Path Finding Problem Research Articles

Application of the Laminar Navier–Stokes Equations for Solving 2D and 3D Pathfinding Problems with Static and Dynamic Spatial Constraints: Implementation and Validation in Comsol Multiphysics

Pathfinding problems consist in determining the optimal shortest path, or at least one path, between two points in the space. In this paper, we propose a particular approach, based on methods used in computational fluid dynamics, that intends to solve such problems. In particular, we reformulate pathfinding problems as the motion of a viscous fluid via the use of the laminar Navier–Stokes equations completed with suitable boundary conditions corresponding to some characteristics of the considered problem: position of the initial and final points, a-priori information of the terrain, One-way routes and dynamic spatial configuration. Then, we propose and validate a numerical implementation of this methodology by using Comsol Multiphysics (i.e., a finite element methods software) and by considering various experiments. We compare the obtained results with those returned by a classical pathfinding algorithm. Finally, we perform a sensitivity analysis of the proposed algorithms with respect to some key parameters.

Finding lowest-cost paths in settings with safe and preferred zones

We define and study Euclidean and spatial network variants of a new path finding problem: given a set of safe or preferred zones with zero or low cost, find paths that minimize the cost of travel from an origin to a destination. In this problem, the entire space is passable, with preference given to safe or preferred zones. Existing algorithms for problems that involve unsafe regions to be avoided strictly are not effective for this new problem. To solve the Euclidean variant, we devise a transformation of the continuous data space with safe zones into a discrete graph upon which shortest path algorithms apply. A naive transformation yields a large graph that is expensive to search. In contrast, our transformation exploits properties of hyperbolas in Euclidean space to safely eliminate graph edges, thus improving performance without affecting correctness. To solve the spatial network variant, we propose a different graph-to-graph transformation that identifies critical points that serve the same purpose as do the hyperbolas, thus also avoiding the extraneous edges. Having solved the problem for safe zones with zero costs, we extend the transformations to the weighted version of the problem, where travel in preferred zones has nonzero costs. Experiments on both real and synthetic data show that our approaches outperform baseline approaches by more than an order of magnitude in graph construction time, storage space, and query response time.

Distributed scheduling approach for dynamic evacuation networks

ABSTRACTThe aim of this paper is to propose a novel distributed scheduling model for evacuation route scheduling from buildings and out of an affected area. The model is based on a hybrid approach that is spatio-temporal algorithm with optimization models as subproblems. The proposed distributed scheduling approach is an iterative process optimizing the one-step arrival of objects to each intermediate destination nodes at a time. To illustrate such an approach, we consider the problem of finding and scheduling evacuation paths from an urban building and out of a predetermined neighbourhood of the building on foot; the evacuation route involves pathways such as corridors, and stairs in buildings and road networks and sidewalks outside the building, there is a predefined set of exit points out of the target building and out of the road network serving the building. A well-known efficient heuristic algorithm is selected as a reference for comparative analysis and to illustrate the outperformance of the proposed approach in large-scale scenarios. The key results are the step-based optimal route schedules and the competitive evacuation time provided by the proposed distributed scheduling approach.

A Framework for Optimal Grasp Contact Planning

We consider the problem of finding grasp contacts that are optimal under a given grasp quality function on arbitrary objects. Our approach formulates a framework for contact-level grasping as a path finding problem in the space of supercontact grasps. The initial supercontact grasp contains all grasps and in each step along a path grasps are removed. For this, we introduce and formally characterize search space structure and cost functions under which minimal cost paths correspond to optimal grasps. Our formulation avoids expensive exhaustive search and reduces computational cost by several orders of magnitude. We present admissible heuristic functions and exploit approximate heuristic search to further reduce the computational cost while maintaining bounded suboptimality for resulting grasps. We exemplify our formulation with point-contact grasping for which we define domain specific heuristics and demonstrate optimality and bounded suboptimality by comparing against exhaustive and uniform cost search on example objects. Furthermore, we explain how to restrict the search graph to satisfy grasp constraints for modeling hand kinematics. We also analyze our algorithm empirically in terms of created and visited search states and resultant effective branching factor.

Network-oriented Household Activity Pattern Problem for System Optimization

Abstract: The recently emerging trend of self-driving vehicles and information sharing technologies, made available by private technology vendors, starts creating a revolutionary paradigm shift in the coming years for traveler mobility applications. By considering a deterministic traveler decision making framework at the household level in congested transportation networks, this paper aims to address the challenges of how to optimally schedule individuals’ daily travel patterns under the complex activity constraints and interactions. We reformulate two special cases of household activity pattern problem (HAPP) through a high-dimensional network construct, and offer a systematic comparison with the classical mathematical programming models proposed by Recker (1995). Furthermore, we consider the tight road capacity constraint as another special case of HAPP to model complex interactions between multiple household activity scheduling decisions, and this attempt offers another household-based framework for linking activity-based model (ABM) and dynamic traffic assignment (DTA) tools. Through embedding temporal and spatial relations among household members, vehicles and mandatory/optional activities in an integrated space-time-state network, we develop two 0-1 integer linear programming models that can seamlessly incorporate constraints for a number of key decisions related to vehicle selection, activity performing and ridesharing patterns under congested networks. The well-structured network models can be directly solved by standard optimization solvers, and further converted to a set of time-dependent state-dependent least cost path-finding problems through Lagrangian relaxation, which permit the use of computationally efficient algorithms on large-scale high-fidelity transportation networks.

CAPRA: A contour-based accessible path routing algorithm

Existing journey planners and route recommenders mainly focus on calculating the shortest path with minimum distance or travel time. However, elderly people and those with special needs (i.e. those in wheelchairs or walking with sticks) often prefer a safer and more gentle journey. Given that their route options are affected by accessibility issues such as climbing a steep slope, it is important to design a journey planner that takes in to account the accessibility of the route, as well as the standard metrics, such as travel time and distance. Accessibility has not been explored widely in path finding problems. There are two key challenges for computing accessibility. First, the accessibility of a route is not well-defined. Second, the accessibility of a route varies from user to user. In this paper, a new algorithm is designed to tackle the above two challenges. Two metrics are defined to reflect the accessibility of a route, in terms of the total vertical distance and the maximum slope. Then, a multi-objective A* search algorithm is designed to obtain a set of Pareto-optimal routes in terms of the total distance covered and the two accessibility metrics. The user can then choose from the routes provided by the new algorithm, the most suitable one according to their own preferences. The experimental results show that the proposed algorithm is able to provide a diverse set of routes with different accessibility options, including the shortest path which does not consider any accessibility metrics. In other words, the new journey planner can satisfy the preferences of a wide range of users including both the healthy and those with special needs.

An Intelligent of Navigation and Path finding Technique of Fuzzy logic

In all path finding and navigation problems the inputs are its environment space and the output of path finding and navigation algorithm is a route from source location to destination location. It seems very simple to choose a path from source to destination in theory but in real world it is very difficult to decide a route that is safe and optimal. This paper presents the navigation method which uses the human intelligence to navigate for path finding using fuzzy logic. The procedure simulates decision-making process of human for navigation and path finding.

Many-objective stochastic path finding using reinforcement learning

In this paper, we investigate solutions to path finding problems with many conflicting objectives, and introduce a new model-free many objective reinforcement learning algorithm, called Voting Q-learning, that is capable of finding a set of optimal policies in an initially unknown, stochastic environment with several conflicting objectives. Current methods for solving this type of problem rely on Pareto dominance to determine which actions are optimal, which decreases in effectiveness as the number of objectives increases, ultimately selecting actions at random in environments where all potential actions are Pareto optimal. Alternative methods for addressing this problem require interaction with a decision maker or a priori knowledge of the problem structure for guidance towards optimal solutions, making them insufficient for fully autonomous use or problems where preferred solutions are initially unknown. As an alternative, we propose the use of voting methods from social choice theory to determine a set of Pareto optimal policies by aggregating preferences determined by the evaluation of environment conditions for each objective. We demonstrate the effectiveness of this method with multiple deterministic and stochastic many-objective path finding problems that are solved optimally without any advance knowledge of the problem or interaction with a decision maker, showing that our approach is the first to provide optimal performance for an autonomous, intelligent system operating in a many objective environment.

Optimal path-finding through mental exploration based on neural energy field gradients

Rodent animal can accomplish self-locating and path-finding task by forming a cognitive map in the hippocampus representing the environment. In the classical model of the cognitive map, the system (artificial animal) needs large amounts of physical exploration to study spatial environment to solve path-finding problems, which costs too much time and energy. Although Hopfield’s mental exploration model makes up for the deficiency mentioned above, the path is still not efficient enough. Moreover, his model mainly focused on the artificial neural network, and clear physiological meanings has not been addressed. In this work, based on the concept of mental exploration, neural energy coding theory has been applied to the novel calculation model to solve the path-finding problem. Energy field is constructed on the basis of the firing power of place cell clusters, and the energy field gradient can be used in mental exploration to solve path-finding problems. The study shows that the new mental exploration model can efficiently find the optimal path, and present the learning process with biophysical meaning as well. We also analyzed the parameters of the model which affect the path efficiency. This new idea verifies the importance of place cell and synapse in spatial memory and proves that energy coding is effective to study cognitive activities. This may provide the theoretical basis for the neural dynamics mechanism of spatial memory.

The joint movement of pebbles in solving the ( $$N^2-1$$ N 2 - 1 )-puzzle suboptimally and its applications in rule-based cooperative path-finding

The present paper deals with the problem of solving the ($$n^2 - 1$$n2-1)-puzzle and cooperative path-finding (CPF) problems sub-optimally by rule-based algorithms. To solve the puzzle, we need to rearrange $$n^2 - 1$$n2-1 pebbles in the $$n \times n$$n×n-sized square grid using one vacant position to achieve the goal configuration. An improvement to the existing polynomial-time algorithm is proposed and experimentally analyzed. The improved algorithm represents an attempt to move pebbles in a more efficient way compared to the original algorithm by grouping them into so-called snakes and moving them together as part of a snake formation. An experimental evaluation has shown that the snakeenhanced algorithm produces solutions which are 8---9 % shorter than the solutions generated by the original algorithm. Snake-like movement has also been integrated into the rule-based algorithms used in solving CPF problems sub-optimally, which is a closely related task. The task in CPF consists in moving a group of abstract robots on an undirected graph to specific vertices. The robots can move to unoccupied neighboring vertices; no more than one robot can be placed in each vertex. The ($$n^2 - 1$$n2-1)-puzzle is a special case of CPF where the underlying graph is a 4-connected grid and only one vertex is vacant. Two major rule-based algorithms for solving CPF problems were included in our study--BIBOX and PUSH-and-SWAP (PUSH-and-ROTATE). The use of snakes in the BIBOX algorithm led to consistent efficiency gains of around 30 % for the ($$n^2 - 1$$n2-1)-puzzle and up to 50 % in for CPF problems on biconnected graphs with various ear decompositions and multiple vacant vertices. For the PUSH-and-SWAP algorithm, the efficiency gain achieved from the use of snakes was around 5---8 %. However, the efficiency gain was unstable and hardly predictable for PUSH-and-SWAP.

Distributed Optimal Path Generation Based on Delayed Routing in Smart Camera Networks

With the rapid development of urban traffic system and fast increasing of vehicle numbers, the traditional centralized ways to generate the source-destination shortest path in terms of travel time(the optimal path) encounter several problems, such as high server pressure, low query efficiency, roads state without in-time updating. With the widespread use of smart cameras in the urban traffic and surveillance system, this paper maps the optimal path finding problem in the dynamic road network to the shortest routing problem in the smart camera networks. The proposed distributed optimal path generation algorithm employs the delay routing and caching mechanism. Real-time route update is also presented to adapt to the dynamic road network. The test result shows that this algorithm has advantages in both query time and query packet numbers.

Review of A* (A Star) Navigation Mesh Pathfinding as the Alternative of Artificial Intelligent for Ghosts Agent on the Pacman Game

Shortest pathfinding problem has become a populer issue in Game’s Artificial Intelligent (AI). This paper discussed the effective way to optimize the shortest pathfinding problem, namely Navigation Mesh (NavMesh). This method is very interesting because it has a large area of implementation, especially in games world. In this paper, NavMesh was implemented by using A* (A star) algorithm and examined in Unity 3D game engine. A* was an effective algorithm in shortest pathfinding problem because its optimization was made with effective tracing using segmentation line. Pac-Man game was chosen as the example of the shortest pathfinding by using NavMesh in Unity 3D. A* algorithm was implemented on the enemies of Pac-Man (three ghosts), which path was designed by using NavMesh concept. Thus, the movement of ghosts in catching Pac-Man was the result of this review of the effectiveness of this concept. In further research, this method could be implemented on several optimization programmes, such as Geographic Information System (GIS), robotics, and statistics.

Traveler Centric Trip Planning: A Behavioral-Driven System

Trip planning is a well-cited problem that has been typically addressed, to a large extent, as a shortest distance path-finding problem that can be extended to reflect temporal objectives and/or constraints. This paper takes an alternative perspective to the trip-planning problem in the sense of it being a behavioral driven problem, thus allowing for multitudes of traveler centric objectives and constraints, as well as aspects of the environment, as they pertain to the traveler preferences to be incorporated in the process. This paper introduces a Behavior Driven Trip Planner (BDTP) to operate as an in-vehicle guidance system. The BDTP is designed as a modular system that combines linguistic road assessment with traveler-centric decision-making. This paper introduces traveler's doctrines , a concept that synthesizes the traveler's specific demands. Hard attributes/objectives, such as time windows and trip monetary allowances, are enforced in the process of determining the final decision about the trip. This paper introduces the underlying mathematical formulation for the developed system and explains how the formulation works to achieve the optimal performance. Simulation results are presented to demonstrate the efficacy of the system to capture and respond to traveler preferences under a wide range of scenarios.

Multi-Agent Path Finding with Payload Transfers and the Package-Exchange Robot-Routing Problem

We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robot-routing problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multi-agent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of conflict-based search. Our empirical results demonstrate that these solvers scale well and that PERR instances often have smaller makespans and flowtimes than the corresponding MAPF instances.

Selecting variables with the least correlation based on physarum network

In spectroscopy, redundant information makes the number of input variables for a prediction model larger than required. We present a method based on the physarum network to select the variable with the least correlation. This method transforms the variable selection problem into a path finding problem and then solves the problem based on the mechanism of foraging of Physarum polycephalum. Experimental results show that the physarum network, combined with other feature selection or extraction methods, can select the least number of wavelengths without sacrificing the prediction performance.

Multi-objective path finding in stochastic networks using a biogeography-based optimization method

Multi-objective path finding (MOPF) problems are widely applied in both academic and industrial areas. In order to deal with the MOPF problem more effectively, we propose a novel model that can cope with both deterministic and random variables. For the experiment, we compared five intelligence-optimization algorithms: the genetic algorithm, artificial bee colony (ABC), ant colony optimization (ACO), biogeography-based optimization (BBO), and particle swarm optimization (PSO). After a 100-run comparison, we found the BBO is superior to the other four algorithms with regard to success rate. Therefore, the BBO is effective in MOPF problems.

Path Finding in Stochastic Time Varying Networks with Spatial and Temporal Correlations for Heterogeneous Travelers

This paper studies the path finding problem in stochastic networks with known travel time distributions on each link of the network, in the presence of spatial and temporal travel time correlations. As a result of traffic dynamics and the decisions of network users, distributions with different characteristics can be observed for the link travel time at different time intervals. Considering correlations in a dynamic stochastic network and applying simulation-based realistic travel time distributions and correlations in the path finding problem in stochastic networks are the main contributions of this study. Two reliability-based optimal path finding problems were considered: the shortest path problem with on-time arrival probability and the minimum travel time budget path problem. For each problem, user heterogeneity can be considered in the developed approach, as users are allowed to have different preferences for travel time reliability. Solution algorithms for both problems were implemented and tested on a large-scale network in Chicago, Illinois, with networkwide link travel time distributions and correlations obtained from a traffic simulator. Numerical results demonstrate the impacts of correlations in a dynamic stochastic network on the optimal path travel time distribution. The developed approach can be used in the reliability-based user equilibrium problem to solve the main subproblem, the path finding problem, in dynamic stochastic networks.

Terramechanics and Path Finding

Abstract Planetary rovers on rough terrain are likely to encounter hazards such as rocks as well as loose soil or regolith that causes the wheels to slip and potentially get stuck. These missions need autonomous navigation for avoiding these hazards. The slippage of the wheels depends dynamically on the wheel properties, soil mechanical properties, speed and pose of the rover. In this paper, we investigate the path finding problem for a planetary rover on rough sandy terrain. Insights from terramechanics, ie. the wheel soil interaction model, is used to determine path cost to be used for the A ∗ algorithm, which is used on a sample grid to determine the best path. The proposed model incorporates the slippage required to develop drawbar pull to climb up a slope, as well as steering angle needed to counter lateral force. The path thus found is evaluated based on the slip ratio and steering angle required to traverse it.

Adaptive Application Component Mapping for Parallel Computation Offloading in Variable Environments

Distinguished with traditional strategies which offload an applications computation to a single server, parallel computation offloading can promote the performance by simultaneously delivering the computation to multiple computing resources around the mobile terminal. However, due to the variability of communication and computation environments, static application component multi-partitioning algorithms are difficult to maintain the optimality of their solutions in time-varying scenarios, whereas, over-frequent algorithm executions triggered by changes of environments may bring excessive algorithm costs. To this end, an adaptive application component mapping algorithm for parallel computation offloading in variable environments is proposed in this paper, which aims at minimizing computation costs and inter-resource communication costs. It can provide the terminal a suitable solution for the current environment with a low incremental algorithm cost. We represent the application component multi-partitioning problem as a graph mapping model, then convert it into a pathfinding problem. A genetic algorithm enhanced by an elite-based immigrants mechanism is designed to obtain the solution adaptively, which can dynamically adjust the precision of the solution and boost the searching speed as transmission and processing speeds change. Simulation results demonstrate that our algorithm can promote the performance efficiently, and it is superior to the traditional approaches under variable environments to a large extent.

A technique for semiautomatic segmentation of echogenic structures in 3D ultrasound, applied to infant hip dysplasia.

Automatic segmentation of anatomical structures and lesions from medical ultrasound images is a formidable challenge in medical imaging due to image noise, blur and artifacts. In this paper we present a segmentation technique with features highly suited to use in noisy 3D ultrasound volumes and demonstrate its use in modeling bone, specifically the acetabulum in infant hips. Quantification of the acetabular shape is crucial in diagnosing developmental dysplasia of the hip (DDH), a common condition associated with hip dislocation and premature osteoarthritis if not treated. The well-established Graf technique for DDH diagnosis has been criticized for high inter-observer and inter-scan variability. In our earlier work we have introduced a more reliable instability metric based on 3D ultrasound data. Visualizing and interpreting the acetabular shape from noisy 3D ultrasound volumes has been one of the major roadblocks in using 3D ultrasound as diagnostic tool for DDH. For this study we developed a semiautomated segmentation technique to rapidly generate 3D acetabular surface models and classified the acetabulum based on acetabular contact angle (ACA) derived from the models. We tested the feasibility and reliability of the technique compared with manual segmentation. The proposed segmentation algorithm is based on graph search. We formulate segmentation of the acetabulum as an optimal path finding problem on an undirected weighted graph. Slice contours are defined as the optimal path passing through a set of user-defined seed points in the graph, and it can be found using dynamic programming techniques (in this case Dijkstra's algorithm). Slice contours are then interpolated over the 3D volume to generate the surface model. A three-dimensional ACA was calculated using normal vectors of the surface model. The algorithm was tested over an extensive dataset of 51 infant ultrasound hip volumes obtained from 42 subjects with normal to dysplastic hips. The contours generated by the segmentation algorithm closely matched with those obtained from manual segmentation. The average RMS errors between the semiautomated and manual segmentation for the 51 volumes were 0.28 mm/1.1 voxel (with 2 node points) and 0.24 mm/0.9 voxel (with 3 node points). The semiautomatic algorithm gave visually acceptable results on images with moderate levels of noise and was able to trace the boundary of the acetabulum even in the presence of significant shadowing. Semiautomatic contouring was also faster than manual segmentation at 37 versus 56 s per scan. It also improved the repeatability of the ACA calculation with inter-observer and intra-observer variability of 1.4 ± 0.9 degree and 1.4 ± 1.0 degree. The semiautomatic segmentation technique proposed in this work offers a fast and reliable method to delineate the contours of the acetabulum from 3D ultrasound volumes of the hip. Since the technique does not rely upon contour evolution, it is less susceptible than other methods to the frequent missing or incomplete boundaries and noise artifacts common in ultrasound images. ACA derived from the segmented 3D surface was able to accurately classify the acetabulum under the categories normal, borderline and dysplastic. The semiautomatic technique makes it easier to segment the volume and reduces the inter-observer and intra-observer variation in ACA calculation compared with manual segmentation. The method can be applied to any structure with an echogenic boundary on ultrasound (such as a ventricle, blood vessel, organ or tumor), or even to structures with a bright border on computed tomography or magnetic resonance imaging.