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]

In this study, a complete solution of the Navier-Stokes equations has been obtained along with those for heat and mass transfer. The results obtained herein are compared with those for the potential flow situation. Calculations were performed for an isolated single bubble surrounded by matte

Applicability of potential flow assumption for bubbles in copper-making condition

Hybrid Multi-Objective Optimization Approach in Water Flooding

The efficacy of biologically inspired genetic algorithms for optimization is now well established. This article discusses the scope of using such an algorithm as an equation solver and presents detailed calculations on the Pb-S-O vapor system containing a total of 20 species as a paradigm case. This further increases the scope of applications of this evolutionary methodology in the domain of phase equilibria research, and this methodology is expected to be more advantageous than many other conventional techniques.

Pb-S-O vapor system re-evaluated using genetic algorithms

Background/purpose: Low grade nickeliferrous ore recently discovered in Sukinda, India is still not commercially exploited. Selective reduction of nickel followed by alkaline leaching is however a suggested strategy for Ni extraction from this lateritic deposit. This paper examines the reduction process in detail under a packed bed configuration with gas flowing vertically through the bed. Methods: Reduction roasting of Indian Nickeliferrous ores was performed in a laboratory scale packed bed reactor using hydrogen as the reducing agent. A mathematical model was also developed, considering a steady state solution for fluid flow though the packed bed by Ergun's equation, and simultaneous transient solutions for the heat and mass balances of the gas and solid phases, giving rise to a quasi-steady state formulation. Results: The experimental and simulated results showed a reasonably good match. Effect of some of the important parameters such as pellet size, gas velocity and composition were also studied computationally, providing further insight into the process. Conclusion: Based upon the laboratory and modeling studies undertaken during the present investigation, the packed bed selective reduction of Indian lateritic ore appears to be a feasible process. The results can be further extended for analyzing the industrial shaft furnaces where gas-solid contacting is similar to that used in the laboratory experiments.

Nirupam Chakraborti

Papers

Applicability of potential flow assumption for bubbles in copper-making condition

Hybrid Multi-Objective Optimization Approach in Water Flooding

Pb-S-O vapor system re-evaluated using genetic algorithms

Reduction of Indian nickeliferrous ore in a fixed bed reactor with gas flowing vertically through the bed

Editorial: Following a Genetic Hunch