Single string based global optimizer for geometry optimization in strongly coupled finite clusters: An adaptive mutation-driven strategy

Abstract

We propose and implement a simple adaptive heuristic to optimize the geometries of clusters of point charges or ions with the ability to find the global minimum energy configurations. The approach uses random mutations of a single string encoding the geometry and accepts moves that decrease the energy. Mutation probability and mutation intensity are allowed to evolve adaptively on the basis of continuous evaluation of past explorations. The resulting algorithm has been called Completely Adaptive Random Mutation Hill Climbing method. We have implemented this method to search through the complex potential energy landscapes of parabolically confined 3D classical Coulomb clusters of hundreds or thousands of charges--usually found in high frequency discharge plasmas. The energy per particle (EN∕N) and its first and second differences, structural features, distribution of the oscillation frequencies of normal modes, etc., are analyzed as functions of confinement strength and the number of charges in the system. Certain magic numbers are identified. In order to test the feasibility of the algorithm in cluster geometry optimization on more complex energy landscapes, we have applied the algorithm for optimizing the geometries of MgO clusters, described by Coulomb-Born-Mayer potential and finding global minimum of some Lennard-Jones clusters. The convergence behavior of the algorithm compares favorably with those of other existing global optimizers.

Evolutionary optimization of PAW data-sets for accurate high pressure simulations

“…Thus CARMHC is a smartly coded prescription to quickly generate initial trial solutions for the GA. More details can be found in the cited references. [35][36][37][38] Once the external archive is populated with 2 × n p solution strings (or individuals, or chromosomes), they are fed into a second in-house GA code's initial population and are evaluated for their fitness (Eqs. 7 and 8).…”

“…For more details about CARMHC algorithm, we refer to the existing literature. 38 The underlying principle is to randomly search for a better solution (s ′ ) in the neighborhood of the current solution (s) by mutating the string s with some chosen meta-heuristics (problem-independent rule to perturb the solution string). The atomic program generates the mutated PAW data-set in every generation and the atomic fitness value f s atom is evaluated according to Eqs.…”

“…[35][36][37][38] The GA starts with a population of potential solutions S = {s} i , i = 1, n p , where n p is the cardinality of the population, that is allowed to undergo a simulated evolution in a sense that in each generation (iteration step) the relatively good solutions are allowed to stay on and reproduce while the bad ones die out, moving the population toward better solutions. The evolution usually starts with a randomly generated population of individuals (candidate solutions).…”

“…One or more elements in s have been chosen for mutation with probability p m . Both parameters p m and ∆ m in the meta-heuristics CARMHC have been adaptively determined based on previous exploratory performances of this algorithm 35,38.…”

Flying onto global minima on potential energy surfaces: A swarm intelligence guided route to molecular electronic structure

“…In‐built mechanism for escape from traps coupled with energy minimization has led to a number of successful strategies for the search for global minimum on static PESs. Notables in this category are basin hopping, minima hopping, genetic algorithms, and the more recently proposed completely adaptive random mutation hill climbing, modified artificial Bee colony, and dynamic lattice searching algorithms . The task of effectively combining such techniques with a recipe for simultaneous search for the global optimum charge distribution is a demanding one and the current state of development in this rapidly evolving field has been extensively reviewed recently by Heiles and Johnston and later by Sarkar and Bhattacharyya .…”