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.

/pdf/on-the-performance-of-artificial-bee-colony-abc-algorithm-5234goeamq.pdf

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]

Chapter 4 Evolutionary Algorithms In Ironmaking Applications

A review of the metallurgical and chemical literature involving foams and emulsions is presented. Experimental techniques for the measurement of drop sizes in such systems are reviewed, and the basic mechanisms of drop breakup and coalescence are discussed, along with an analysis of the pertinent mass-transfer processes. A detailed discussion on a number of industrial processes using foams and emulsions is also presented.

Emulsions in metallurgical and chemical processes

Little attention has been paid during process development studies to possible changes in cost of metal production when a process plant is exposed to varying degrees of metal grades emanating from a sea nodules mining area. Study of these aspects requires process optimization. An approach for optimization of a process technology at a given throughput of nodules has been developed. This uses a robust multi-objective process optimization technique coupled with process simulation and indicative cost economics. A case study illustrates the approach; minimization of process chemical cost with simultaneous maximization of metal values produced is considered. The approach may easily be extended to include other objectives, including energy, for any process technology. laboratory scale studies were conducted leading to solubilization of all metals including manganese. Other potentially novel reagents for manganese nodules have been reviewed by Mukherjee et.al. (2004). Whereas these studies were directed at improving the performance of sulfuric acid leaching, the results cannot be analyzed from the point of view of flow sheet development and subsequent process design. A major challenge in process design is to assess the viability of processing such a widely varying grade of an oceanic low grade manganese resource for recovery of manganese and other valuable metals. Any process scheme developed for multi metal recovery would need to be assessed from the angle of sensitivity of the proposed scheme to metal throughput and direct chemical costs incurred with input ore grade variation. As any developed process scheme would have certain constraints with regard to the operating variables, the proposed scheme could be optimal only for a certain range of input grades of the raw materials. Chemical composition of these nodules changes from location to location across the vast sea bed. Manganese, which is present as manganese dioxide, is the major metallic component, varying over a wide range of 17 % to 30 %. Other associated metals present in the nodule matrix are of lower proportions in comparison to manganese. The composition of medium grade sea nodules on average vary between Mn: 17 - 28%, Cu: 0.5 - 1.3%, Ni: 0.5 - 1.3% and Co: 0.1- 0.26%. Higher grade sea nodules, as is typically displayed for Pacific sea nodule, have the range of Mn: 24-30%, Cu: 0.8-1.4%, Ni: 0.8-1.4% and Co: 0.16%-0.26%. The present paper brings into focus the methodology for choosing an appropriate ore grade range for a given process flow sheet. As any developed process scheme would have certain constraints with regard to the operating variables, the proposed scheme could be optimal only for a certain range of input grades of the raw materials. Use of a process optimization strategy would be a vital requirement for that. Pareto optimal solutions can be developed and appropriate decisions regarding the varying grades of raw material to be used for a given flow sheet can then be arrived at. Only use of different optimal solutions, however, may not permit choice of the input grade of nodules; indicative profitability for the different input grades for a given flow sheet under known recovery conditions would be useful to arrive at decisions with respect to ore grades. Thus, the present paper would be dealing additionally with the development of an indicative cost model.

Use of Process Optimization And Cost Model For Metal Recovery From Manganese Nodules:The Role of Manganese Recovery

A hot rolled strip produced by any integrated steel plant would require satisfying some stringent requirements of its surface profile. Crown and Flatness are two industrially accepted quantifiers that relate to the geometric tolerances in the rolled strips.

This study attempts to regulate both crown and flatness within an acceptable limit, satisfying more than one objective at a time. Mathematically, this leads to a multi-objective optimization problem where the solution is no longer unique and a family of equally feasible solutions leads to the so called Pareto-Front, where each member is simply as good as the others. To implement this concept in the present context, one needs to realize that the surface deformation, which is ultimately imparted to the rolled sheets, comes from more than one source. The wear of the rolls, their thermal expansion, bending, and also deformation, contribute significantly towards the crown and flatness that is ultimately observed. During this study a detailed mathematical model has been worked out for this process incorporating all of these phenomena. Computation for the Pareto-optimality has been carried out using different forms of biologically inspired Genetic Algorithms, often integrated with an Ant Colony Optimization Scheme. Ultimately the model has been fine tuned for the hot rolling practice in a major integrated steel plant and tested against their actual operational data.

https://drops.dagstuhl.de/opus/volltexte/2005/245/pdf/04461.ChakrabortiNirupam1.Paper.245.pdf/

Optimizing Surface Profiles during Hot Rolling: A Genetic Algorithms based Multi-objective Analysis

Background/purpose: Although the principle of gas injection in molten pig iron is of utmost importance in the steel industry, the visualization studies of bubbles in molten metal are quite rare in the metallurgical literature due to the extreme difficulty of experimentation. The present study attempts one such visualization which is supported by the pertinent theoretical analysis. Methods: Direct observation of Ar bubbles in molten pig iron was conducted using a recently-developed high voltage X-ray fluoroscopic technique. A large number of bubble photographs were subjected to theoretical analysis revealing some fundamental information regarding the mechanism of bubble formation in a molten iron bath. Results: A large number of deformed bubbles were visualized during this study which were earlier predicted by theoretical analysis and computer simulation. The theoretical analysis carried out during this study highlighted the fundamental principles behind such bubble deformation. Conclusion: A further insight into the process of formation of bubbles inside a molten metal is obtained in this study and the findings of this work are expected to be more reliable than the conventional water model studies.

Nirupam Chakraborti

Papers

Chapter 4 Evolutionary Algorithms In Ironmaking Applications

Emulsions in metallurgical and chemical processes

Use of Process Optimization And Cost Model For Metal Recovery From Manganese Nodules:The Role of Manganese Recovery

Optimizing Surface Profiles during Hot Rolling: A Genetic Algorithms based Multi-objective Analysis

In situ observation of bubbles in molten pig iron