


  Nonlinear programming 

  On multiobjective linear and nonlinear programming Author: Lakhan, Nirma Narayan Institution: University of the South Pacific. Award: M.Sc. Subject: Linear programming, Nonlinear programming Date: 2015 Call No.: Pac T 57 .74 .L35 2015 BRN: 1200946 Copyright:Under 10% of this thesis may be copied without the authors written permission Abstract: Traditionally, most linear and nonlinear programming methods have tackled problems under the assumption that a single quantifiable objective either to maximize profit or minimize cost or loss. However, many real life conditions in areas such as health care, scheduling and timetabling, location problems, engineering, statistics, finance, transport, production, project planning, environment and so forth are of linear and nonlinear objectives in which posing a single objective is not much practical use. Decision makers may need to solve multiple dependent objectives or criteria in decision makers have increased recognitions that most real life decision problems are characteristically of multiple objectives. These decision making problems with multiple objectives or criteria are generally known as multiobjective optimization or multiobjective programming (MOP) problems. In MOP, several objective functions have to be optimized simultaneously. Further, when the optimum values of several variables are to be obtained, the optimum solution attained for a single objective is not much useful because a solution that is optimum for an objective will generally be far from optimum for others. Thus, MOP is usually conflicting objectives nature or incommensurable objectives. To resolve such conflict, a compromise criterion is sought to reach optimal solutions, in some sense all the objectives are satisfied. The multiobjective problems have been discussed by many authors. They developed several techniques that are available in the literature. A traditional technique that deals with most multiobjective problems is known as goal programming which seeks a compromise solution by setting the relative importance of each objective known as goal. However, there is some situations where there may be no feasible solution satisfying all the goals. These situations certainly advocate the need to search for a technique that considers the optimization of several objectives instead of searching for an optimal solution of each objective. This manuscript deals with the problems of multiobjective linear and nonlinear programming in which several objective functions are optimized simultaneously. It develops solution procedures for determining the optimum compromised solution for the problem. The proposed viii multiobjective linear and nonlinear programming techniques are illustrated on several numerical examples. Applications of real life situations are also presented. Finally, the results are compared with other techniques to demonstrate the strength of the proposed method.


