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Solving Multi-objective Integer Optimization Problems by Using Benders Decomposition Method

Mohammadi Siahroudi, Mohammad Hossein | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52137 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Eshghi, Kourosh
  7. Abstract:
  8. Real-world decision-making problems usually have several criteria for evaluating the performance of alternatives. On the other hand, mathematical programming is a very practical tool for modeling and solving decision-making problems and multi-objective mathematical programming has high importance among researchers and managers in this field of study. However, the field of multi-objective integer programming is considered a rigorous category. Methods for solving these types of problems can be divided into three different approaches. There are few approaches and methods for solving multi-objective mixed-integer optimization problems in litreture.In this research, an extension of benders decomposition method for solving multi-objective mixed-integer optimization problems has been studied. The proposed algorithm decomposes the main problem into two sub-problems, which are multi-objective linear programming and pure multi-objective integer programming. The output of this algorithm consists of all efficient solutions which are basic feasible solution in linear sub problem with integer value for integer variables. The algorithm has also been tested on knapsack problem as well as some randomly generated test problems
  9. Keywords:
  10. Multi-Objective Mixed-Integer Programming ; Multi-Objective Benders Decomposition ; Multi-Objective Decision Making ; Integer Programming ; Duality Theory ; Multiobjective Optimization

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