求解机组组合问题的改进混合整数二次规划算法

An Improved Mixed Integer Quadratic Programming Algorithm for Unit Commitment

混合整数二次规划(MIQP)算法求解机组组合问题具有全局优化能力,但是针对大规模优化问题,其计算速度和计算精度将受影响。文中提出了求解机组组合问题的改进MIQP算法。该算法的核心思想是引入了松弛和解耦2种改进策略。通过求解松弛整数变量的二次规划模型,首先获得机组组合的下界空间,然后再通过拉格朗日解耦算法获得机组组合的上界空间,进而在上下界确定的寻优空间内采用MIQP算法进行再优化。不同测试算例表明,改进的MIQP算法快速且有效,可以降低优化问题的复杂度,显著减少计算时间。

The mixed integer quadratic programming （MIQP） algorithm for solving unit commitment problems has global optimization capability. For a large-scale optimization problem,however,its computation speed and accuracy will be affected. To deal with this problem,an improved mixed integer quadratic programming algorithm is presented. The crucial idea of the algorithm is the introduction of two kinds of improvement strategies of relaxation and decoupling. First,the lower bound space of unit commitment is obtained by solving a quadratic integer programming model with slacking integer variables. Then,the upper bound space of unit commitment is obtained using the Lagrangian decoupling algorithm. Finally,in the optimizing space determined by the upper and lower bounds,unit commitment is re-optimized with the MIQP algorithm. Different simulation results show that the improved MIQP algorithm is fast and effective and capable of reducing the complexity of optimization,especially the computational time.