Comparison study of pivot methods for global optimization

Abstract

Articles you may be interested inFast optimization of binary clusters using a novel dynamic lattice searching method We compare two implementations of a new algorithm called the pivot method for the location of the global minimum of a multiple minima problem. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The original implementation, called the ''lowest energy pivot method,'' chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the ''nearest neighbor pivot method,'' chooses the pivot probes to be the nearest neighbor points in the phase space. We examine the choice of distribution by comparing the efficiency of the methods for Gaussian versus generalized q-distribution, based on the Tsallis entropy in the relocation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones clusters of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is superior to previous methods.

A time performance comparison of particle swarm optimization in mobile devices

“…The objective of this experiment is to evaluate the performance of an implementation of the Particle Swarm Optimization algorithm running on 3 smartphones with different mobile OS each (Android, iOS, and Windows Mobile) which evaluates 7 well-known benchmark functions for optimization (Ackley [25], Goldstein-Price [26], Rastrigin [27], Rosenbrock [28], Rotated HyperEllipsoid [29], Sphere [30] and Sum Squares [31]). Table 2 provides a brief overview of the tested benchmark functions, while Table 3 outlines the relevant specifications of the 3 mobile devices [32] used for the analysis.…”

Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians

“…The general structure of the algorithm is made up by dividing the population into several disjunct groups each of which has its leader (the best member of the group) and members. The algorithm which is different from the earlier evolutionary algorithms and the pivot method algorithm [22][23][24] consists of two parts. In the first part, the member itself-the group leader with possible random part-and a new-created random solution are used to form a new member.…”

Particle Swarms and Nonextensive Statistics for Nonlinear Optimisation

“…Nonextensive statistical mechanics has successfully been applied in physics (astrophysics, astronomy, cosmology, nonlinear dynamics etc.) [35][36][37], chemistry [38], biology [39], economics [40], computer science [41], and other disciplines [30].…”