基于Clifford代数的露天矿山路径优化算法

露天矿山路径优化问题是指在满足特定物理和经济约束之下,搜索最佳运输线路的组合优化问题,对于降低矿山运营成本具有重要的现实意义。但目前常规的露天矿山路径优化算法,主要从静态的道路有向图网络优化出发,无法实现大规模时变动态网络的高效分析和优化决策。本文以扎哈淖尔露天矿为例,将欧式空间内经典的有向图网络分析方法扩展至Clifford代数空间,建立了节点、有向边以及路径的统一表达,提出了路径几何拓扑连通性和标量约束指标的计算方法,实现了几何拓扑计算和数值最优化求解问题的分离;针对传统静态网络分析方法无法动态表达系统能耗变化的问题,建立了基于时变运输功最小化的路径优化模型,并结合行驶阻力特征给出了时变阻力的计算方法;研究了因路面频繁碾压破坏和周期性维护而导致的滚动阻力系数周期性时变效应,并提出计算时变滚动阻力系数的方法;最后为进一步提高算法收敛效率,提出了两组推论和一组数值计算优化策略对遗传算法的数值计算进行了改进。经多次仿真实验验证,算法能快速收敛于全局最优解,说明了算法对于解决矿山实际路径优化问题可行且有效。其次,几何代数化方法的引入也为传统路径优化问题求解提供了一种有效实现拓扑关系计算和数值计算解耦的新方法,弥补了静态网络无法实现时变动态网络分析的不足,为提高露天矿运输系统大规模路网模型的快速效率,提供了一种全新的求解思路。

Route optimization algorithm of open-pit mine based on Clifford algebra

Routing optimization at open pit is a combinatorial optimization problem in searching for the best transportation routes under certain physical and economic constraints. It has important practical significance for reducing mine operation cost. However,some conventional routing optimization algorithms for open pit mainly start from the static road directed graph network optimization,which cannot realize the efficient analysis and optimization decision of large-scale time-varying dynamic network. In this paper,the classical directed graph network analysis method in Euclidean spaceis extended to Clifford algebraic space by taking Zhahannaoer open-pit as an example. The uniform expression of the node,the directed edge and the route is established. The method for calculating the route geometric topology connectivity and scalar constraint indexes is proposed to separate the geometric topology calculation and the numerical optimization problem from the programming model. In order to overcome the problem that the traditional static network analysis method cannot dynamically express the change of system energy consumption,a route optimization model based on time-varying transportation work minimization is established,and the calculation method of time-varying resistance is given according to the characteristics of rolling resistance. Periodic time-varying effect of rolling resistance coefficient caused by the frequent rolling failure and periodic maintenance of haul road is studied,and a method for calculating the rolling resistance coefficient of time-varying rolling is proposed. In order to further improve the convergence efficiency of the algorithm,two sets of inference and one set of numerical calculation optimization strategies are proposed to improve the numerical calculation of genetic algorithm. It has been verified by many simulation experiments that the algorithm can converge to the global optimal solution quickly,which proves that the algorithm is feasible and effective to solve the practical path optimization problem of mine. Secondly,the introduction of geometric-algebraic method also provides a new method to effectively realize the decoupling of topological relation calculation and numerical calculation for traditional path optimization problems,which makes up for the deficiency of time-varying dynamic network analysis that static network cannot realize and provides a new idea to improve the efficiency of large-scale road network model of open-pit transportation system.