteration-indexed binary linear program, whose size turns out to be too large for practical purposes. We use a fixed-point argument to remove the iteration indices and obtain a more compact bilevel formulation. We then reformulate the latter to a single-level mixed-integer linear program, which performs better than the natural formulation. Lastly, we provide an algorithm that solves the bilevel program directly and much faster than a commercial solver can solve the previous models. We also discuss robust variants and extensions of the problem.
In his 2018 Stockholm prize winner lecture, Goldstein highlighted the need for problem-oriented policing (POP) to be not only effective but also fair. Contributing to the development of POP, this study examines how a wider perspective on problem-solving generally, and scoping in particular, can be adopted to address some of the growing challenges in 21st century policing. We demonstrate that the concept of ‘problem’ was too narrowly defined and that, as a result, many problem-solving models found in criminology are ill-structured to minimize the negative side-effects of interventions and deliver broader benefits. Problem-solving concepts and models are compared across disciplines and recommendations are made to improve POP, drawing on examples in architecture, conservation science, industrial ecology and ethics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.