Cable-Driven Parallel Robots (CDPRs) are a class of parallel robots whose legs consist of cables. In most previous studies, the positions of the cable connection points on the moving platform and on the base frame are fixed, these positions being determined during the CDPR design. However, such fixed-configuration CDPRs are not always suitable and some situations require reconfiguration capabilities, e.g. a cluttered environment where cable collisions with objects in the CDPR workspace cannot be completely avoided without reconfigurations. This paper deals with Reconfigurable Cable-Driven Parallel Robots (RCDPRs) whose cable connection points on the base frame can be positioned at a possibly large but discrete set of possible locations. Means to select and optimize the sequence of discrete reconfigurations allowing the RCDPR moving platform to follow a prescribed path are introduced. A so-called feasibility map is first generated. For each possible configuration of the RCDPR, this map stores the feasible or unfeasible character of each point of the discretized prescribed path, according to user-defined constraints which ensure a proper functioning of the RCDPR. The feasibility map is next analyzed in order to determine minimum sets of configurations which allow the RCDPR to follow the whole prescribed path. Finally, the corresponding discrete reconfiguration planning problem is represented as a graph whose nodes correspond to feasible RCDPR reconfigurations. The arcs of the graph are weighted by a user-defined cost function so that the graph can be searched for an optimal reconfiguration strategy using Dijkstras algorithm.