Applications of vector optimization problems

Abstract

The research work titled Applications of Vector Optimization Problems focuses on various perspectives of formation and solutions of Multi Criteria Decision Making (MCDM) problems. Over the last few decades, various new approaches have been developed and the methodologies of decision making processes have been improving gradually. Decision-making approaches are broadly employed for the selection of the best compromise solution, as any alternative cannot usually excel in all the criteria under consideration simultaneously. Besides the real criteria values by which a decision is made, the selection of the best solution also depends on the decision maker s individual preferences. Though a lot of mathematical advances have been made in this area, yet these research areas are still contemporary and innovative. In this study, integrated solution methodologies for general MCDM problems are fostered based on various optimization techniques. Model-based MCDM is investigated, with the focus being on improving and employing approaches based on interactive application layouts. With regard to the subject under consideration, the problems of decision making in this research cover various techniques of MCDM Models. Some of the MCDM methods used in the present work are: Analytical Hierarchy Process (AHP), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), Simple Additive Weighting (SAW), Rank Order Centroids(ROC), Ratio Method, Technique for Order Preference by newlineApplications of Vector Optimization Problems Similarity to Ideal Solution (TOPSIS), Lexicographic Approach etc. In addition to the methodological aspects, there has been a focus on applying the interactive optimization techniques to the application areas that contain complex processes and conflicting targets, which have gathered increasing interest of modeling and optimization during recent years. The contribution of this thesis lies in a state of decision making from the applications in various scenarios taken up during the research.