Geometric/Matrix Method of Solving Multicriteria Optimization Problems
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This book examines the multicriteria optimization problem and constructs a new methodology to solve it. It applies geometric concepts to define and determine the inferior_1 and superior_1 boundary sets, which are subsets of the inferior and superior boundary sets of the image, and then applies logic to filter out the non-dominated image points from these sets.This book combines theory and practice. The reader may ignore all the proofs and only focus on the applications if desired. For example, chapters 3, 4 and 5 can be ignored without harm to the later chapters dealing with the algorithm impl...
This book examines the multicriteria optimization problem and constructs a new methodology to solve it. It applies geometric concepts to define and determine the inferior_1 and superior_1 boundary sets, which are subsets of the inferior and superior boundary sets of the image, and then applies logic to filter out the non-dominated image points from these sets.This book combines theory and practice. The reader may ignore all the proofs and only focus on the applications if desired. For example, chapters 3, 4 and 5 can be ignored without harm to the later chapters dealing with the algorithm implementation, computer codes in MALTAB and several examples.This book opens up the scope of applications of multicriteria optimization in many fields including management, engineering and medical science, and establishes new directions for future research.This book is based on the PhD thesis, "A Direct Method of Solving Multicriteria Optimization Problems", submitted by Yongkui Wang in April 2018, and some new results from recent research. To respect the original thesis style, the book does not alter the Acknowledgements, Abstract, and some of the chapters.
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