Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys (International Series in Operations Research & Management Science (52))

The generalized area of multiple criteria decision making (MCDM) can be defined as the body of methods and procedures by which the concern for multiple conflicting criteria can be formally incorporated into the analytical process. MCDM consists mostly of two branches, multiple criteria optimization and multi-criteria decision analysis (MCDA). While MCDA is typically concerned with multiple criteria problems that have a small number of alternatives often in an environment of uncertainty (location of an airport, type of drug rehabilitation program), multiple criteria optimization is typically directed at problems formulated within a mathematical programming framework, but with a stack of objectives instead of just one (river basin management, engineering component design, product distribution). It is about the most modern treatment of multiple criteria optimization that this book is concerned. I look at this book as a nicely organized and well-rounded presentation of what I view as ”new wave” topics in multiple criteria optimization. Looking back to the origins of MCDM, most people agree that it was not until about the early 1970s that multiple criteria optimization c- gealed as a field. At this time, and for about the following fifteen years, the focus was on theories of multiple objective linear programming that subsume conventional (single criterion) linear programming, algorithms for characterizing the efficient set, theoretical vector-maximum dev- opments, and interactive procedures.

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.

Many practically important problems can be described by a multicriteria optimization problem with more than one objective function.