THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

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Evolutionary algorithms for solving multi-objective problems

Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art

: This research organizes, presents, and analyzes contemporary Multiobjective Evolutionary Algorithm (MOEA) research and associated Multiobjective Optimization Problems (MOPs). Using a consistent MOEA terminology and notation, each cited MOEAs' key factors are presented in tabular form for ease of MOEA identification and selection. A detailed quantitative and qualitative MOEA analysis is presented, providing a basis for conclusions about various MOEA-related issues. The traditional notion of building blocks is extended to the MOP domain in an effort to develop more effective and efficient MOEAs. Additionally, the MOEA community's limited test suites contain various functions whose origins and rationale for use are often unknown. Thus, using general test suite guidelines appropriate MOEA test function suites are substantiated and generated. An experimental methodology incorporating a solution database and appropriate metrics is offered as a proposed evaluation framework allowing absolute comparisons of specific MOEA approaches. Taken together, this document's classifications, analyses, and new innovations present a complete, contemporary view of current MOEA "state of the art" and possible future research. Researchers with basic EA knowledge may also use part of it as a largely self-contained introduction to MOEAs.

Multiobjective evolutionary algorithms: classifications, analyses, and new innovations

Particle Swarm Optimization (PSO) is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. PSO is similar to the Genetic Algorithm (GA) in the sense that these two evolutionary heuristics are population-based search methods. In other words, PSO and the GA move from a set of points (population) to another set of points in a single iteration with likely improvement using a combination of deterministic and probabilistic rules. The GA and its many versions have been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly nonlinear, mixed integer optimization problems that are typical of complex engineering systems. The drawback of the GA is its expensive computational cost. This paper attempts to examine the claim that PSO has the same effectiveness (finding the true global optimal solution) as the GA but with significantly better computational efficiency (less function evaluations) by implementing statistical analysis and formal hypothesis testing. The performance comparison of the GA and PSO is implemented using a set of benchmark test problems as well as two space systems design optimization problems, namely, telescope array configuration and spacecraft reliability-based design.

http://web.mit.edu/deweck/www/PDF_archive/3%20Refereed%20Conference/3_50_AIAA-2005-1897.pdf

A comparison of particle swarm optimization and the genetic algorithm

A parallel genetic algorithm (GA) methodology was developed to generate a family of two-dimensional airfoil designs that address rotorcraft aerodynamic and aeroacoustic concerns The GA operated on 20 design variables, whichconstitutedthecontrolpointsforasplinerepresentingtheairfoilsurfaceTheGAtookadvantageofavailable computer resources by operating in either serial mode, where the GA and function evaluations were run on the same processor or “ manager/worker” parallel mode, where the GA runs on the manager processor and function evaluations areconducted independently on separate workerprocessors The multiple objectives of this work were to minimizethedrag and overall noiseof the airfoil Constraintswereplaced on liftcoefe cient, moment coefe cient, andboundary-layerconvergenceTheaerodynamicanalysiscodeXFOILprovidedpressureandsheardistributions in addition to liftand drag predictions Theaeroacousticanalysis code, WOPWOP, provided thicknessand loading noise predictions The airfoils comprising the resulting Pareto-optimal set exhibited favorable performance when compared with typical rotorcraft airfoils under identical design conditions using the same analysis routines The relationship between the quality of results and the analyses used in the optimization is also discussed The new airfoil shapes could provide starting points for further investigation

Aerodynamic and Aeroacoustic Optimization of Rotorcraft Airfoils via a Parallel Genetic Algorithm

A parallel genetic algorithm (GA) methodology was developed to generate a family of two-dimensional airfoil designs that address rotorcraft aerodynamic and aeroacoustic concerns. The GA operated on 20 design variables, which constituted the control points for a spline representing the airfoil surface. The GA took advantage of available computer resources by operating in either serial mode, where the GA and function evaluations were run on the same processor or manager/worker parallel mode, where the GA runs on the manager processor and function evaluations are conducted independently on separate worker processors. The multiple objectives of this work were to minimize the drag and overall noise of the airfoil. Constraints were placed on lift coefficient, moment coefficient, and boundary-layer convergence. The aerodynamic analysis code XFOIL provided pressure and shear distributions in addition to lift and drag predictions. The aeroacoustic analysis code, WOPWOP, provided thickness and loading noise predictions. The airfoils comprising the resulting Pareto-optimal set exhibited favorable performance when compared with typical rotorcraft airfoils under identical design conditions using the same analysis routines

Aerodynamic and aeroacoustic optimization of rotorcraft airfoils via a parallel genetic algorithm

The phrase "system-of-systems" describes a large system of multiple systems, each capable of independent operation, which have been brought together to provide capabilities beyond those of each individual constituent system. Formulating and solving a system-of-systems design problem has become increasingly important in the aerospace and defense industries as customers have begun to ask contractors for broad capabilities and solutions rather than for specific individual systems. Part of a system-of-systems design problem is determining the appropriate mix of both existing and yet-to-be-designed systems. Whereas determining an appropriate mix of existing systems falls into the category of resource allocation, including features of a yet-to-be-designed system complicates the problem by requiring the allocation of a variable resource. In this paper, an airline wishing to investigate how a new, yet-to-be-designed aircraft will impact the fleet operating costs provides a simple example of this type of problem. The resulting statement is a mixed-integer, nonlinear programming problem. Both a traditional approach and a new decomposition approach were used to solve the problem. The traditional approach is a mixed-integer nonlinear branch-and-bound. The decomposition approach applied to the problem is analogous to those of multidisciplinary optimization, in which there is an allocation domain and an aircraft sizing domain. When the problem size increases to the point where the traditional mixed-integer, nonlinear programming approaches cannot obtain a solution, the decomposition approach can find solutions for these larger problems. The multidisciplinary design optimization-motivated decomposition approach appears to have promise for the allocation of variable resources challenge presented by many system-of-systems design problems.

System-of-Systems Inspired Aircraft Sizing and Airline Resource Allocation via Decomposition

Morphing aircraft are multi-role aircraft that use innovative actuators, effectors, and mechanisms to change their state to perform select missions with substantially improved system performance. State change in this study means a change in the cross-sectional shape of the wing itself, not chord extension or span extension. Integrating actuators and mechanisms into an effective, light weight structural topology that generates lift and sustains the air loads generated by the wing is central to the success of morphing, shape changing wings and airfoils. The objective of this study is to explore a process to link analytical models and optimization tools with design methods to create energy efficient, lightweight wing/structure/actuator combinations for morphing aircraft wings. In this case, the energy required to change from one wing or airfoil shape to another is used as the performance index for optimization while the aerodynamic performance such as lift or drag is constrained. Three different, but related, topics are considered: energy required to operate articulated trailing edge flaps and slats attached to flexible 2D airfoils; optimal, minimum energy, articulated control deflections on wings to generate lift; and, deformable airfoils with cross-sectional shape changes requiring strain energy changes to move from one lift coefficient to another. Results indicate that a formal optimization scheme using minimum actuator energy as an objective and internal structural topology features as design variables can identify the best actuators and their most effective locations so that minimal energy is required to operate a morphing wing. Background

http://dnc.tamu.edu/projects/flowcontrol/Morphing/public_html/papers/opt2.pdf

Morphing airfoil shape change optimization with minimum actuator energy as an objective

The Genetic Algorithm (GA) is employed by different users to solve many problems; however, various challenges and issues surround the appropriate form and parameter settings of the GA. One of these issues is the conflict between theory and experiment regarding the crossover operator. Experimental results suggest that the uniform crossover can provide better results for optimization, so many users wish to employ this approach. Unlike for the single-point crossover GA, no established set of guidelines exists to assist in choosing appropriate population sizes and mutation rates when using the uniform crossover. This paper presents the results of an empirical study to determine such guidelines by examining several parameter combinations on four mathematical functions and one engineering design problem. The resulting guidelines appear to be valid over these test problems. They are presented and discussed, with the intent that they may provide assistance to users of GAs with uniform crossover.

William A. Crossley

Papers

Aerodynamic and Aeroacoustic Optimization of Rotorcraft Airfoils via a Parallel Genetic Algorithm

Aerodynamic and aeroacoustic optimization of rotorcraft airfoils via a parallel genetic algorithm

System-of-Systems Inspired Aircraft Sizing and Airline Resource Allocation via Decomposition

Morphing airfoil shape change optimization with minimum actuator energy as an objective

Empirically-Derived Population Size and Mutation Rate Guidelines for a Genetic Algorithm with Uniform Crossover