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Combining the cross-entropy algorithm and ∈-constraint method for multiobjective optimization

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This paper aims to propose a new hybrid approach for solving multiobjective optimization problems. This approach is based on a combination of global and local search procedures.

The cross-entropy method is used as a stochastic model-based method to solve the multiobjective optimization problem and reach a first elite set of global solutions. In the local search step, an ∈-constraint method converts the multiobjective optimization problem to a series of parameterized single-objective optimization problems. Then, sequential quadratic programming (SQP) is used to solve the derived single-objective optimization problems allowing to reinforce and improve the global results. Numerical examples are used to demonstrate the efficiency and effectiveness of the proposed approach.