Multi-Objective Optimization is an area of Multiple Criteria Decision Making(MCDM), that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-Objective Optimization has been applied in many fields of Management Science and Engineering where optimal decisions need to be taken in the presence of two or more conflicting objectives. Minimizing cost, maximizing profit, maximizing performance and minimizing loss are examples of Multi-Objective Optimization problems with at least two objectives. In some real life problems, there can be several conflicting objectives. For a typical Multi-Objective Optimization problem, there does not exist a single optimal solution that simultaneously optimizes each objective. In that case, the objective functions are said to be conflicting, and there exists a infinite number of Pareto optimal solutions. We study multi-objective optimization problems from different viewpoints. Mainly, we find optimal compromise solution using fuzzy programming and fuzzy goal programming techniques. In some of the Multi-Objective Optimization problems the parameters are treated as some continuous type random variables. We develop methodologies to find the optimal compromise solutions of such problems. In a Multi-Objective Optimization problem, we have several goals. Some of the goal are flexible and some are rigid in nature. We observe that some of the flexible goals are also multi-choice type in nature. Methods have been developed to tackle the multi-choice type goals in a Multi-Objective Optimization problem.
Area of Research: Operations Research
Area of Research: Optimization