Grey Wolf Optimizer

The Whale Optimization Algorithm

A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

Salp Swarm Algorithm

http://trama.deib.polimi.it/allegati/Kadaba_1990.pdf

Measurement of lower extremity kinematics during level walking

Introduction to Optimum Design, Fourth Edition, carries on the tradition of the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level in engineering departments of all disciplines, with a primary focus on mechanical, aerospace, and civil engineering courses. Through a basic and organized approach, the text describes engineering design optimization in a rigorous, yet simplified manner, illustrates various concepts and procedures with simple examples, and demonstrates their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text using Excel and MATLAB as learning and teaching aids. This fourth edition has been reorganized, rewritten in parts, and enhanced with new material, making the book even more appealing to instructors regardless of course level. * Includes basic concepts of optimality conditions and numerical methods that are described with simple and practical examples, making the material highly teachable and learnable* Presents applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems* Provides practical design examples that introduce students to the use of optimization methods early in the book* Contains chapter on several advanced optimum design topics that serve the needs of instructors who teach more advanced courses

Introduction to Optimum Design

As a common concept in multi-objective optimization, minimizing a weighted sum constitutes an independent method as well as a component of other methods. Consequently, insight into characteristics of the weighted sum method has far reaching implications. However, despite the many published applications for this method and the literature addressing its pitfalls with respect to depicting the Pareto optimal set, there is little comprehensive discussion concerning the conceptual significance of the weights and techniques for maximizing the effectiveness of the method with respect to a priori articulation of preferences. Thus, in this paper, we investigate the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values. We determine the factors that dictate which solution point results from a particular set of weights. Fundamental deficiencies are identified in terms of a priori articulation of preferences, and guidelines are provided to help avoid blind use of the method.

The weighted sum method for multi-objective optimization: new insights

A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

A study of mathematical programming methods for structural optimization. Part I: Theory

Design sensitivity analysis plays a central role in structural optimization, since virtually all optimization methods require computation of derivatives of structural response quantities with respect to design variables. Three fundamentally different approaches to design sensitivity analysis are presented. These have been used extensively in the structural optimization literature. They are the virtual load method, the state space method, and the design space method. An analysis of these methods indicates that the state space and design space methods are more general than the virtual load method. Moreover, the virtual load method, when applicable, is a special case of the state space method. Any one of these procedures may be incorporated into an optimality criterion or a mathematical programming method for structural optimization.

Jasbir S. Arora

Papers

Survey of multi-objective optimization methods for engineering

Introduction to Optimum Design

The weighted sum method for multi-objective optimization: new insights

A study of mathematical programming methods for structural optimization. Part I: Theory

Methods of Design Sensitivity Analysis in Structural Optimization