There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Artificial bee colony (ABC) algorithm is an optimization algorithm based on a particular intelligent behaviour of honeybee swarms. This work compares the performance of ABC algorithm with that of differential evolution (DE), particle swarm optimization (PSO) and evolutionary algorithm (EA) for multi-dimensional numeric problems. The simulation results show that the performance of ABC algorithm is comparable to those of the mentioned algorithms and can be efficiently employed to solve engineering problems with high dimensionality.

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On the performance of artificial bee colony (ABC) algorithm

A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multi-objective optimization problems. However, there lacks an upto-date and comprehensive software platform for researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multiobjective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]

The Ti-Co-C system (titanium-cobalt-carbon)

Shear deformation analysis and diffusion behavior of Copper-Zirconium Bulk Metallic Glasses (BMG) is studied for different combinations of processing parameters. Melt holding temperature, melt holding duration, cooling rate of melt and composition of BMG are varied to obtain BMGs of different structures. The as-quenched structures are characterized using Radial Distribution Function (RDF) and Self-Diffusion constant values (of each atom type). The objective of this study is to design a Cu-Zr BMG which can absorb maximum energy and still deform as little as possible while maximizing its diffusivity during shear deformation of the structure. For this, metamodels were constructed by feeding the Molecular Dynamics (MD) results to an Evolutionary Neural Network (EvoNN) so as to generate the desired objective functions which are then optimized through multiobjective genetic algorithm. This led to identification of some hitherto unknown structures, characterized by atomic coordinates, which have good resistance ...

Designing Cu-Zr Glass Using Multiobjective Genetic Algorithm and Evolutionary Neural Network Metamodels–Based Classical Molecular Dynamics Simulation

Microwave plasma discharges of CF4, SF6 and CHF3 at high pressures (0.5-1.5 Torr) have been used for rapid etching of silicon, silicon dioxide and silicon nitride suitable for single-wafer etching applications. Etch rates and selectivities have been studied as a function of pressure, gas flow and the amount of O2 as the additive gas. Extremely high etch rates of 2.0-3.6 mu m min-1 and 5.0 mu m min-1 for silicon, obtained respectively in an CF4 and a CF4+20% O2 plasma can be useful for deep-trench etching applications. Formation of a sidewall passivation layer in silicon at high CF4 pressure ( approximately=1.2 Torr) gives rise to good etching anisotropy. The variation of etch selectivity between SiO2 and Si3N4 has been studied as a function of gas flow rates in SF6 plasma. The formation of a thin fluorocarbon polymer film on the etching surface in a CHF3 plasma, which has resulted in selective etching of SiO2 over Si3N4, has been observed by X-ray photoelectron spectroscopy.

http://iopscience.iop.org/article/10.1088/0268-1242/8/4/019/pdf

Rapid plasma etching of silicon, silicon dioxide and silicon nitride using microwave discharges

The anisotropic coefficients of Hill’s yield criterion are determined through a novel genetic algorithms-based multi-objective optimization approach. The classical method of determining anisotropic coefficients is sensitive to the effective plastic strain. In the present procedure, that limitation is overcome using a genetically evolved meta-model of the entire stress strain curve, obtained from uniaxial tension tests conducted in the rolling direction and transverse directions, and biaxial tension. Then, an effective strain that causes the least error in terms of two theoretically derived objective functions is chosen. The anisotropic constants evolved through genetic algorithms correlate very well with the classical results. This approach is expected to be successful for more complex constitutive equations as well.

Nirupam Chakraborti

Papers

The Ti-Co-C system (titanium-cobalt-carbon)

Designing Cu-Zr Glass Using Multiobjective Genetic Algorithm and Evolutionary Neural Network Metamodels–Based Classical Molecular Dynamics Simulation

Rapid plasma etching of silicon, silicon dioxide and silicon nitride using microwave discharges

A Novel Multi-objective Genetic Algorithms-Based Calculation of Hill’s Coefficients

Interfacial energy of copper clusters in Fe-Si-B-Nb-Cu alloys