Multiple Criteria Optimization

by Ehrgott, Matthias; Gandibleux, Xavier

• ISBN13: 9781402071287
• ISBN10: 1402071280
• Format: Hardcover
• Copyright: 2002-06-01
• Publisher: Kluwer Academic Pub

Summary

The roots of Multiple Criteria Decision Making and Multiple Criteria Optimization were laid by Pareto at the end of the 19th century, and since then the discipline has prospered and grown, especially during the last three decades. Today, many decision support systems incorporate methods to deal with conflicting objectives. The foundation for such systems is a mathematical theory of optimization under multiple objectives. Since its beginnings, there have been a vast number of books, journal issues, papers and conferences that have brought the field to its present state. Despite this vast body of literature, there is no reliable guide to provide an access to this knowledge. Over the years, many literature surveys and bibliographies have been published. With the ever rapidly increasing rate of publications in the area and the development of subfields, these were mostly devoted to particular aspects of multicriteria optimization: Multiobjective Integer Programming, Multi-objective Combinatorial Optimization, Vector Optimization, Multiobjective Evolutionary Methods, Applications of MCDM, MCDM Software, Goal Programming. Hence the need for a comprehensive overview of the literature in multicriteria optimization that could serve as a state of the art survey and guide to the vast amount of publications. Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys is precisely this book. Experts in various areas of multicriteria optimization have contributed to the volume. The chapters in this book roughly follow a thread from most general to more specific. Some of them are about particular types of problems (Theory of Vector Optimization, Nonlinear Multiobjective Programming, Fuzzy Multiobjective Programming, Multiobjective Combinatorial Optimization, Multicriteria Scheduling Problems), while the others are focused on multi-objective methodologies (Goal Programming, Interactive Methods, Evolutionary Algorithms, Data Envelopment Analysis). All contributing authors invested great effort to produce comprehensive overviews and bibliographies and to have references that are as precise as possible.

Table of Contents

List of Figures	ix
List of Tables	xi
Preface	xiii
Ralph E. Steuer
Introduction	xv
Matthias Ehrgott
Xavier Gandibleux
References	xviii
Theory of Vector Optimization	1	(70)
Christiane Tammer
Alfred Gopfert
Solution Concepts	1	(12)
Optimality Conditions	13	(11)
Duality	24	(10)
Vector Variational Inequalities and Vector Equilibria	34	(2)
Multicriteria Fractional Programming	36	(6)
Multicriteria Control Problems	42	(29)
References	46	(25)
Nonlinear Multiobjective Programming	71	(58)
Tetsuzo Tanino
Hun Kuk
Introduction	72	(1)
Solution Concepts	73	(3)
Scalarization and Optimality Conditions	76	(4)
Stability and Sensitivity Analysis	80	(1)
Duality	81	(5)
Vector Variational Inequalities	86	(3)
Concluding Remarks	89	(40)
References	89	(40)
Goal Programming in the Period 1990-2000	129	(42)
Dylan F. Jones
Mehrdad Tamiz
Introduction	129	(4)
Details of Literature Review	133	(3)
Classification of GP Extension Articles	136	(4)
Integration and Combination of Goal Programming with Other Techniques	140	(4)
Conclusion and Comment	144	(27)
References	148	(23)
Fuzzy Multiobjective and Multilevel Optimization	171	(56)
Masatoshi Sakawa
Fuzzy Decision	172	(6)
Multiobjective Programming and Solution Concepts	178	(1)
Interactive Multiobjective Programming	179	(4)
Fuzzy Multiobjective Linear Programming	183	(3)
Interactive Fuzzy Multiobjective Linear Programming	186	(7)
Interactive Fuzzy Multiobjective Linear Programming with Fuzzy Parameters	193	(10)
Related Works and Applications	203	(1)
Interactive Fuzzy Two-level Linear Programming	204	(8)
Interactive Fuzzy Two-level Linear Programming with Fuzzy Parameters	212	(15)
References	217	(10)
Interactive Nonlinear Multiobjective Procedures	227	(50)
Kaisa Miettinen
Introduction	227	(1)
Concepts	228	(3)
Methods	231	(22)
Comparing the Methods	253	(1)
Conclusions	254	(23)
References	256	(21)
Evolutionary Algorithms and Multiple Objective Optimization	277	(56)
Carlos A. Coello Coello
Carlos E. Mariano Romero
Introduction	278	(1)
Definitions	279	(1)
Notions of Evolutionary Algorithms	280	(1)
Classifying Techniques	281	(1)
Non-Pareto Techniques	281	(10)
Pareto-Based Techniques	291	(7)
Recent A roaches	298	(4)
Diversity	302	(3)
Test Functions	305	(1)
Metrics	306	(2)
Applications	308	(1)
Future Research Paths	309	(2)
Summary	311	(22)
References	312	(21)
Data Envelopment Analysis in Multicriteria Decision Making	333	(36)
Hirotaka Nakayama
Masao Arakawa
Ye Boon Yun
Introduction	334	(1)
Data Envelopment Analysis	335	(2)
Basic DEA Models	337	(6)
GDEA Based on Parametric Domination Structure	343	(4)
GDEA Based on Production Possibility	347	(6)
Comparison between GDEA and DEA Models	353	(4)
GDEA for Multiple Criteria Decision Making	357	(7)
Conclusions	364	(5)
References	365	(4)
Multiobjective Combinatorial Optimization	369	(76)
Matthias Ehrgott
Xavier Gandibleux
Introduction	370	(1)
Multiple Objective Combinatorial Optimization Problems	371	(2)
Properties of MOCO Problems	373	(3)
Solution Methods for MOCO Problems	376	(12)
Classification of the Literature	388	(1)
Annotation of the Literature Problem by Problem	389	(15)
Open Questions and Conclusions	404	(41)
References	407	(38)
Multicriteria Scheduling Problems	445	(48)
Vincent T'Kindt
Jean-Charles Billaut
Scheduling Theory	446	(5)
Overview of Multicriteria Optimization Theory	451	(3)
Solving Multicriteria Scheduling Problems	454	(4)
Complexity Results	458	(7)
Single Machine Problems	465	(10)
Parallel Machines Problems	475	(4)
Shop Problems	479	(14)
References	482	(11)
Index	493