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

Multi-objective optimization using genetic algorithms: A tutorial

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Abstract: A new method is proposed for multi-objective optimization with discrete alternatives: MOORA (Multi-Objective Optimization on the basis of Ratio Analysis). This method refers to a matrix of responses of alternatives to objectives, to which ratios are applied. A well established other method for multi-objective optimization is used for comparison, namely the reference point method. Later on, it is demonstrated that this is the best choice among the different competing methods. In MOORA the set of ratios has the square roots of the sum of squared responses as denominators. These ratios, as dimensionless, seem to be the best choice among different ratios. These dimensionless ratios, situated between zero and one, are added in the case of maximization or subtracted in case of minimization. Finally, all alternatives are ranked, according to the obtained ratios. Eventually, to give more importance to an objective, an objective can be replaced by different sub-objectives or a coefficient of importance can be specified. An example on privatization in a transition economy illustrates the application of the method. If application is situated originally in a “welfare” economy, centered on production, MOORA becomes even more significant in a “wellbeing economy”, where consumer sovereignty is assumed.

The MOORA method and its application to privatization in a transition economy

Goal programming for decision making: an overview of the current state-of-the-art

Multi-objective meta-heuristics: An overview of the current state-of-the-art

Practical Goal Programming is intended to allow academics and practitioners to be able to build effective goal programming models, to detail the current state of the art, and to lay the foundation for its future development and continued application to new and varied fields. Suitable as both a text and reference, its nine chapters first provide a brief history, fundamental definitions, and underlying philosophies, and then detail the goal programming variants and define them algebraically. Chapter 3 details the step-by-step formulation of the basic goal programming model, and Chapter 4 explores more advanced modeling issues and highlights some recently proposed extensions. Chapter 5 then details the solution methodologies of goal programming, concentrating on computerized solution by the Excel Solver and LINGO packages for each of the three main variants, and includes a discussion of the viability of the use of specialized goal programming packages. Chapter 6 discusses the linkages between Pareto Efficiency and goal programming. Chapters 3 to 6 are supported by a set of ten exercises, and an Excel spreadsheet giving the basic solution of each example is available at an accompanying website. Chapter 7 details the current state of the art in terms of the integration of goal programming with other techniques, and the text concludes with two case studies which were chosen to demonstrate the application of goal programming in practice and to illustrate the principles developed in Chapters 1 to 7. Chapter 8 details an application in healthcare, and Chapter 9 describes applications in portfolio selection.

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Practical Goal Programming

This paper presents a review of the current literature on the branch of multi-criteria decision modelling known as Goal Programming (GP). The result of our indepth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Some guidelines to the scope of GP as an application tool are given and methods of determining which problem areas are best suited to the different GP approaches are proposed. The correlation between the method of assigning weights and priorities and the standard of the results is also ascertained.

A review of Goal Programming and its applications

This paper looks at connections between the multi-criteria techniques of goal programming, compromise programming, and the reference point method. The utility function structure of each method is examined and interpretation of the techniques in terms of pareto efficiency and the equilibrated nature of the solution is given. Means of ensuring pareto efficiency whilst maintaining as much as possible the equilibrated character are given for a certain class of model. Methods for ensuring conceptual correctness and computational accuracy by reducing reference point models to equivalent goal programmes are given. The findings are illustrated by means of an example.

Mehrdad Tamiz

Papers

Goal programming for decision making: an overview of the current state-of-the-art

Multi-objective meta-heuristics: An overview of the current state-of-the-art

Practical Goal Programming

A review of Goal Programming and its applications

Goal programming, compromise programming and reference point method formulations : linkages and utility interpretations