Algorithms for the model configuration problem

A very large scale neighborhood search algorithm for theq-mode problem

“…Note that the 1-mode problem is simply the problem of finding the mode of the given collection of vectors, and hence it can be solved efficiently as discussed earlier. For q ≥ 2 the q-mode problem is conjectured to be NP-hard, although no proof is available in the open literature as of this writing (Morgan et al, 2004).…”

“…For a given collection of p vectors in CV nm (i.e., vectors of categorical data as defined above), say Φ = U 1 , · · · , U p , it can be shown that the total distance between these vectors and their mode is smaller than or equal to the total distance between these vectors and any other vector of the same size in CV nm (Morgan et al, 2004). In other words:…”

“…We now define the mode of Φ as a vector of size n where its jth element is i * (j), for all j = 1 to n. We denote this vector by mod(Φ) and its jth element by mod j (Φ) = i * (j) for all j. Note that given a collection of vectors Φ ⊆ CV nm its mode vector can be determined efficiently and the corresponding computational requirement is O(np) (Morgan et al, 2004), where p is the cardinality of the set Φ.…”

“…In Morgan et al (2004) this problem arises in the context of a manufacturing process. The product is a "switching cabinet" that needs to be configured according to a certain set of specifications for each customer.…”

“…Its applications include the problem of pattern discovery in computational biology (Rigoutsos et al, 2000), design of cluster-based document retrieval systems (Jain et al, 1999), creating clusters among a given collection of transactional data in market analysis (Guha et al, 2000), and the model configuration problem in the context of switching cabinet manufacturing (Morgan et al, 2004), among others. Of course each application could have certain distinguishing characteristics that are unique to that application.…”