Global optimization by excitable walkers Giulia Rossi, Riccardo Ferrando * Dipartimento di Fisica dell’Universita ` di Genova, and IMEM/CNR via Dodecaneso 33, 16146 Genova, Italy Received 31 January 2006; in final form 1 March 2006 Abstract A new global optimization algorithm, based on the concept of excitable walkers, is proposed. The walkers perform parallel Monte Carlo walks on the locally minimized potential energy surface, and effectively repel each other in an appropriate order parameter space. The algorithm is applied to different nanocluster systems (Lennard–Jones and binary metallic clusters) and is proved to be very efficient in locating the global minima of multiple-funnel potential energy surfaces. Ó 2006 Elsevier B.V. All rights reserved. Global optimization techniques are of great interest in physics, chemistry and biology [1]. The location of the lowest lying minimum of the potential energy surface (PES) is a basic issue in cluster, molecular and protein science, and the same computational methods can be successfully applied to different research areas [2]. The PES of atomic clusters can be considered a good test function for global optimization methods. As the litera- ture reports [1], cluster PES can be very different and their minimization can be classified among the NP-hard prob- lems [3]. Cluster PES can exhibit either single or multiple funnels, and the number of local minima can be further increased if the chemical composition is not homogeneous [4,5]. Multiple-funnel PES are in principle much more difficult to optimize. Several global optimization algorithms have been pro- posed in the literature. Some of them are based on the architecture of genetic codes (see for example [6]). Others, like basin-hopping (BH), combine local minimization with Monte Carlo (MC), using the temperature parameter to tune the efficiency of the code [7]. The BH algorithm has revealed as an effective tool to deal with global optimiza- tion problems. Its major values reside in its simple architec- ture, and in its great efficiency in reaching the bottom inside a given funnel. Nevertheless it has been noted [7] that BH can have great difficulties in escaping from a funnel (and thus in exploring multiple-funnel PES), so that the optimization may fail if the starting configuration is not already in the funnel of the global minimum. Some optimi- zation methods build a history path [8], so as to avoid to repeat the same minima sequence more than once during a single optimization. This can be achieved also by defining an order parameter, and building the history path in the space of the parameter itself [2,9] rather than in the cluster configuration space. The counter-indication in using this kind of methods, as already pointed out in [8], is that some minima could play the role of transition basin, and so the return to them should be encouraged rather than penalized. Other methods, like the basin hopping with occasional jumping (BHOJ) algorithm, include a short-time memory [10] into the BH algorithm, forcing the cluster to accept any move if it has been trapped in a minimum for a given number of MC steps. In this Letter, we present a new global optimization algorithm (parallel excitable walkers, PEW) of general applicability, which is especially suited for dealing with multiple-funnel PES. It combines the merit of a simple implementation with a very high efficiency in optimizing multiple funnel PES, such as those of many pure and bin- ary clusters, due to its ability in exploring simultaneously different funnels. PEW is also a fast method for mapping the most significant part of any PES by the exploration of the bottom part of all important funnels. This can be 0009-2614/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.03.003 * Corresponding author. E-mail address: ferrando@fisica.unige.it (R. Ferrando). www.elsevier.com/locate/cplett Chemical Physics Letters 423 (2006) 17–22 ARTICLE IN PRESS