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

An extension of TOPSIS for group decision making

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Linear And Nonlinear Programming

This paper reviews currently available goal programming (GP) and multi-objective programming (MOP) interactive algorithms and discusses design issues of interactive algorithms specifically for GP. Two factors which distinguish GP applications from most MOP application are the capability to incorporate a large number of objectives in the modelling and solution practice, and the possible use of a lexicographic priority structure. Therefore any interactive GP or adapted MOP algorithm should be capable of performing well under these conditions. In practice, many existing algorithms fail to operate efficiently under these conditions due to a large amount of information required from, or presented to, the decision maker or the time taken per interactive iteration. The use of the lexicographic structure also adds an extra degree of complexity and may cause problems with utility function based algorithms. Therefore, the remainder of this paper presents a general purpose GP interactive algorithm capable of handling both large scale, and lexicographic, goal programmes. The algorithm is designed to present a suitable amount of information to the decision maker and be efficient both in number of interactive iterations and in time taken per interactive iteration.

A General Purpose Interactive Goal Programming Algorithm

A classic problem in operational research and finance is the selection of a portfolio of shares, investments, or financial products. The set of shares chosen and their percentage of the total portfolio are the decision variables of this model. The classic models tend to consider the minimisation or some measure of risk and the maximisation of return, with an ‘efficient frontier’ of possible portfolios being considered in the resulting bi-objective space. Markowitz (1952) introduced the mean–variance model for portfolio selection. In this model, the mean represents average return and variance represents a measure of risk. It can be seen that this problem is a multiple objective one by definition. It can also be expanded to contain further objectives related to issues such as liquidity, portfolio size or composition, social responsibility, or size of dividends (Steuer et al., 2007). If the decision makers (i.e. the portfolio manager or owners) have set goals for levels of return and risk or other measures of portfolio performance then the goal programming framework is a natural choice for modelling and solving this problem.

Case Study: Application of Goal Programming in Portfolio Selection

This paper proposes a method to measure robustness of weighted goal programming (WGP) models by focusing on random percentage changes in the set of observed technological coefficients that characterize the goal equations. The issue under consideration is to estimate the impact of the random percentage changes on the WGP deviations from the goal targets, the solution to the model before changes being kept equal. Normally distributed and independent percentage changes are assumed. As a result, a measure of robustness is obtained dependent on the parameters of the model, standard deviations of percentage changes, and the solution to the model before changes. A demonstration of the proposed robustness measure on an offshore wind-farm site location model from the literature is developed. The results indicate that robustness of proposed solution to the energy project is high. Conclusions are drawn as to the practicality and usage of the proposed model in comparison to other methodologies for handling uncertainty within the goal programming model.

Robustness of weighted goal programming models: an analytical measure and its application to offshore wind-farm site selection in United Kingdom

Multi-criteria mapping and prioritization of Arctic and North Atlantic maritime safety and security needs

Wind energy is becoming an increasingly substantial component of many nations’ energy portfolios. The intermittent nature of wind energy is traded off in a multi-objective sense against its environmental benefits when compared to conventional thermal energy sources. This gives rise to the multi-criteria sustainable dispatch problem considered in this paper. A relevant multi-objective model is formulated considering both environmental and economic criteria as well as ensuring adequate production levels. The techniques of weighted goal programming (WGP) and the progressive bounded constraint method (PBC) are combined in a novel manner in order to overcome computational challenges associated with the sinusoidal nature of the model. This allows the generation of a representative set of Pareto efficient solutions. The proposed methodology is demonstrated on a test set of relevant examples, and conclusions are drawn from both methodological and application perspectives. The results provide a quantification of the economic and environmental benefits of added wind power to a solely thermal system. However, a trade-off between the levels of economic versus environmental benefits gained is also demonstrated.

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Dylan Jones

Papers

A General Purpose Interactive Goal Programming Algorithm

Case Study: Application of Goal Programming in Portfolio Selection

Robustness of weighted goal programming models: an analytical measure and its application to offshore wind-farm site selection in United Kingdom

Multi-criteria mapping and prioritization of Arctic and North Atlantic maritime safety and security needs

A Hybrid Multi-Criteria Methodology for Solving the Sustainable Dispatch Problem