Treating multi-objective problems using special approximations / Sameh Hussein Ahmed Eldeeb ; Supervised Mohamed Hassan Gadallah , Omar Soliman Soliman , Hamiden Abdelwahed Khalifa

Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Operations Research

Multi objective optimization is a powerful technique to show the pareto frontier for systems with many objectives. Interpretation of the pareto front is possible for 3 dimension problems, but the multi-objective problems with more than two objectives are solved by priority of the objectives set by the owner or the weight for every objective to determine, the pareto frontier. This solution is not complete because the solution depends on the priority of objectives, the objectives of high priority and neglect the objectives of low priority accordingly. In this thesis we use an approximation technique called response surface methodology (RSM) with weighted method to transfer multi objective problems into a series of bi-objective optimization problems. We also determine the pareto frontier, so that in the end, we have many of the pareto frontiers depending on the number of sub problems and not depending on the priority of objectives to satisfy the following purposes: The validity of the method to approximate the original multi-objective problem into a series of bi-objective problems. Possibility of seeing all Pareto optimal solutions by dividing the problem into a series of bi-objective problems. The computational savings related to this transformation, especially with large size problems. The Pareto frontier resulting from the bi-objective formulation versus the original multi-objective formulation

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