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Direct Multi-search for Multiobjective Optimization

Shojaee, Meysam | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46051 (02)
  4. University: Sharif University of Technology
  5. Department: Pure Mathematics
  6. Advisor(s): Mahdavi Amiri, Nezameddin
  7. Abstract:
  8. Multi-objective optimization is an important branch of optimization. One of the most common methods to solve multi-objective problems is to find the Pareto efficient points. In practical applications, there are many instances in which there are no analytical formula for the function and only approximate values at some points are available. Derivative-free optimization is one approach to solve these problems.Here, we consider one of the multi-objective derivative-free optimization techniques called direct multisearch (DMS), recently proposed in the literature. In this method, a commonly used single objective optimization method is generalized to the multiobjective case. A popular category of derivative-free methods is direct search. In each iteration of such method, there are a search step and a poll step. In single objective optimization, poll step assesses the objective function in several neighboring points. In DMS, a similar technique is applied for multi-objective optimization, with the difference that the acceptance criterion in the new step using the concept of Pareto efficiency changes. Application of this method for optimizing a single function reduces to the direct search method. We describe the DMS method and implement the algorithm in MATLAB. The program is then tested on a set of test problems to show the effectiveness of the described method
  9. Keywords:
  10. Multiobjective Optimization ; Direct Search ; Derivative-free Optimization ; Pareto Efficient Point

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