Stopping rules in k-adaptive global random search algorithms

Abstract

In this paper we develop a methodology for defining stopping rules in a general class of global random search algorithms that are based on the use of statistical procedures. To build these stopping rules we reach a compromise between the expected increase in precision of the statistical procedures and the expected waiting time for this increase in precision to occur.

Performance of global random search algorithms for large dimensions

“…In view of (14), this efficiency tends to 1/k if k is fixed and α → ∞. The asymptotic behaviour of the efficiency (15) is illustrated in Figure 8.…”

Statistical Estimation in Global Random Search Algorithms in Case of Large Dimensions

“…3. The exact expression of C k,α (solid) and the approximation (4) (dashed) for k = 2 (left) and k = 10 (right); α varies in [5,50]. Fig.…”

“…Asymptotic efficiency eff(y1,n) of y1,n. Left: k = 2 (solid) and k = 10 (dashed); as α varies in [5,40]. Right: α = 5 (solid) and α = 25 (dashed); as k varies in [2,20].…”

“…Statistical inference about f * can serve for the following purposes: (i) devising specific GRS algorithms like the branch and probability bounds methods, see [2,6] and [4,Sect. 4.3], (ii) constructing stopping rules, see [5], and (iii) increasing efficiency of population-based GRS methods, see discussion in [3, Sect. 2.6.1].…”