Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression

The importance of subset selection in multiple regression has been recognized for more than 40 years and, not surprisingly, a variety of exact and heuristic procedures have been proposed for choosing subsets of variables. In the case of polynomial regression, the subset selection problem is complicated by two issues: (1) the substantial growth in the number of candidate predictors, and (2) the desire to obtain hierarchically well‐formulated subsets that facilitate proper interpretation of the regression parameter estimates. The first of these issues creates the need for heuristic methods that can provide solutions in reasonable computation time; whereas the second requires innovative neighborhood search approaches that accommodate the hierarchical constraints. We developed tabu search and variable neighborhood search heuristics for subset selection in polynomial regression. These heuristics are applied to a classic data set from the literature and, subsequently, evaluated in a simulation study using synthetic data sets. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Book reviews

Red Banner: the Soviet Military System in Peace and War. By Christopher Donnelly. Jane's Information Group, Coulsdon, UK (1988), 288 pp., £35.00

Images of T. E. Lawrence. By S. E. Tabachnick and C. Matheson. Jonathan Cape, London (1988); The Letters of T. E. Lawrence. Edited by Malcolm Brown. Dent, London (1988); T. E. Lawrence. By J. Wilson. National Portrait Gallery Publications, London (1988); Lawrence and the Arab Revolts. By D. Nicolle. Osprey, London (1989)

Liddell Hart and the Weight of History. By John Mearsheimer. Brassey's, London (1989), £15.95

Science and Mythology in the Making of Defence Policy. Edited by Margaret Blunden and Owen Greene. Brassey's, London (1989), £27.50/$44.00

Warfare in the Twentieth Century. Edited by Colin McInnes and G. D. Sheffield. Unwin Hyman, London (1988), 239 pp., £25.00     

Closure properties of the relevation transform*

Sufficient conditions under which the relevation of two probability distributions is (i) NBU, (ii) IFRA, (iii) IFR are derived. The result for case (iii) corrects an error in a previous article by Baxter.