Thisbook opens the door to multiobjective optimization for students in fields suchas engineering, management, economics and applied mathematics. It offers acomprehensive introduction to multiobjective optimization, with a primaryemphasis on multiobjective linear programming and multiobjective integer/mixedinteger programming. A didactic book, it is mainly intended for undergraduateand graduate students, but can also be useful for researchers andpractitioners. Further, it is accompanied by an interactive software package -developed by the authors for Windows platforms - which can be used for teachingand decision-making support purposes in multiobjective linear programmingproblems. Thus, besides the textbook"s coverage of the essential concepts,theory and methods, complemented with illustrative examples and exercises, thecomputational tool enables students to experiment and enhance their technicalskills, as well as to capture the essential characteristics of real-worldp
roblems.
Introduction.- Problem formulation and definitions.- Surrogate scalar functions and scalarization techniques.- Interactive methods in multiobjective linear programming.- A guided tour of the iMOLPe.- Multiobjective integer and mixed-integer linear programming._
Arvustused
This tutorial on multiobjective programming is based on the vast teaching and research experience of the authors. Readers do not require an advanced mathematics background to grasp the whole content of the book. It is clearly written, accompanied with exercises at the end of each chapter, making it a great contribution to acquiring knowledge in the field of multiobjective optimization. (Hans W. Ittmann, IFORS News, Vol.11 (2), 2017)
A peculiar feature of this book is the authors' intention to explain concepts and methods of multiobjective linear programming through examples in low dimensional spaces without any theorems or proofs. This enables the readers grasp the whole content of the book without advanced mathematics background. The book is clearly written, accompanied with exercises for training at the end of each chapter. It is a nice contribution to the field of multiobjective optimization. (Dinh The Luc, zbMATH 1358.90123, 2017)
The authors present a textbook in multiobjective programming, based on their vast teaching and research experience. They focus in particular on linear and integer multiobjective programming problems. The authors provide many illustrative examples, as well as exercise (many of them with solution). This makes the book very useful for undergraduate and graduate students in all the areas where multiobjective programming appears, e.g. students in engineering or economics. (Marcin Anholcer, Mathematical Reviews, October, 2016)
|
|
|
1 | (8) |
|
2 Formulations and Definitions |
|
|
9 | (18) |
|
|
|
9 | (2) |
|
|
|
11 | (13) |
|
|
|
24 | (3) |
|
3 Surrogate Scalar Functions and Scalarizing Techniques |
|
|
27 | (30) |
|
3.1 Optimizing One of the Objective Functions and Transforming the Remaining p---1 into Constraints |
|
|
28 | (3) |
|
3.2 Optimizing a Weighted-Sum of the Objective Functions |
|
|
31 | (10) |
|
3.2.1 Indifference Regions on the Weight Space in MOLP |
|
|
33 | (8) |
|
3.3 Minimizing a Distance/Achievement Function to a Reference Point |
|
|
41 | (7) |
|
3.3.1 A Brief Review of Metrics |
|
|
41 | (7) |
|
3.4 Classification of Methods to Compute Nondominated Solutions |
|
|
48 | (1) |
|
3.5 Methods Based on the Optimization of an Utility Function |
|
|
49 | (1) |
|
3.6 The Lexicographic Method |
|
|
50 | (1) |
|
|
|
50 | (1) |
|
3.8 The Multiobjective Simplex Method for MOLP |
|
|
50 | (1) |
|
|
|
51 | (6) |
|
4 Interactive Methods in Multiobjective Linear Programming |
|
|
57 | (80) |
|
|
|
57 | (2) |
|
|
|
59 | (9) |
|
4.2.1 General Description |
|
|
59 | (1) |
|
|
|
59 | (2) |
|
|
|
61 | (2) |
|
4.2.4 Illustrative Example of the STEM Method |
|
|
63 | (5) |
|
4.3 Zionts and Wallenius Method |
|
|
68 | (12) |
|
|
|
68 | (1) |
|
4.3.2 Zionts and Wallenius Algorithm |
|
|
69 | (6) |
|
|
|
75 | (1) |
|
4.3.4 Illustrative Example of the Zionts and Wallenius Method |
|
|
75 | (5) |
|
|
|
80 | (22) |
|
4.4.1 Method Presentation |
|
|
80 | (4) |
|
4.4.2 Teaching Multiobjective Linear Programming Using TRIMAP |
|
|
84 | (3) |
|
|
|
87 | (1) |
|
4.4.4 Illustrative Example of the TRIMAP method |
|
|
87 | (15) |
|
4.5 Interval Criterion Weights Method |
|
|
102 | (13) |
|
|
|
102 | (1) |
|
4.5.2 ICW (Interval Criterion Weights) Algorithm |
|
|
103 | (2) |
|
|
|
105 | (1) |
|
4.5.4 Illustrative Example of the Interval Criterion Weights Method |
|
|
105 | (10) |
|
|
|
115 | (15) |
|
|
|
115 | (4) |
|
|
|
119 | (2) |
|
4.6.3 Illustrative Example of the Pareto Race Method |
|
|
121 | (9) |
|
|
|
130 | (7) |
|
5 A Guided Tour of iMOLPe |
|
|
137 | (24) |
|
|
|
137 | (1) |
|
5.2 iMOLPe: Interactive MOLP Explorer |
|
|
138 | (18) |
|
|
|
139 | (4) |
|
|
|
143 | (6) |
|
|
|
149 | (3) |
|
|
|
152 | (3) |
|
|
|
155 | (1) |
|
|
|
156 | (5) |
|
6 Multiobjective Integer and Mixed-Integer Linear Programming |
|
|
161 | (44) |
|
|
|
161 | (1) |
|
6.2 Generating Methods and Scalarizing Processes |
|
|
162 | (11) |
|
|
|
173 | (5) |
|
6.3.1 Bi-objective Interactive Methods |
|
|
174 | (1) |
|
6.3.2 Multiobjective Interactive Methods |
|
|
175 | (3) |
|
6.4 An Interactive Reference Point Method Using Branch-And-Bound: Performing Directional Searches in MOMLLP |
|
|
178 | (22) |
|
6.4.1 Interactive Algorithm |
|
|
179 | (9) |
|
6.4.2 An Illustrative Example |
|
|
188 | (5) |
|
6.4.3 Generating Method for Bi-Objective Problems |
|
|
193 | (2) |
|
|
|
195 | (5) |
|
|
|
200 | (5) |
| References |
|
205 | |
Carlos Henggeler Antunes is Professor at the Department of Electrical and Computer Engineering of the Faculty of Sciences and Technology of the University of Coimbra, Portugal, and researcher at the R&D Institute INESC Coimbra. He received the PhD degree in Electrical Engineering, specialization in Optimization and Systems Theory, at the University of Coimbra. He has published papers in international journals including the European Journal of Operational Research, Annals of Operations Research, Energy Conversion and Management, Omega, OR Spectrum, Neurocomputing, Optimization and Engineering, Energy, Renewable and Sustainable Energy Reviews, IEEE Transactions on Sustainable Energy, Computers and Operations Research, Journal of the Operational Research Society. He is Editor of the EURO Journal on Decision Processes and member of the Editorial Board of the Journal of Energy Markets. His research interests are focused on multiple objective optimization and metaheuristics, multiple criteria decision analysis, energy systems and policies, energy efficiency.
Maria João Alves is Professor at the Faculty of Economics of the University of Coimbra, Portugal, and researcher at the R&D Institute INESC Coimbra. She received a first degree in Computer Engineering from the Faculty of Sciences and Technology of the University of Coimbra and a PhD in Management (specialization in Operational Research) from the Faculty of Economics of the University of Coimbra. She is author of several scientific papers published in international journals, including European Journal of Operational Research, Computers and Operations Research, Journal of Heuristics, Journal of Multi-Criteria Decision Analysis, Optimization, Journal of Global Optimization, Applied Mathematics and Computation, and an article in the Encyclopaedia of Optimization. Her research activities are mainly focused on multiobjective optimization, in particular multiobjective linear, mixed-integer, fractional and bilevel programming. Her interests include exact methods and metaheuristics, namely multiobjective evolutionary algorithms and particle swarm optimization, applications and decision support systems.
João Clímaco is Retired Professor at the Faculty of Economics of the University of Coimbra, and researcher at the R&D Institute INESC Coimbra. He is member of the Editorial Board of Coimbra University Press. Presently he is collaborating in several projects of SAGE/UFRJ Rio de Janeiro, Brazil, as special invited researcher of the Science without Borders Program. He obtained the MSc degree in Control Systems at the Imperial College of Science and Technology, University of London, and the PhD in Electrical Engineering, specialization in Optimization and Systems Theory, at the University of Coimbra. In 2013 the International Society on MCDM awarded him the Georg Cantor Award. He is past Vice-President of ALIO - Latin Ibero-American OR Association and past member of the International Executive Committee of the International Society on Multiple Criteria Decision Making. He is a member of the Editorial Board of Group Decision and Negotiation, International Transactions in Operational Research, International Journal of Decision Support Systems. He has co-authored about 130 papers mostly devoted to MCDA methodology, algorithms, telecommunication applications, and environmental applications in journals including European Journal of Operational Research, 4OR, Computers and Operations Research, Journal of Heuristics, Journal of Multi-Criteria Decision Analysis, Networks, Decision Support Systems, Group Decision and Negotiation, International Transactions in Operational Research, Telecommunication Systems, Photonic Network Communications, Technological Forecasting and Social Change.
