Constrained Light Deployment for Reducing Energy Consumption in Buildings

Abstract

Lighting systems account for a major part of the energy consumed by large commercial buildings. This paper aims at reducing this energy consumption by defining the Contrained Light Deployment Problem. This new problem is related to the classical Art Gallery Problem (AGP) in computational geometry. In contrast to AGP, which asks for the minimum number of guards to monitor a polygonal area, our problem, CLDP, poses a new challenging requirement: not only must each point p have an unobstructed line-of-sight to a light source, but also, the combined illuminance at p from all light sources must exceed some given threshold value. We provide evidence that our new problem is NP-hard, based on known results for AGP. Then we propose fast heuristics for floor plans shaped like orthogonal polygons, with and without holes. Our problem formulation allows lights to be placed internally, not only at vertices. Our algorithm, which combines ideas from computational geometry, clustering and binary search, computes a set of light placements that satisfies the illumination requirement. The algorithm seeks a light set of minimum size by an iterative binary search procedure that progressively tightens upper and lower bounds.