Some Algorithms for “Bond Energy” Data Analysis, Including Simulated Annealing

Abstract

The applicability of Simulated Annealing (SA) (Kirkpatrick et al. (1983)) is studied in the context of the data analysis scheme of the “bond energy algorithm” originally proposed by McCormick et al. (1972) for permuting rows and columns of data matrices into visually interpretable forms. To evaluate the performance of three variations of SA, they were compared to two deterministic, heuristic methods known to perform well for the particular type of data analysis task chosen: (1) the streamlined implementation of the Bond Energy Algorithm (BEA) of Arabie et al. (1988) and Schleutermann (1989) that improves upon the original version of McCormick et al. (1972), and (2) the well-known Lin and Kernighan Algorithm (LK) (1973) for the Traveling Salesman Problem (TSP). Contrary to earlier findings (e.g., De Soete et al. (1988a, 1988b)), a version of simulated annealing was developed that performs well in a time complexity comparable to that of our implementation of Lin and Kernighan’s algorithm. From the empirical results, it appears that suitable implementation of a simulated annealing algorithm can outperform good deterministic algorithms in some data analysis applications. For speeding up execution of the SA algorithm, the focus here is on the use of a state transition scheme less randomized than others often suggested in the literature on SA.