Search

In order to mitigate congestion of urban transportation network, this paper propose a reservation scheme. Given users’ preferred departure time, arrival time and flexible time windows at both origins and destinations, the centralized reserving and scheduling system determines agents’ departure times, routes and trajectories with appropriate resolution, which aims to minimize the total traveling disutility involving travel times, waiting times queues and delays. After dividing traffic condition into various modes such as free flow, congestion, hyper-congestion and so on, the reservation model is built on a high-dimensional discretized space-time-mode network. This reservation and sketching timetabling problem can be formulated as a multi-commodity flow optimization problem with additional side constraints, such as capacity constraints under different operating mode. The multi-commodity flow problem (i.e. the master problem) is divided into two sub-problems. One is knapsack problem which determine the sequence of activated space-time-mode arcs. The other is agents’ shortest path problem. We further use Alternative Direction Method of Multiplier (ADMM) to solve the shortest path problem above based on dual decomposition methodology. Finally numerical cases are used to show the benefits of reservation timetabling.

The shortest path is an issue that involves the route from one point (nodes) to another. It is to find a path with a minimum travelling time. Nowadays, traffic problems have affected many transport users especially in Kuala Lumpur area. The time wasted on the road causes a lot of problems to the users. Furthermore, the costs between two destinations are rather expensive. Therefore, the inability of users to use the shortest path has attracted the researcher to propose several travel alternatives to overcome this problem. In addition, this study will help to improve the efficiency of the road and make people want to use it more often. The objectives of this study are to find the shortest path from Bandar Tun Razak to Berjaya Times Square and to cut down the cost between these two destinations. The time of the shortest path problem and the cost problem are drawn separately. Moreover, Dijkstra algorithm is applied to find the shortest path. The shortest path is calculated by using C programming of Dev C++. Nevertheless, both time and cost of shortest path are constructed in different paths. The time and cost of the journey are described by driving a car from Bandar Tun Razak to Lebuhraya SMART to Kampung Pandan, then Berjaya Times Square. The total time taken is 23 minutes (RM8.00), whereas, the cost is based on the shortest path from Bandar Tun Razak to Taman Maluri to Seasons Tower and Berjaya Times Square. The minimum cost is RM4.00 (30 minutes).

Accurate and fast path calculation is essential for applications such as vehicle navigation systems and transportation network routing. Although many shortest path algorithms for restricted search areas have been developed in the past ten years to speed up the efficiency of path query, the performance including the practicability still needs to be improved. To settle this problem, this paper proposes a new method of calculating statistical parameters based on a unidirectional road network model that is more in line with the real world and a path planning algorithm for dynamically restricted search areas that constructs virtual boundaries at a lower confidence level. We conducted a detailed experiment on the proposed algorithm with the real road network in Zhengzhou. As the experiment shows, compared with the existing algorithms, the proposed algorithm improves the search performance significantly in the condition of optimal path under the premise of ensuring the optimal path solution.

The shortest path problem has been studied to be solved through diverse deterministic and also stochastic approaches such as Ant Colony Optimization. One of the most challenging issues with the implication of Ant Colony Optimization to solve the shortest path problem is parameter selection and tuning which is found crucial to improve the computational performance of problem-solving. To tune parameters, it is vital to observe the response of each parameter to different values and study their effect on the final results. In this research, two experiments are designed and conducted to study the behavior of parameters in terms of generated results and computational performance. In the first experiment, evaporation, updating, and transition rule parameters are studied by iterative execution of shortest path generation between nodes considering different parameter values. In the second experiment, the number of initial ants is studied. Inspecting the results, it is observed that to avoid premature stagnation decreasing α value is recommended. On the other hand, ρ is observed to be considered for tuning of speed and number of diffusions of the algorithm. Moreover, it is realized that a high Q value would result in more correct results. Inspecting the initial number of ants, a threshold is realized where increasing the number of ants over this threshold would drastically result in more optimized paths.

When an emergency occurs in the city, a large area of road congestion usually occurs. Therefore, it is particularly important to provide an effective emergency path planning strategy for vehicles. However, existing emergency path planning methods do not take into account the connectivity characteristics of the road network and commuting capacity. For this purpose, a Grid Map Emergency Path Planning (GMEPP) framework based on a novel model Grid Road Network (GRN) is designed in this paper. First, the road network data is divided into grids under equal spacing bands, and the roads data divided into different grids and use the commuting capacity of each road as the weight of each edge in the grid. Then a Grid PageRank (GPR) algorithm will be introduced, the output value of this methodology is calculated based on the capacity and number of connected edges of all vertices pointed by the external grid in each grid. The higher value of the grid will be recommended to users first when the path is planning. According to the GRN model, an improved Bidirectional Dijkstra will be applied to query the shortest path between two points, which is called Gird Bidirectional Dijkstra (GBD). At last, GMEPP uses Reverse Contraction Hierarchies (RCH) and Multiple Reverse Contraction Hierarchies (MRCH) originality methodologies based on intersection type to speed up the query algorithm GBD. To compare the efficiency of the proposed method, this paper conducted extensive experiments to verify. The results of the test showed that the Gird Bidirectional Dijkstra Multiple Reverse Contraction Hierarchies (GBD-MRCH) is better than other methods in different grid distributions.

Automated systems require controllers which guarantee machine safety and specified functionality even in case of occurring defects. In literature, several methods can be found for formally deriving a supervisor providing such guarantees, including the existence of failure recovery. In this paper, an extension is proposed so that the derived supervisor not only guarantees the existence of failure recovery, but also enforces a shortest path for it. To this end, a two-step procedure is defined for supervisor derivation, in which two algorithms are involved.

Vehicle path selection follows the shortest path principle, while taking the shortest travel time as the optimization goal. In the real road network, affected by signal control, the travel time of the vehicle path has significant uncertainty. The shortest path algorithm with static road indicators as the weights has obvious defects in path selection. In order to solve this problem, according to the theory of distributed wave, the operating state of the vehicle under the influence of the downstream signal control is classified. The travel time of the vehicle on the road segment is classified and predicted, and the travel time prediction value set is further transformed into the travel time reliability. For the vehicle route selection of a dynamic road network, the path travel time reliability determined by the product of the road segment travel time reliability is logarithmically converted, and the Dijkstra algorithm is used to find the most reliable path as the target solution. Then, a simulation model is constructed to verify the validity of the algorithm. The experimental results prove that using the reliability of travel time as the weight of path selection and solving by Dijkstra algorithm can reflect the actual vehicle path selection more accurately. This method is a beneficial improvement to the problem of static path selection.

Previous studies on pipe auto-routing algorithms generally used such algorithms as A∗, Dijkstra, Genetic Algorithm, Particle Swarm Optimization, and Ant Colony Optimization, to satisfy the relevant constraints of its own field and improve the output quality. On the other hand, this study aimed to significantly improve path-finding speed by applying the Jump Point Search (JPS) algorithm, which requires lower search cost than the abovementioned algorithms, for pipe routing. The existing JPS, however, is limited to two-dimensional spaces and can only find the shortest path. Thus, it requires several improvements to be applied to pipe routing. Pipe routing is performed in a three-dimensional space, and the path of piping must be parallel to the axis to minimize its interference with other facilities. In addition, the number of elbows must be reduced to the maximum from an economic perspective, and preferred spaces in the path must also be included. The existing JPS was improved for the pipe routing problem such that it can consider the above-mentioned problem. The fast path-finding speed of the proposed algorithm was verified by comparing it with the conventional A∗ algorithm in terms of resolution.

This paper studies the trajectory optimization problem of a single cellular-enabled unmanned aerial vehicle (UAV), taking into account the outage performance of the entire trajectory. To provide real-time control, it is critical for UAV to maintain reliable connectivity with the ground base station (GBS). We first consider the connectivity outage performance, which is defined as the sum of the time duration of the outage performance not meeting a predefined threshold during the entire UAV mission. Then we formulate a trajectory optimization problem to minimize the mission completion time, while ensuring a sum constraint of the connectivity outage performance. We show that the connectivity outage constraint can be transformed into a flying area constraint. Since the formulated problem is NP-hard, a low-complexity method is proposed to solve the problem by finding the shortest path in an undirected weighted graph with enlarged GBS coverage. Simulation results demonstrate the superiority of the proposed scheme over other state-of-the-art schemes, in terms of trajectory length and computational complexity.

Rapidly-exploring Random Trees (RRTs) have been widely used for motion planning problems due to their ability to efficiently find solutions. Informed RRT* is an optimized version of RRT, which not only implements the rewiring process to optimize the tree but also limits the search area to a subset of the state space to return near-optimal solutions faster. However, limiting the state space is a function of the obtained shortest path so that before a solution is found, the planner cannot limit the state space to a subset. Moreover, unidirectional RRTs such as Informed RRT* take more time to find initial solutions in comparison to the bidirectional RRTs. In this paper, we propose Hybrid RRT, which divides the planning process into three parts: finding initial solutions by a dual-tree search, combining two trees into one, and optimizing the solution. In order to obtain an initial solution, Hybrid RRT implements a dual-tree search, which helps it find solutions faster than unidirectional searches. Then, it combines the start tree and the goal tree of the dual-tree search into one so as to implement informed sampling for a single tree to optimize the current solution. The simulation carried out in Open Motion Planning Library (OMPL), which shows that Hybrid RRT achieved outstanding improvement over RRT* and Informed RRT*.

Simple heuristics for combinatorial optimization problems often show a remarkable performance in practice. Worst-case analysis often falls short of explaining this performance. Because of this, ‘beyond worst-case analysis’ of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many combinatorial optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2015), who have used random shortest path metrics generated from complete graphs to analyse heuristics. In this thesis we look at several variations of the random shortest path metrics, and perform probabilistic analyses for some simple heuristics for several combinatorial optimization problems on these random metric spaces. A random shortest path metric is constructed by drawing independent random edge weights for each edge in a graph and setting the distance between every pair of vertices to the length of a shortest path between them, with respect to the drawn weights. We provide some basic properties of the distances between vertices in random shortest path metrics. Using these properties, we perform several probabilistic analyses. For random shortest path metrics generated from (dense) Erdős-Rényi random graphs we show that the greedy heuristic for the minimum-distance perfect matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the k-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem in this model. For random shortest path metrics generated from sparse graphs we show that the greedy heuristic for the minimum-distance perfect matching problem, and the nearest neighbor and insertion heuristics for the traveling salesman problem all achieve a constant expected approximation ratio. Additionally, we show that the 2-opt heuristic for the traveling salesman problem also achieves a constant expected approximation ratio in this model. For random shortest path metrics generated from complete graphs we analyse a simple greedy heuristic for the facility location problem: opening the κ cheapest facilities (with κ only depending on the facility opening costs). If the facility opening costs are such that κ is not too large, then we show that this heuristic is asymptotically optimal. For large values of κ we provide a closed-form expression as upper bound for the expected approximation ratio and we evaluate this expression for the special case where all facility opening costs are equal. Moreover, we show in this model that a simple 2-approximation algorithm for the Steiner tree problem is asymptotically optimal as long as the number of terminals is not too large. We also present some numerical results that imply that the 2-opt heuristic for the traveling salesman problem seems to perform rather poorly in this model.

We commence an algorithmic study of Bulk-Robustness, a new model of robustness in combinatorial optimization. Unlike most existing models, Bulk-Robust combinatorial optimization features a highly nonuniform failure model. Instead of an interdiction budget, Bulk-Robust counterparts provide an explicit list of interdiction sets, comprising the admissible set of scenarios, thus allowing to model correlations between failures of different components in the system, interdiction sets of variable cardinality and more. The resulting model is suitable for capturing failures of complex structures in the system. We provide complexity results and approximation algorithms for Bulk-Robust counterparts of the Minimum Matroid Basis problems and the Shortest Path problem. Our results rely on various techniques, and outline the rich and heterogeneous combinatorial structure of Bulk-Robust optimization., Mathematical Programming, 149 (1-2), ISSN:0025-5610, ISSN:1436-4646

With the growing complexity of indoor living environments, people have an increasing demand for indoor navigation. Currently, navigation path options in indoor are monotonous as existing navigation systems commonly offer single-source shortest-distance or fastest paths. Such path options might be not always attractive. For instance, pedestrians in a shopping mall may be interested in a path that navigates through multiple places starting from and ending at the same location. Here, we name it as the indoor traveling salesman problem (ITSP) path. As its name implies, this path type is similar to the classical outdoor traveling salesman problem (TSP), namely, the shortest path that visits a number of places exactly once and returns to the original departure place. This paper presents a general solution to the ITSP path based on Dijkstra and branch and bound (B&amp, B) algorithm. We demonstrate and validate the method by applying it to path planning in a large shopping mall with six floors, in which the QR (Quick Response) codes are assumed to be utilized as the indoor positioning approach. The results show that the presented solution can successfully compute the ITSP paths and their potentials to apply to other indoor navigation applications at museums or hospitals.

A communication network management system takes the measurements of its state variables at specific instants of time, considering them constant in the interval between two consecutive measurements. Nevertheless, this assumption is not true, since these variables evolve in real time. Therefore, uncertainty is inherent in the processing of the measurements during the intervals so that they cannot be efficiently managed using crisp variables. In this paper, we face this problem by modeling the communications network as a type-V fuzzy graph, where both the nodes and the links are described with precision, but the cost of each link is modeled as a triangular fuzzy number. Different fuzzy cost allocation functions and fuzzy optimization strategies are described and applied to the search for the shortest path between two nodes. An experimental study has been conducted using two representative networks: the backbone network of Nippon Telegraph and Telephone Corporation (NTT) and the National Science Foundation’s Network (NFSNET). In these networks, our fuzzy cost functions and strategies have been compared with the well-known crisp equivalents. The optimal search strategies are based on the proposed Fuzzy Dijkstra Algorithm (FDA), which is described deeply. The simulation results demonstrate that in all cases the fuzzy alternatives surpass or equal the crisp equivalents with statistically significant values. Specifically, the so-called Strategy 8 presents the best throughput, as it significantly exceeds the performance of all those evaluated, achieving a Global Mean Delivery Rate (GMDR) close to 1.

Route planning is an important part of road network. To select an optimized route several factors such as flow of traffic, speed limits of road. are concerned. Total cost of such a network depends on the number of junctions between the source and the destination. Due to the growth of the nodes in the network it becomes a tough job to determine the exact path using deterministic algorithms so in such cases genetic algorithms (GA) plays a vital role to find the optimized route. Crossover is an important operator ingenetic algorithm. The efficiency of thegenetic algorithmis directlyinfluenced by the time of a crossover operation. In this paper a new crossoveroperator closest-node pairing crossover (CNPC) is recommended which is explicitly designed to improve the performance of the genetic algorithm compared to other well-known crossover operators such as point based crossover and order crossover. The distance aspect of the network problem has been exploited in this crossover operator. This proposed technique gives a better result compared to the other crossover operator with the fitness value of 0.0048. The CNPC operator gives better rate of convergence compared to the other crossover operators.

Greedy method, as an efficient computing tool, can be applied to various combinatorial or nonlinear optimization problems where finding the global optimum is difficult, if not computationally infeasible. A greedy algorithm has the nature of making the locally optimal choice at each stage and then solving the subproblems that arise later. It iteratively makes one greedy choice after another, reducing each given problem into a smaller one. In other words, a greedy algorithm never reconsiders its choices. Clearly, greedy method often fails to find the globally optimal solution. However, a greedy algorithm can be proven to yield the global optimum for a given class of problems such as Kruskal's algorithm and Prim's algorithm for finding minimum spanning tree, Dijkstra's algorithm for finding single-source shortest path, and the algorithm for finding optimum Huffman tree [5]. Even for some optimization problems proven to be NP hard, a greedy algorithm may generate near optimal solution with high probability if one exploits the problem structure properly. In this chapter, we focus on the optimization problems arising from plume detection, localization and tracking and provide convincing argument on the usefulness of greedy algorithms. Detection, identification, localization, tracking and prediction of chemical, biological or nuclear propagation is crucial to battlefield surveillance and homeland security. In addition, post-accident management for public protection relies critically on detecting and tracing dangerous gas leakages promptly. The determination of source origins and release rates is useful for the forecast of gas concentration in the atmosphere and for the management staff to prioritize off-site evacuation plans. A lot of research has been focused on detecting and localizing single or multiple plume sources with autonomous vehicles [11] or sensor networks such as [22] for a vapor-emitting source, [2] for a nuclear source, and [14, 15] for a chemical source. In [12] the plume detection and localization problem is formulated as abrupt change detection using sparse sensor measurements. The development of a large scale testbed has been reported in [8] for plume detection, identification and tracking. In [3] dense sensor coverage has been used for radioactive source detection while [26] showed that using three error-free intensity sensors, one can identify the plume origin to any desired accuracy with high probability. Although this approach offers an effective solution with linear complexity of the hypothesis space, a major limitation is that the continuous time dynamic model of plume propagation has to be in the product form. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

The Probability of Reachability (POR) is defined as fraction of possible reachable routes to all possible routes between all different sources to all different destinations. In network like Mobile Ad-hoc Network (MANET) adequate level of POR is desirable for its smooth functioning. Its value depends upon various factors such as Transmission Range (T), Number of Nodes (N), node mobility, channel fading, shape and size of the region where the ad-hoc network is to be deployed. To find the impact of N,T, size and shape on the value of POR, a shortest path routing algorithm was implemented in MATLAB and effect of the above said parameters was studied. We observe significant impact of varying not only N and T but also of varying size and shape of the region on the POR values.

The aim of each company/industry is to provide a final product to customers at the minimum possible cost, as well as to protect the environment from degradation. Ensuring the shortest travel distance between involved locations plays an important role in achieving the company’s/industry’s objective as (i) the cost of a final product can be minimized by minimizing the total distance travelled (ii) finding the shortest distance between involved locations will require less fuel than the longest distance between involved locations. This will eventually result in lesser degradation of the environment. Hence, in the last few years, various algorithms have been proposed to solve different types of shortest path problems. A recently proposed algorithm for solving interval-valued Pythagorean fuzzy shortest path problems requires excessive computational efforts. Hence, to reduce the computational efforts, in this paper, firstly, an alternative lexicographic method is proposed for comparing interval-valued Pythagorean fuzzy numbers. Then, using the proposed lexicographic comparing method, a new approach (named as Mehar approach) is proposed to solve interval-valued Pythagorean fuzzy shortest path problems. Furthermore, the superiority of the proposed lexicographic comparing method, as well as the proposed Mehar approach, is discussed.

In this variant of the constrained shortest path problem, the time of traversing an arc is given by a non-negative continuous random variable. The problem is to find a minimum cost path from an origin to a destination, ensuring that the probability of reaching the destination within a time limit meets a certain reliability threshold. To solve this problem, we extend the pulse algorithm, a solution framework for short- est path problems with side constraints. To allow arbitrary non-negative continuous travel-time distributions, we model the random variables of the travel times using Phase-type distributions and Monte Carlo simulation. We conducted a set of experi- ments over small- and medium-size stochastic transportation networks with and without spatially-correlated travel times. As an alternative to handling correlations, we present a scenario-based approach in which the distributions of the arc travel times are conditioned to a given scenario (e.g., variable weather conditions). Our methodology and experiments highlight the relevance of considering on-time arrival probabilities and correlations when solving shortest path problems over stochastic transportation networks.

The shortest path-searching with the minimal weight for multiple destinations is a crucial need in an indoor applications, especially in supermarkets, warehouses, libraries, etc. However, when it is used for multiple item searches, its weight becomes higher as it searches only the shortest path between the single sources to each destination item separately. If the conventional Dijkstra algorithm is modified to multi-destination mode then the weight is decreased, but the output path is not considered as the real shortest path among multiple destinations items. Our proposed algorithm is more efficient for finding the shortest path among multiple destination items with minimum weight, compared to the single source single destination and modified multi-destinations of Dijkstra’s algorithm. In this research, our proposed method has been validated by real-world data as well as by simulated random solutions. Our advancement is more applicable in indoor environment applications based on multiple items or destinations searching.

The shortest path problem is widely applied in transportation, communication and computer networks. It addresses the challenges of determining a path with minimum distance, time or cost from a source to the destination. Network analysis provides strong decision support for users in searching shortest path. A lot of algorithms are designed for solving shortest path but most of them did not considered the conditions of the networks. Genetic Algorithm is a kind of Algorithm that has a lot of efficiency and it can be used for solving many kinds of problems. It also can be used based on the condition of the problems.In this paper, Genetic Algorithm is used for solving shortest path in multistage process planning (MPP) problem. New mutations as well as crossover parameters are defined for each network based on the conditions of them. The results of our experimental demonstrate the effectiveness of the models.

We study a multicommodity, multiperiod, resource-constrained pickup-and-delivery problem inspired by the short-term planning of maintenance services at offshore wind farms. To begin a maintenance service, different types of relatively scarce servicemen need to be delivered (transported) to the service locations. We develop resource-exceeding route (RER) inequalities, which are inspired by knapsack cover inequalities, to model the scarcity of servicemen. In addition to a traditional separation approach, we present a column-dependent constraints approach so as to include the RER inequalities in the mathematical formulation. An alternative pricing strategy is developed to correctly include the column-dependent constraints. The resulting approach is broadly applicable to any routing problem that involves a set of scarce resources. We present a branch-and-price-and-cut algorithm to compare both approaches that include RER inequalities. The branch-and-price-and-cut algorithm relies on efficiently solving a new variant of the elementary resource-constrained shortest-path problem, using a tailored pulse algorithm developed specifically to solve it. Computational experiments show that the RER inequalities significantly tighten the root node relaxations. The column-dependent constraints approach then searches the branch-and-bound tree more effectively and appears to be competitive with the traditional separation procedure. Both approaches are able to solve instances of up to 92 nodes over 21 periods to optimality.

Facility layout problem is one of the most important problems in a huge range of industries and services organizations. Simultaneous study of some qualitative and quantitative parameters like closeness relationship between facilities, physical constraints such as input/output points and how to arrange facilities can play a key role to determine the facility layout. Considering these parameters can lead to reduce production costs, increase production capacity, and remove additional displacements. A two-stage approach is proposed to achieve these goals. In the first stage, a goal programming model is proposed to determine weights of the attributes based on the experts' opinions with different preference representation structures. Afterwards, the closeness ratings of the facilities are calculated using weights of attributes. In the second stage, an efficient layout is designed by determining facilities placement sequence, location of the next facility adjacent to the previous one, location of input/output points, and rectilinear feasible shortest path between facilities. Two meta-heuristic algorithms including particle swarm optimization and genetic algorithm are designed due to computational complexity. The objective function is to minimize the sum of products distance between facilities and closeness rating and also to minimize the dead space. A case study of an Auto Body Parts company is demonstrated to verify the efficiency of the proposed two-stage approach. Furthermore, in order to assess the performance of the proposed approach, a comparison is drawn between the proposed approach and five existing approaches in the literature to solve different problems by using the two meta-heuristic algorithms.

Traffic congestion is one of the major problems in transportation field. To reduce unfavorable impact of that problem, one of the conventional applications is to find optimal or near-optimal configuration of one-way streets on road networks. When some of two-way streets in the network are converted to one-way, which may be cheaper than other possible improvements, the performance of the road system may increase. Thus, this arrangement should be evaluated in order to determine its possible effects. For this purpose, a bilevel heuristic solution algorithm is proposed to find optimal configuration of one-way streets on road networks in this study. The upper level deals with finding optimal configuration of one-way streets by minimizing the total flow (demand) weighted shortest path travel costs (distance) while user equilibrium link flows are determined in the lower level. Shortest path travel costs between OD pairs are obtained after executing traffic assignment module of VISUM software by considering link travel times according to created network configuration in the upper level. To make more attractive one-way streets, we have used the parameter of a which is multiplied with the length of one-way streets to increase its speed. The bilevel heuristic solution algorithm is combined with VISUM and applied to Sioux-Falls city network. The results of near-optimal arrangement of one-way streets are compared with those of base case in terms of objective function considered. Additionally, sensitivity analysis was performed to investigate how the algorithm reacts to the variation of the parameter of a. Results showed that developed algorithm may be considered for finding optimal configuration of one-way streets on urban road networks.

This paper proposes a new network topology design method that considers all the road nodes, energy stations and load centers to ensure the distribution of pipes along the road. The traditional graph theory and Prim Minimum Spanning Tree (MST) are used to simplify the map and minimize the length of the pipeline. After analyzing the limitations of the traditional network topology model, Point-to-Point (PTP), we present a new model, Energy Station-to-Load Point (ESLP). The model is optimized by minimum cost, not the shortest path. Finally, Pipe Diameter Grading (PDG) is proposed based on ESLP by solving for the pipe diameter that gives the minimum cost under different load demands in the process of optimization. The network design method is effectively applied in a case, and the results show that the path of the optimized plan is 1.88% longer than that of the pre-optimized plan, but the cost is 2.38% lower. The sensitivity analysis shows that the cost of pipeline construction, project life and electricity price all have an impact on the optimization results, and the cost of pipeline construction is the most significant. The difference between the different classifications of pipelines affects whether PDG is effective or not.

Real-time vehicle guidance effectively reduces traffic jams and improves the operational efficiency of urban transportation. The trip time on a route is considered as a random process that changes with time, and the shortest path selection requires a random dynamic model and the solution of a decision-making problem. Thus, the shortest trip time is the criterion to determine the dynamic path selection by a random dynamic programming (DP) model which discretizes the trip times in the continuous segments on the route. In this study, a numerical model of random dynamic programming is established by using a probability tree model and an AND/OR (AO∗) algorithm to select the path of the shortest trip time. The results show that the branches of the probability tree are only accumulated on the “quantity” and do not cause a “qualitative” change. The inefficient accumulation of “quantity” affects the efficiency of the algorithm, so it is important to separate the accumulation of “quantity” from node expansion. The accumulation of “quantity” changes the trip time according to the entering time into a segment, which demands an improved AO∗ algorithm. The new AO∗ algorithm balances between efficiency and the trip time and provides the optimal real-time vehicle guidance on the road.

Aviation transport is one of the most important and critical infrastructures in today’s global economy. Failure in its proper operations can seriously impact regional economic development, which is why it is important to evaluate network robustness. Previous analyses of robustness have mainly been conducted with an unweighted approach. In the development of air transport, however, the demand for route configuration has gradually decreased, while the demand for flight adjustments has increased. Consequently, the aviation network has developed unevenly, so adhering to a uniform approach for evaluating network robustness may lead to inaccurate results. Therefore, we examined which centrality sequence is the most sensitive to network robustness in both unweighted and weighted approaches. The air transport network selected for the case study comprised the six subregions of the Eurasian landmass of the Belt and Road region. The study results showed the following: (a) in the network constructed as an unweighted one, betweenness, and degree centrality had higher priorities in preserving network functionalities than eigenvector and closeness centrality; (b) in the network constructed as a weighted one, recursive power had a higher priority in preserving network functionalities than recursive centrality; and (c) no particular centrality measurement had a significant advantage in representing the totality of robustness. The betweenness centrality sequence was sensitive to the average shortest path length and global efficiency; the recursive power sequence was sensitive to the clustering coefficient, while degree centrality was sensitive to graph diversity. The findings of this study support the decisions about managing air transportation in the Belt and Road region.

This paper investigates an integrated rolling stock deadhead routing and timetabling problem from the rolling stock scheduling in a complicated urban rail transit line. Given the train sequences composed of passenger train trips within an operation day, the deadhead routing sub-problem aims at selecting the rolling stock deadhead routes between the depots and the first/last stations of each train sequence. The task of the deadhead timetabling sub-problem is to determine the arrival and departure times of rolling stocks along these selected routes. By means of a time-space network representation, we formulate the studied problem as a new (generalized set partitioning type) binary linear model, to minimize the weighted sum of total deadhead distance and total deadhead running time of rolling stocks during the depot exiting and entering operations. Owing to large numbers of constraints and decision variables in our model, a row and column generation-based algorithm is developed to solve practical-size problems efficiently. A row generation and a column generation are executed iteratively to reduce the numbers of considered constraints and decision variables in our algorithm, respectively. The pricing sub-problem (to identify new variables) in column generation is decomposed into multiple simplified problems, each of which is equivalent to a shortest path problem in the constructed time-space sub-network for any candidate route of each train sequence. These shortest path problems can be solved efficiently by using an existing shortest path algorithm. Computational experiments on a set of hypothetical, realistic, and real-world instances demonstrate that our approach can compute both tight lower bounds and (near-)optimal solutions (with a maximum relative optimality gap of 1.07%) for all the tested instances within a maximum computation time of approximately 3 hours for the studied tactical problem. Furthermore, our best-known solution for the real-world instance is better than the empirical solution designed by the rail managers mainly based on experience.

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.

This paper analyzes the path planning problem in the automatic parking process, and studies a path planning method for automatic parking. The grid method and the ant colony optimization are combined to find the shortest path from the parking start point to the end point. The grid method is used to model the parking environment to simulate the actual parking space of automatic parking; then this paper makes some improvements to the basic ant colony optimization, finds the destination by setting the ants’ movement rules in the grid, and finds the shortest path after N iterations; since the optimal path found is a polyline, it will increase the difficulty of controlling vehicle path tracking and affect the accuracy of vehicle path tracking. The bezier curve is used to generate a smooth path suitable for vehicle walking. Finally, through matlab simulation, the obstacles in the environment are simulated, and the parking trajectory is obtained. The results show that the path planning method proposed in this paper is feasible.

Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively and to avoid obstacles in a forward-looking way. The task of collision avoidance can be divided into a global and a local level. Regarding the global level, we propose an approach called "Predictive Collision Management Path Planning" (PCMP). At the local level, solutions for collision avoidance are used that prevent an inevitable collision. Therefore, the aim of PCMP is to avoid unnecessary local collision scenarios using predictive collision management. PCMP is a graph-based algorithm with a focus on the time dimension consisting of three parts: (1) movement prediction, (2) integration of movement prediction into a time-dependent graph, and (3) time and risk-dependent path planning. The algorithm combines the search for a shortest path with the question: is the detour worth avoiding a possible collision scenario? We evaluate the evasion behavior in different simulation scenarios and the results show that a risk-sensitive agent can avoid 47.3% of the collision scenarios while making a detour of 1.3%. A risk-averse agent avoids up to 97.3% of the collision scenarios with a detour of 39.1%. Thus, an agent's evasive behavior can be controlled actively and risk-dependent using PCMP., Extended version of the SIGSPATIAL '20 paper

International audience; This study is inspired by a challenging dynamic Dial-a-Ride Problem (DARP) encountered in a mobility service operated by the company Padam.1 . Customers ask for a transportation service either in advance or in real-time and get an immediate answer about whether their requests are accepted or rejected. The main goal is to maximize the number of accepted requests during the service while respecting maximum capacity of limited number of vehicles. In this study, we propose novel methods based on reinsertion techniques to improve Padam's online system. The proposed reinsertion techniques aim to exploit the neighborhood of a solution and must be run in real-time whenever a request is rejected by an online system. Three main online reinsertion heuristics based on different neighborhoods are proposed. The first heuristic called HDR uses destruction and repair operators, the second heuristic called GH (graph heuristic) uses the ejection chain concept, and allow modeling the reinsertion problem as a constrained shortest path problem on directed graph built from a current solution, and the third heuristic called IGH (improved graph heuristic) based on GH with intensive exploration of the neighborhood. Our proposed approaches were extensively tested on real and hard instances provided by Padam. These instances contain up to 1011 requests and 14 vehicles and with very tight time windows. The obtained results revealed the performance of the proposed reinsertion methods compared to the online heuristic, where the number of served requests is increased and the number of vehicles is reduced while maintaining operating costs close to those of the online system. The results confirm the interest of using reinsertion techniques in the dynamic DARP service.

Stochastic shortest path problems (SSPPs) have many applications in practice and are subject of ongoing research for many years. This paper considers a variant of SSPPs where times or costs to pass an edge in a graph are, possibly correlated, random variables. There are two general goals one can aim for, the minimization of the expected costs to reach the destination or the maximization of the probability to reach the destination within a given budget. Often one is interested in policies that build a compromise between different goals which results in multi-objective problems. In this paper, an algorithm to compute the convex hull of Pareto optimal policies that consider expected costs and probabilities of falling below given budgets is developed. The approach uses the recently published class of PH-graphs that allow one to map SSPPs, even with generally distributed and correlated costs associated to edges, on Markov decision processes (MDPs) and apply the available techniques for MDPs to compute optimal policies., Math Meth Oper Res;93

We study the classic problem in which a Searcher must locate a hidden point, also called the Hider in a network, starting from a root point. The network may be either bounded or unbounded, thus generalizing well-known settings such as linear and star search. We distinguish between pathwise search, in which the Searcher follows a continuous unit-speed path until the Hider is reached, and expanding search, in which, at any point in time, the Searcher may restart from any previously reached point. The former has been the usual paradigm for studying search games, whereas the latter is a more recent paradigm that can model real-life settings such as hunting for a fugitive, demining a field, or search-and-rescue operations. We seek both deterministic and randomized search strategies that minimize the competitive ratio, namely the worst-case ratio of the Hider’s discovery time, divided by the length of the shortest path to it from the root. Concerning expanding search, we show that a simple search strategy that applies a “waterfilling” principle has optimal deterministic competitive ratio; in contrast, we show that the optimal randomized competitive ratio is attained by fairly complex strategies even in a very simple network of three arcs. Motivated by this observation, we present and analyze an expanding search strategy that is a 5 4 -approximation of the randomized competitive ratio. Our approach is also applicable to pathwise search, for which we give a strategy that is a 5-approximation of the randomized competitive ratio, and which improves upon strategies derived from previous work.

International audience; An extension of the bi-level optimization for the energy management of hybrid electric vehicles (HEVs) proposed in Le Rhun et al. (2019a) to the eco-routing problem is presented. Using the knowledge of traffic conditions over the entire road network, we search both the optimal path and state of charge trajectory. This problem results in finding the shortest path on a weighted graph whose nodes are (position, state of charge) pairs for the vehicle, the edge cost being evaluated thanks to the cost maps from optimization at the 'micro' level of a bi-level decomposition. The error due to the discretization of the state of charge is proven to be linear if the cost maps are Lipschitz. The classical A * algorithm is used to solve the problem, with a heuristic based on a lower bound of the energy needed to complete the travel. The eco-routing method is validated by numerical simulations and compared to the fastest path on a synthetic road network.

This paper presents a defense approach to safeguard a protected area against an attack by a swarm of adversarial agents in three-dimensional (3D) space. We extend our 2D `StringNet Herding' approach, in which a closed formation of string-barriers is established around the adversarial swarm to confine their motion and herd them to a safe area, to 3D spaces by introducing 3D-StringNet. 3D-StringNet is a closed 3D formation of triangular net-like barriers. We provide a systematic approach to generate three types of 3D formations that are used in the 3D herding process and modifications to the finite-time convergent control laws developed in \cite{chipade2020swarmherding} that are required for a 3D environment. Furthermore, for given initial positions of the defenders, we provide conditions on the initial positions of the attackers for which the defenders are guaranteed to gather as a specified formation at a position on the shortest path of the attackers to the protected area before attackers reach there., Submitted to CDC 2020, 9 pages, 6 figures

This paper presents an integrated model for energy consumption and range estimation, capable of energy-efficient routing. This integrated model predicts the energy consumption on all road segments in the road network and applies shortest path algorithms to calculate energy-efficient routes. A temperature-dependent model of the battery internal resistance based on real-world data translates the energy consumption prediction into driving range. The graph representation of the road network is transformed from a node-based graph to an edge-based graph to allow cost allocation of one edge based on the characteristics of the preceding edge. The integrated model is used to perform an analysis of energy-efficient routes for a real-life scenario. The analysis showed that the energy-optimal route is different from the time- and distance-optimal route with energy-efficiency gains up to 37% for the chosen scenario. The energy-efficient route tends to lean toward a distance-optimal route in the case of low auxiliary consumption and to lean toward a time-optimal route in the case of high auxiliary consumption. The energy-efficient route generation is tested in real life for one case of the chosen scenario. The measured results showed a good match with the predicted values for the energy consumption with a 9% mean relative error and preserved the ranking of all routes in terms of the travel distance, travel time, and energy consumption. The proposed integrated model is a functional model for energy consumption in real-life that differentiates many energy consumption influencing factors and produces energy-efficient routes with good accuracy.

We face a growing ecosystem of applications that produce and consume data at unprecedented rates and with strict latency requirements. Meanwhile, the bursty and unpredictable nature of their traffic can induce highly dynamic environments within networks which endanger their own viability. Unencumbered operation of these applications requires rapid (re)actions by Network Management and Control (NMC) systems which themselves depends on timely collection of network state information. Given the size of today's networks, collection of detailed network states is prohibitively costly for the network transport and computational resources. Thus, judicious sampling of network states is necessary for a cost-effective NMC system. This paper proposes a deep reinforcement learning (DRL) solution that learns the principle of significant sampling and effectively balances the need for accurate state information against the cost of sampling. Modeling the problem as a Markov Decision Process, we treat the NMC system as an agent that samples the state of various network elements to make optimal routing decisions. The agent will periodically receive a reward commensurate with the quality of its routing decisions. The decision on when to sample will progressively improve as the agent learns the relationship between the sampling frequency and the reward function. We show that our solution has a comparable performance to the recently published analytical optimal without the need for an explicit knowledge of the traffic model. Furthermore, we show that our solution can adapt to new environments, a feature that has been largely absent in the analytical considerations of the problem.

In the literature on Network Optimization, k-splittable flows were introduced to enhance modeling accuracy in cases where an upper bound on the number of supporting paths for each commodity needs to be imposed, thus extending the suitability of network flow tools for an increased number of practical applications. Such modeling feature has recently been extended to dynamic flows with the introduction of the novel strongly NP-hard Quickest Multicommodity k-splittable Flow Problem (QMCkFP). Such a flows over time problem asks for routing and scheduling of each commodity demand through at most k different paths in a dynamic network with arc capacities per time step, while minimizing the time required by the overall process. In this work, we propose the first exact algorithm for solving the QMCkSFP. The developed technique falls within the Branch and Price class and is based on original relaxation, pricing and branching procedures. Linearization and variable substitution are used to obtain the relaxation problem from the path-based formulation of the QMCkSFP. The pricing problem is modeled as a Shortest Path Problem with Forbidden Paths with additional node-set resources on a time expansion of the original digraph and is solved via a tailored dynamic programming algorithm. Two branching rules are designed for restoring feasibility whenever k-splittable or binary variable domain constraints are violated. The results of an extensive batch of computational experiments conducted on small to medium-size reference instances are presented, showing a highly satisfactory performance of the proposed algorithm. The paper concludes with a discussion on further lines of research.

Cost reduction is a cornerstone of the Lean administration&rsquo, s sustainability through modify its algorithms scheme to become multi-useful. This paper focuses on control &ldquo, movement&rdquo, waste, to minimize pipeline, cabling and sewerage network deployments time, to avoid demurrages (i.e., constructor sectors) and quickens planning through two stages. The first belongs to the build constrained hybridization of published heuristic routing methods (e.g., S-Shape, Mid-point, Largest-Gap, Return, Ascending, FLA-5, FLA-6 [Flow Line Analysis], and Composite) to select the shortest path that serves many locations (i.e., Plan-A), while allowing for the modification of these locations during service (i.e., Plan-B). The new locations are grouped into two clusters, the first of which lay on the shortest preferred path, while the second cluster contains locations that do not lay on the preferred path and are therefore moved on the backlogs-list, then use Simulated Annealing when to serve them. Finally, the impact of the selected performance is investigated after studying its correlation with another published effective one under cost considerations. The computational results of proposed Minimize-Route-Length aided with simulated annealing (MRL-SA) significantly outperform others in terms of the performance of the routing heuristics and total costs and develop the Last Planner System, which has a good reputation in construction projects and approve the proposed algorithm to maintain its competitiveness sustainability.

This paper presents an algorithm for solving a minimum cost flow (MCF) problem with a dual approach. The algorithm holds the complementary slackness at each iteration and finds an augmenting path by updating node potential iteratively. Then, flow can be augmented at the original network. In contrast to other popular algorithms, the presented algorithm does not find a residual network, nor find a shortest path. Furthermore, our algorithm holds information of node potential at each iteration, and we update node potential within finite iterations for expanding the admissible network. The validity of our algorithm is given. Numerical experiments show that our algorithm is an efficient algorithm for the MCF problem, especially for the network with a small interval of cost of per unit flow.

In order to achieve the fastest fire-fighting purpose, warehouse autonomous mobile fire-fighting robots need to make an overall optimal planning based on the principle of the shortest time for their traveling path. A∗ algorithm is considered as a very ideal shortest path planning algorithm, but the shortest path is not necessarily the optimal path for robots. Furthermore, the conventional A∗ algorithm is affected by the search neighborhood restriction and the theoretical characteristics, so there are many problems, which are closing to obstacles, more inflection points, more redundant points, larger total turning angle, etc. Therefore, A∗ algorithm is improved in eight ways, and the inflection point prior strategy is adopted to compromise Floyd algorithm and A∗ algorithm in this paper. According to the criterion of the inflection point in this paper, the path inflection point arrays are constructed and traveling all path nodes are replaced by traveling path inflection points for the conventional Floyd algorithm backtracking, so it greatly reduces the backtracking time of the smooth path. In addition, this paper adopts the method of the extended grid map obstacle space in path planning safety distance. According to the relationship between the actual scale of the warehouse grid map and the size of the robot body, the different safe distance between the planning path and the obstacles is obtained, so that the algorithm can be applied to the safe path planning of the different size robots in any map environments. Finally, compared with the conventional A∗ algorithm, the improved algorithm reduces by 7.846% for the path length, reduces by 71.429% for the number of the cumulative turns, and reduces by 75% for the cumulative turning angle through the experiment. The proposed method can ensure robots to move fast on the planning path and ultimately achieve the goal of reducing the number of inflection points, reducing the cumulative turning angle, and reducing the path planning time.