基于改进NSGA-Ⅱ的列车运行多目标优化方法

Multi-objective optimization method of train operation based on improved NSGA-Ⅱ

针对目前城市轨道交通列车运行节能控制必须满足工程校验、实时高精度需求以及快速非支配排序遗传算法(NSGA-Ⅱ)在优化列车运行速度曲线时解集分布性差的问题,提出一种基于改进NSGA-Ⅱ的列车运行多目标优化方法。首先建立以站间牵引能耗、到站时间、停车精度为优化目标,以多种规范约束为支配惩罚,以实数编码的位置-工况组合为变量下的列车节能运行数学模型。然后,以限速曲线与坡度变化原则分段离散化站间线路,基于NSGA-Ⅱ加入动态矫正计算适应度值并引进自适应选择与混合交叉算子。最后,采用北京地铁8号线数据进行优化仿真。结果表明,改进NSGA-Ⅱ算法在标准测试函数上解集分布性指标最高提升27%,在列车节能工程优化问题上,运行备选方案数量提升2倍以上,方案分布性提升26%,牵引能耗降低4.8%。本方法为城轨列车节能运行的优化设计及决策者对目标条件的权衡提供了更广泛的选择。

Since the energy-saving control of train must meet the requirements of engineering verification,real-time and high-precision,a multi-objective optimization method based on improved Non-dominated Sorting Genetic AlgorithmⅡ(NSGA-Ⅱ)which had faster convergence rate and uniform Pareto solution set was proposed.Firstly,the mathematical model of train operation was given by the minimal optimization objectives:traction energy consumption,arrival time and parking accuracy;the real-coded position and condition who violates the restriction were punished.Secondly,the rail was discretized by the unique principle of speed limit and ramp;basing on NSGA-Ⅱ,dynamic correction was added to calculate fitness value,and operators of adaptive selection and hybrid crossover were introduced.Finally,in the comparison experiments of standard test functions,the distribution indexes of solution sets increased by 27%at most;in the comparison experiments of optimizing train operation behavior,the alternatives increased by more than 2 times,the distribution index of solution sets increased by 26%,and the traction energy consumption reduced by 4.8%.Without considering the braking energy recovery,this method provides wider choices for trade-off of target conditions for decision-makers.