This paper describes an automated planner for visual inspection and monitoring tasks using a robot mounted CCD camera. It is capable of finding heuristically near-optimal viewing positions for a series of visual tasks, and of ordering them and planning robot paths between them to produce a near minimal cost overall task plan for the sequence. It has been optimized for intervention-style tasks with relatively large, cluttered workspaces, where it is difficult for a human operator to take account of all the constraints involved. The guiding principle of the work has been to aim for reliability by using quantitative, physically-based measures of quality wherever possible, and by using global search to ensure that possible solutions are not overlooked. We discuss a novel global function optimization technique based on decision theory and subjective models of function behaviour, that allows global viewpoint searches to run in the time usually required for local ones.