MULTI-CRITERIA DECISION MAKING TECHNIQUES FOR ENGINEERING AND MANAGEMENT PROBLEMS

Abstract

Decision making involves the use of a rational process for selecting the best of several alternatives. In real life, decisions are often made on the basis of multiple, conflicting and non-commensurable criteria/objectives in uncertain/imprecise environments. Multi-criteria decision making in crisp and fuzzy environments is growing and challenging issue for researchers. In this thesis fuzzy set theory and real coded genetic algorithm are used to develop efficient interactive methods for multi-criteria decision making (both multi-objective decision making and multi-attribute decision making) in crisp and fuzzy environments. Subsequently, these techniques are used to solve some realistic problems arising in water resources management and other disciplines. This thesis is described in two parts. The first part deals with development of methodologies (Chapter 2, 3, 4, 5) and the second part deals with their applications to real life problems (Chapter 6, 7). Conclusions and future scope are summarized in Chapter 8. A real coded genetic algorithm, named as MI-LXPM, for integer and mixed integer non-linear optimization problems is developed. Superiority of this algorithm over other genetic algorithm (AXNUM) and random search technique (RST2ANU) is shown. Sub-sequently, MI-LXPM algorithm is used as an optimization technique in the interactive method for multi-objective problems in crisp and fuzzy environments. In interactive iii iv method, compensatory product operator is used for aggregation of different fuzzy goals and minimum reservation level is used for interaction with decision maker. In each in-teractive phase, decision maker (DM) gives the value of minimum reservation level for each objective, which is used as additional constraint. Finally, the resultant single ob-jective crisp optimization problem is solved using MI-LXPM algorithm. Based on the outcomes of previous iteration, during the interactive phase, the DM has the option to change his(er) specified reservation levels and/or goals for some or all objectives. The process is repeated till the DM is satisfied. Further, this interactive method is extended for bi-level and multi-level programming problems. Two techniques are also developed for multi-attribute decision making (ranking of al-ternatives) in fuzzy environment. In first technique, fuzzy weighted average of each alternative is formulated as a pair of non-linear programming and then for different val-ues of a-cut its left and right bounds are computed using MI-LXPM algorithm. Finally, Yager's ranking index is used to compute the final ranking order of alternatives. In the second techniques, pooling approach is used to aggregate the different evaluations of alternatives and after that, fuzzy integral value approach with index of optimism is used to compute the final ranking of alternatives. Two different class of problems related to water resources management are solved using these proposed techniques. In first application, MI-LXPM algorithm in conjunction with Newton Raphson method is used to determine the optimal design of water distribution networks (WDNs). Three different problems, taken from literature, are solved. In all the three cases the obtained solutions are equivalent or better than the known solutions. In second application, interactive method is used to solve the multipurpose multireservoir problem. Further, to demonstrate the applicability of interactive method, in other multi-objective problems which may have restrictions on some or all decision variables to be integer, problems related to reliability optimization, engineering optimization and portfolio management are solved.