铁路施工多目标均衡优化模型与改进NSGA-Ⅲ算法

Multi-objective equilibrium optimization model and improved NSGA-Ⅲalgorithm of railway construction

分析了铁路基础设施建设施工方案的特点、优化模型与优化算法,绘制双代号网络图,以工序所需时间为自变量计算了总工期,提出一种考虑资金时间价值的施工成本计算方法;引入系统可靠性理论对施工质量进行量化评估,探讨施工质量安全水平与时间、成本之间相互关系,计算了施工质量安全水平,提出铁路基础设施施工质量-安全-工期-成本多目标均衡优化模型;引入随机整数基因编码方式与惩罚函数法改进NSGA-Ⅲ算法,以求得模型的帕累托解集,对比了改进NSGA-Ⅲ算法与NSGA-Ⅱ算法的求解性能,并利用轨道工程施工案例对模型进行验证。分析结果表明:设定种群数量为140,迭代次数为900,试验次数为40时,改进NSGA-Ⅲ算法对NSGA-Ⅱ算法的每代平均覆盖率均值比算法NSGA-Ⅱ对改进NSGA-Ⅲ算法的每代平均覆盖率均值提高了将近27倍,改进NSGA-Ⅲ算法的每代平均超体积均值比NSGA-Ⅱ算法的每代平均超体积均值提高了将近54%,表明改进NSGA-Ⅲ算法明显优于传统的NSGA-Ⅱ算法;提出的铁路施工多目标均衡优化模型与改进NSGA-Ⅲ算法能很好地适用于铁路施工管理的多目标均衡优化,在轨道工程施工案例中,当设定种群数量为140,迭代次数为900,每个维度上参考点个数为8时,求解得到140个帕累托解,其中质量水平最大优化0.1121,安全水平最大优化0.1073,工期最大优化36 d,成本最大优化将近720万元,可以更好地指导决策者进行施工安排。

The characteristics,optimization models and optimization algorithms of railway infrastructure construction schemes were analysis,the double code-network diagrams were drawn,the time required for the construction process was taken as independent variable,and a method for calculating the construction cost was proposed under considering the time cost of capital.The system reliability theory was introduced to quantitatively assess the construction quality,the interrelationship between the safety level,time and cost of construction quality was explored,the safety level was calculated,and a multi-objective equilibrium optimization model of quality-safety-duration-cost for railway infrastructure construction was put forward.The NSGA-Ⅲalgorithm was improved by introducing the random integer genetic coding method and penalty function method to solve the Pareto solution set of the model,the solution performance of the improved algorithm was compared with the NSGA-Ⅱalgorithm,and the model was verified by using a railway construction case.Analysis results show that when the population number is 140,the iteration number is 900,and the test number is 40,the average coverage rate per generation of the improved NSGA-Ⅲalgorithm to the NSGA-Ⅱalgorithm is nearly 27 times higher than that of the NSGA-Ⅱalgorithm to the improved NSGA-Ⅲalgorithm,and the mean supervolume per generation of the improved NSGA-Ⅲalgorithm is nearly 54%higher than that of the NSGA-Ⅱalgorithm,therefore,the improved NSGA-Ⅲalgorithm is obviously superior to the traditional NSGA-Ⅱalgorithm.The proposed model and improved NSGA-Ⅲalgorithm are well applied to the multi-objective equilibrium optimization of railway construction management.In the construction case of track engineering,when the population number is 140,the iteration number is 900,and the reference point number in each dimension is 8,140 Pareto solutions are obtained,and the maximum optimizations of quality level,safety level,duration and cost of the engineering are 0.1121,0.1073,36 days and nearly 7.2 million yuan,which can better guide the decision makers to arrange the construction.