A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem

Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.

Extracting multi-objective multigraph features for the shortest path cost prediction:Statistics-based or learning-based?

Efficient airport airside ground movement(AAGM)is key to successful operations of urban air mobility.Recent studies have introduced the use of multi-objective multigraphs(MOMGs)as the conceptual prototype to formulate AAGM.Swift calculation of the shortest path costs is crucial for the algorithmic heuristic search on MOMGs,however,previous work chiefly focused on single-objective simple graphs(SOSGs),treated cost enquires as search problems,and failed to keep a low level of computational time and storage complexity.This paper concentrates on the conceptual prototype MOMG,and investigates its node feature extraction,which lays the foundation for efficient prediction of shortest path costs.Two extraction methods are implemented and compared:a statistics-based method that summarises 22 node physical patterns from graph theory principles,and a learning-based method that employs node embedding technique to encode graph structures into a discriminative vector space.The former method can effectively evaluate the node physical patterns and reveals their individual importance for distance prediction,while the latter provides novel practices on processing multigraphs for node embedding algorithms that can merely handle SOSGs.Three regression models are applied to predict the shortest path costs to demonstrate the performance of each.Our experiments on randomly generated benchmark MOMGs show that(i)the statistics-based method underperforms on characterising small distance values due to severe overestimation;(ii)A subset of essential physical patterns can achieve comparable or slightly better prediction accuracy than that based on a complete set of patterns;and(iii)the learning-based method consistently outperforms the statistics-based method,while maintaining a competitive level of computational complexity.

考虑鲁棒成本与绝对后悔的最短路径问题研究

为克服鲁棒偏差方法在处理区间路网时所求鲁棒最短路径的保守性问题,通过分析鲁棒成本的定义以及鲁棒最短路径过于保守的原因,结合算例分析提出了绝对后悔值的概念,并以鲁棒成本和绝对后悔值为目标函数建立了区间路网的多目标最短路径模型;根据最短路径模型的特点设计了分离路径决策变量与连续变量的Benders分解算法,同时基于传统有效路径的判断依据重新定义了符合该最短路径模型的有效路径,并在分解后的主问题模型中引入了有效路径约束以加快算法收敛速度;利用MATLAB生成了一个包含29个节点、70条双向通行路段的区间路网对模型与算法进行仿真测试。结果表明:考虑鲁棒成本和绝对后悔值的最短路径模型能在区间路网中找到不保守,且同时兼具鲁棒性的最短路径,能够有效克服鲁棒偏差方法的缺陷。

基于二分法和控制信息素量的改进蚁群算法

为弥补蚁群算法易陷入局部最优、收敛速度较慢等不足,提出一种基于二分法和控制信息素量的改进蚁群算法。在每次迭代结束时,利用二分法放弃行走路程较远的半数蚁群的信息素,使收敛速度得到提高;利用3-opt局部优化方法提高解的精度;通过控制信息素量动态调整蚁群选择路径的概率,避免算法早熟;将改进的算法应用于旅行商问题。实验结果表明,该算法在寻优能力、可靠性、收敛速度以及稳定性方面均表现出明显的优越性。

求解多目标点路径规划问题的离散头脑风暴算法

为保证移动机器人以最短路径遍历多目标点,该文提出一种基于离散头脑风暴的多目标点路径规划算法。首先,考虑障碍物对路径规划的影响,将目标点间的最短避障距离作为评判依据,提高规划路径合理性。其次,针对传统离散头脑风暴算法在解决组合类优化问题时提前陷入局部最优的问题,提出一种启发式自适应路径优化策略,通过设计与迭代次数相关的适应度选择函数以及改进启发式交叉算子,增加路径多样性和提高算法收敛速度。基于栅格法建立地图模型,在不同环境地图中选取多个目标进行对比仿真,验证所提算法的有效性以及对不同环境的适应性。

A Dynamic Programming Approach for the Max-Min Cycle Packing Problem in Even Graphs

Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles Ciin G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.

五阶递进的最短路径问题教学模式探索

最短路径问题是计算机科学、地理信息科学、运筹学、管理科学、交通工程、工业工程和复杂系统科学等领域的基础性问题,也是许多相关课程中的教学重点。针对目前教学中存在的被动接受、手工计算、只算不用等问题,按照“精选算法、纵向到底、横向到边”的教学理念,探索“算法原理—数学建模—应用举例—程序实现—算法比赛”五阶递进的最短路径问题教学模式,有助于培养和提升学生的原理掌握深度、优雅学术品位、运筹优化思维、综合应用能力和团队合作精神。

Floyd-Warshall Algorithm Based on Picture Fuzzy Information

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.

疫情防控背景下城市应急生活物资配送

针对疫情防控中应急生活物资调度及科学管理问题,构建以中游节点数量最少且距离上游节点与下游节点里程总和最小为目标的最短路径优化模型,采用熵权法将其转化为单目标。其次,基于模拟退火算法,设计了以增加、减少中游节点数量及随机改变中游节点服务小区个数等为核心的邻域解搜索策略。然后,基于长春市相关数据,对该模型进行了详细求解,并绘制了有序网络图。最后,构建了以货车运行时间及货车开行数量最少为目标的货车服务方案优化模型,采用模拟退火算法进行求解。研究较好地解决了疫情暴发期城市应急生活物资的优化配送问题。

Output-threshold coupled neural network for solving the shortest path problems

This paper presents a coupled neural network, called output-threshold coupled neural network (OTCNN), which can mimic the autowaves in the present pulsed coupled neural networks (PCNNs), by the construction of mutual coupling between neuron outputs and the threshold of a neuron. Based on its autowaves, this paper presents a method for finding the shortest path in shortest time with OTCNNs. The method presented here features much fewer neurons needed, simplicity of the structure of the neurons and the networks, and large scale of parallel computation. It is shown that OTCNN is very effective in finding the shortest paths from a single start node to multiple destination nodes for asymmetric weighted graph, with a number of iterations proportional only to the length of the shortest paths, but independent of the complexity of the graph and the total number of existing paths in the graph. Finally, examples for finding the shortest path are presented.

一种启发式自优化的紫外线消毒机器人路径规划方法

随着新冠病毒全球蔓延,许多杀毒的技术被提出,特定波长、剂量的紫外线杀毒已被证实有效。大部分紫外线杀毒装置定点安置,机动灵活性不足,而现有移动式紫外线杀毒机器人,场景适配性不强,移动路径未优化,缺乏自主规划能力,造成消毒区域不全面。本研究提出了一种启发式自优化的路径规划(HSPP)方法,设计并实现了路径遍历程序和路径优化程序,先基于SCAN算法,达到全区域的覆盖,再通过路径优化程序,给出移动路径轨迹的近似最小环,缩短机器人移动的路径总长度。本研究比较了HSPP、随机法以及SCAN,由实验结果得知,HSPP算法能够让消毒区域达到全覆盖的目标,同时总路径长度短于SCAN与随机法。

插电式混合动力汽车绿色路径规划研究

为了降低插电式混合动力汽车(Plug-in Hybrid Electric Vehicle,PHEV)在驾驶过程中的能耗,本文对插电式混合动力汽车绿色路径规划问题(Plug-in Hybrid Electric Vehicle Green Routing Problem,PHEVGRP)进行了研究。基于脉冲耦合神经网络提出了用时间依赖中继神经网络求解时间依赖车辆路径规划问题。基于可实时获取的道路交通状态量建立PHEV能耗计算模型。采用硬参数共享多任务学习建立道路交通状态量的预测模型。结合两个模型,将时间依赖中继神经网络应用于PHEVGRP的求解。采用真实数据进行试验,结果表明所提出的方法能够求得PHEVGRP的基于预测模型的最优解且求解速度优于启发式算法。

K最短路径算法综述

为了进一步推广应用K最短路径(K shortest paths,KSP)算法并为深入研究该类算法提供相关资料。根据路径限制条件,将KSP问题分为一般KSP问题和限定无环KSP问题,归纳总结了求解每类KSP问题的基本思路、研究现状和研究进展。KSP问题非常复杂,在实际应用中所需处理的数据规模非常庞大,使得算法效率成了评价KSP算法的一个重要指标。在分析各种KSP算法时尤其关注其时间复杂度,指出KSP问题未来的研究方向,将为满足多约束的最短路径等问题的研究提供有益的参考。

适合复杂网络分析的最短路径近似算法

基于互联网抽取的社会网络往往具有较大的规模,这对社会网络分析算法的性能提出了更高的要求.许多网络性质的度量都依赖于最短路径信息,社会网络等现实网络往往表现出"无标度"等复杂网络特征,这些特征指示了现实网络中最短路径的分布规律.基于现实网络的拓扑特征,提出了一种适合于复杂网络的最短路径近似算法,利用通过局部中心节点的一条路径近似最短路径,该算法能够方便地用于需要最短路径信息的社会网络性质的估算,为复杂网络的近似分析提供了一种新的思路.在各种生成网络与现实网络上的实验结果表明,该算法在复杂网络上能够大幅降低计算复杂性并保持较高的近似准确性.

基于“矩阵乘法”的网络最短路径算法

网络最短路径问题可以作为许多实际应用问题的模型,但传统的求解算法其迭代过程复杂.本文描述了基于矩阵乘法的最短路算法,其时间复杂度与Dijkstra算法相同.在给定的一个网络图中,在不改变网络图中的最短路的条件下,删除"多余"的结点或边,可以达到简化网络图和提高求解速度的目的,从而降低计算复杂性.最后,研究了该方法在最短路径问题和旅行商问题中的应用.实例表明,这种算法与传统的动态规划技术相比,具有运算简便、易于理解的优点.

具有多条最短路径的最短路问题

尽管Dijkstra算法是解决正权单源点最短路问题公认的最好算法,但它仅能求得从源点到指定点的一条最短路径,为了给出从源点到指定点的所有最短路径,通过改进临时标号过程,得到了修正的Dijkstra算法.修正后的算法得到的不再是最短路径树,而是最短路径图.相对于原算法,修正后的算法不仅更加简便,而且应用Yen算法能够按照边数由少到多的顺序罗列出所有的最短路径.

一种实用的所有点对之间最短路径并行算法

针对有向图中每对顶点之间的最短路径问题,在基于扩充了路径矩阵的串行Floyd算法上,提出了二维网格结构上的并行算法。选用的任务划分方法为二维均匀块分配方法。该并行算法已经在NOW上的MPI平台上实现,理论分析和数值实验表明它具有较高的扩展性和并行效率。

最短路问题的闭环DNA算法

提出了不等长闭环DNA分子的概念,由此推广了闭环DNA计算模型。给出了固定端点的最短路问题闭环DNA算法,该算法首先对每条弧进行了三组DNA编码,再用有目的的终止技术合成固定端点的所有链,然后通过接入实验和电泳实验得到最短路,并通过检测实验输出所有最短路径。得出了算法的复杂性,为说明算法的有效性给出了一个算例。最后讨论了最短路问题闭环DNA算法在变权网络、自由终点或固定中间点的最短路问题中的应用,并给出了相应的解决方法。由此说明该算法具有广泛的适应性。

国际航线网络中K条最短路径算法改进与仿真

K条最短路径(KSP)问题是国际航线网络实际路径优化问题。通过对航线网络特征与K条最短路径算法的分析,研究了解决KSP问题的典型Yen算法。针对Yen算法求解候选路径占用大量运算时间的问题,提出一种改进Yen算法。改进Yen算法通过借助A*算法的启发式策略,减少了产生候选航线路径的时间,从而提高了算法的搜索效率并减小了算法搜索的规模。通过对国际航线网络实例的仿真,实验结果表明改进Yen算法能够快速求解国际航线网络中的KSP问题;同时,与Yen算法相比,运算效率提升了75.19%以上,能够为航线路径优化提供决策支持。