Pivot method for global optimization

Serra, Pablo; Stanton, Aaron; Kais, Sabre

doi:10.1103/physreve.55.1162

Cited by 39 publications

(30 citation statements)

References 19 publications

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“…The nearest neighbour pivot method [28] with a Gaussian distribution as the pivoting distribution was used to perform the weighted least-squares ®tting. A weighting factor was assigned to each point based on the energy of the point and relative to the point lowest in energy along the containing radial line.…”

Section: Surface ®Ttingmentioning

confidence: 99%

Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex

2002

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A potential energy surface for the system of a hydroperoxy radical and a water molecule is presented. The surface was sampled using constrained density functional theory optimizations performed at the B3LYP level of theory using a 6-311 ‡ ‡G(3df,3pd) basis set. The data points were ®tted to an analytical function based on a common 4-point model for water and a 5-point model for the peroxy radical. A weighted least-squares ®t of the parameters was performed using the nearest neighbour pivot method.

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Section: Surface ®Ttingmentioning

confidence: 99%

Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex

2002

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“…-Pivot strategy This method is inspired by the work of Serra et al (1997). Let us denote the best location of the particle by p, the best position of the informers of the particle by g and the objective function by f .…”

Section: The Strategies Of Displacementmentioning

confidence: 99%

Performance evaluation of TRIBES, an adaptive particle swarm optimization algorithm

2009

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This paper presents a study of the performance of TRIBES, an adaptive particle swarm optimization algorithm. Particle Swarm Optimization (PSO) is a biologicallyinspired optimization method. Recently, researchers have used it effectively in solving various optimization problems. However, like most optimization heuristics, PSO suffers from the drawback of being greatly influenced by the selection of its parameter values. Thus, the common belief is that the performance of a PSO algorithm is directly related to the tuning of such parameters. Usually, such tuning is a lengthy, time consuming and delicate process. A new adaptive PSO algorithm called TRIBES avoids manual tuning by defining adaptation rules which aim at automatically changing the particles' behaviors as well as the topology of the swarm. In TRIBES, the topology is changed according to the swarm behavior and the strategies of displacement are chosen according to the performances of the particles. A comparative study carried out on a large set of benchmark functions shows that the performance of TRIBES is quite competitive compared to most other similar PSO algorithms that need manual tuning of parameters. The performance evaluation of TRIBES follows the testing procedure introduced during the 2005 IEEE Conference on Evolutionary Computation. The main objective of the present paper is to perform a global study of the behavior of TRIBES under several conditions, in order to determine strengths and drawbacks of this adaptive algorithm.

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“…However, in a quantum computer, with enough qubits available, we can perform full optimisation for all atoms. For example, for larger LJ clusters, if we had larger qubits, we could incorporate the partial knowledge that we had by starting with the structure of the smaller (M À k) clusters and adding k additional particles at random [9,42]. In a previous work [9], using the pivot method we have shown that the computational cost (CPU time) scales as M 2.9 with the number of L-J particles to be minimised.…”

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confidence: 97%

“…where Dx i is a randomly generated vector according to a particular distribution such as a Gaussian distribution [9].…”

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Simulated quantum computation of global minima

Zhu¹,

Huang²,

Kais³

2009

Molecular Physics

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Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations N reduced from O(N ) in classical simulation to O( √ N ) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.

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Pivot method for global optimization

Cited by 39 publications

References 19 publications

Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex

Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex

Performance evaluation of TRIBES, an adaptive particle swarm optimization algorithm

Simulated quantum computation of global minima

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Pivot method for global optimization

Cited by 39 publications

References 19 publications

Potential energy surface for the hydroperoxy and water (HO2·H2O) radical complex

Potential energy surface for the hydroperoxy and water (HO2·H2O) radical complex

Performance evaluation of TRIBES, an adaptive particle swarm optimization algorithm

Simulated quantum computation of global minima

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Product

Resources

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Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex

Potential energy surface for the hydroperoxy and water (HO₂·H₂O) radical complex