Comparing search strategies for finding global optima on energy landscapes

Abstract

We provide some tests of the convex global underestimator (CGU) algorithm, which aims to find global minima on funnel‐shaped energy landscapes. We use two different potential functions—the reduced Lennard–Jones cluster potential, and the modified Sun protein folding potential, to compare the CGU algorithm with the simplest versions of the traditional trajectory‐based search methods, simulated annealing (SA), and Monte Carlo (MC). For both potentials, the CGU reaches energies lower on the landscapes than both SA and MC, even when SA and MC are given the same number of starting points as in a full CGU run or when all methods are given the same amount of computer time. The CGU consistently finds the global minima of the Lennard–Jones potential for all cases with up to at least n=30 degrees of freedom. Finding the global or near‐global minimum in the CGU method requires polynomial time [scaling between O(n3) and O(n4)], on average. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1527–1532, 1999

Structural Transitions in Clusters

“…Systematic and fair comparisons of such methods are very rare in the literature, and often limited to small systems 90. At least for the benchmark system of LJ clusters, which was treated with a wide variety of global optimization algorithms,67 “basin hopping”,79 and EAs88, 89 seem to be the only methods able to treat also the notoriously difficult cases n =75–77 and n =102–104 without prior information.…”

Energy-directed tree search: an efficient systematic algorithm for finding the lowest energy conformation of molecules

“…There have been numerous comparative studies in which the relative merits of various conformational search routines have been examined. 8,9,16,21,[31][32][33][34][35] However, it is difficult to identify a definitive optimal method as the criteria by which the methods were assessed varies considerably amongst the studies, and no one study has compared all of the principal types of methods. Nonetheless, a few general observations may be made.…”

“…Amongst the stochastic methods studied, it has been found that those which use the existing results to direct the search outperform purely random methods, 8,9 methods based on genetic algorithms tend to outperform simulated annealing, 15,31 and the quantum annealing method, quantum path minimization, was shown in one study to outperform both simulated annealing and a genetic algorithm. 21 When stochastic methods are compared with (full) systematic methods, the stochastic search methods tend to be more efficient in identifying low energy conformations early in the search, but they rapidly lose this advantage as the search proceeds and are less efficient in finding the global minimum structure.…”

Strukturübergänge in Clustern

“…Systematische und faire Vergleiche derartiger Verfahren sind in der Literatur leider sehr selten und oft beschränkt auf wenig aussagekräftige kleine Systeme 90. Zumindest im mit extrem vielen Methoden67 bearbeiteten Bezugssystem der LJ‐Cluster sind jedoch nach meinen Informationen „Basin Hopping“79 und EAs88, 89 die einzigen Verfahren, die ohne Vorinformationen auch die notorisch schwierigen Fälle n =75–77 und n =102–104 bewältigen können.…”