5. Heuristic Applications of the GDPP
Society for Industrial and Applied Mathematics eBooks · 2001
The various applications of the GDPP in Chapters 3 and 4 to the optimization tasks of cluster analysis and object sequencing were generally limited to object sets of a certain size because of the necessary storage requirements for carrying out the attendant recursive processes. Although some possibilities may exist for reducing the extent of the basic sets, Ω1, …, ΩK, through some type of restriction on what form an optimal solution can take, which then might allow large object sets to be approached (e.g., through linear ordering constraints), lacking such restrictions there is an inherent upper limit on the magnitude of the optimization tasks that can be handled with guaranteed optimality. If the ideal of guaranteed optimality is, for the moment, put aside, it is generally possible to use the GDPP specializations of Chapters 3 and 4 heuristically by allowing (a) the separate analyses of subsets of a (larger) object set, and (b) the use of classes of objects as the basic entities to be considered (in contrast to allowing the use of single objects only). By the judicious (and sequential) application of both these latter two options, it may be possible to analyze large object sets for the same type of clustering and sequencing tasks discussed in the last two chapters. An absolute guarantee of final optimality usually cannot be given, but we still might do quite well in producing good solutions for the optimization tasks at hand. The two major sections of this chapter discuss the heuristic use of the GDPP within the cluster analysis context (Section 5.1) and for object sequencing and seriation (Section 5.2). The various unconstrained programs mentioned thus far in this monograph also exist in generalized forms that allow parts of a (larger) object set to be studied and the prior specification of certain object classes to be the primary units analyzed.