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Constrained optimization problems (COPs) are most commonly encountered problems in science and engineering design field. To solve such kind of problem effectively, in this paper, we put forward a new approach named CAMDE which integrates adaptive differential evolution (DE) with new multi-population-based mutation operators. In CAMDE, some inferior solutions with low objective values are maintained in an external population. During mutation process, this external population is combined with main population to generate promising progress directions toward optimal region. Furthermore, DE's control parameters F and CR are adaptively adjusted according to the statistical information learnt from the previous searches in generating improved solutions. The advantageous performance of CAMDE is validated by comparisons with some representatives of state of the art in constrained optimization over 24 test instances. Moreover, four widely used constrained mechanical engineering problems are selected to validate the search ability of CAMDE for real-world problems. The performance results show that CAMDE is an effective approach to solving COPs, which is basically enabled by the integration of multi-population-based mutation operators and adaptive control strategy for DE's control parameters. [ABSTRACT FROM AUTHOR]

This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newton formulas helps to handle large-scale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a fi rst-order stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving large-scale unconstrained optimization problems. [ABSTRACT FROM AUTHOR]