Path Finding Problem Research Articles

Dynamic path finding for multi-load agent pickup and delivery problem

Recently, the Multi-Agent Pickup and Delivery (MAPD) problem has attracted widespread attention from both academia and industry. In the MAPD problem, each task has its pickup and delivery locations, and the agent needs to pick this task up from the pickup location and deliver it to its delivery location. Therefore, existing works consider the MAPD problem as the core problem in industrial scenarios, e.g., logistics warehouse. Note that the agents considered in the MAPD problem are single-load agents that complete tasks one by one. However, many commercial companies have deployed agents with multi-load instead of single-load agents to improve efficiency and reduce costs. The agents with multi-load can complete multiple tasks at once, so existing solutions cannot work well with the MAPD problem for multi-agents. To solve this issue, we investigate a novel problem in this paper, namely the Multi-Load Agent Pickup and Delivery (MLAPD) problem, where the agents with multi-load not only need to complete assigned real-time tasks but also need to avoid conflicts with each other and the goal is to minimize the total cost in the warehouse. To address this novel problem, we develop a task assignment to complete the assignments between multi-load agents and online tasks in real-time and a dynamic path finding problem that enables multi-load agents to move along conflict-free paths. Finally, extensive experiments in two different warehouses examine the effectiveness of our solutions.

S&Reg v2: a probabilistically complete sampling-based planner to solve multi-goal path finding problem via multi-task learning networks

In this paper, we present a variant of our previous research on multi-goal path finding problem, focusing on finding a feasible and closed path to visit a sequence of goals in an environment with obstacles. The newly proposed method, Segmentation & Regression v2 (S&Reg v2), employs multi-task learning networks to generate regions and estimates of lengths of local paths between pairwise goals. Importantly, the estimates are performed as weights for a complete graph to compute the visiting sequence. Subsequently, the path-finding process is executed following the sequence, and the predicted region works as a sampling domain to enhance the search speed. A hybrid sampler is designed by combining a uniform domain with the region domain, ensuring successful samples, even if the region is disconnected. Besides, a selection rule is introduced to balance the sampling domain during different searching stages. A proof of probabilistic completeness of the S&Reg v2 method is given. Simulations verify the superior performance of the S&Reg v2 method, demonstrating a reduction in calculation time ranging from 3.9% to 13.0%. Furthermore, a practical scenario validates the reliability of S&Reg v2, achieving a 15.0% improvement in success rate and a 9.7% reduction in calculation time.

MET-MAPF: A Metamorphic Testing Approach for Multi-Agent Path Finding Algorithms

The Multi-Agent Path Finding (MAPF) problem, i.e., the scheduling of multiple agents to reach their destinations, has been widely investigated. Testing MAPF systems is challenging, due to the complexity and variety of scenarios and the agents’ distribution and interaction. Moreover, MAPF testing suffers from the oracle problem, i.e., it is not always clear whether a test shows a failure or not. Indeed, only considering whether the agents reach their destinations without collision is not sufficient. Other properties related to the “quality” of the generated paths should be assessed, e.g., an agent should not follow an unnecessarily long path. To tackle this issue, this paper proposes MET-MAPF, a Metamorphic Testing approach for MAPF systems. We identified ten Metamorphic Relations (MRs) that a MAPF system should guarantee, designed over the environment in which agents operate, the behaviour of the single agents, and the interactions among agents. Starting from the different MRs, MET-MAPF automatically generates test cases addressing them, so possibly exposing different types of failures. Experimental results show that MET-MAPF can indeed find MR violations not exposed by approaches that only consider the completion of the mission as test oracle. Moreover, experiments show that different MRs expose different types of violations.

Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Finding the optimal reliable energy consumption path for electric vehicles under rainfall conditions

ABSTRACT This paper presents a new path-finding problem to ensure reliable energy consumption for electric vehicles (EVs) under rainfall conditions. The objective function of the proposed model aims to find a reliable path that minimises energy consumption while ensuring a certain probability of completing the trip without exhausting a given battery energy budget. By considering the influence of adverse weather conditions at different periods, the existing model is expanded. To address the non-additivity and non-linearity characteristics of the optimisation model, an enhanced heuristic algorithm is proposed, incorporating inequality techniques, the K-shortest algorithm, and path-updating strategies. Lastly, the proposed algorithm is validated using Hong Kong’s grid-based road network as a case study, which demonstrates the correctness and effectiveness of the algorithm. The results indicate that by considering adverse weather conditions, the estimation of energy consumption can be significantly improved in terms of accuracy, achieving more efficient and reliable optimal path recommendations.

Uncrewed Vehicle Pathfinding Approach Based on Artificial Bee Colony Method

The presented study is dedicated to the dynamic pathfinding problem for UV. Since the automation of UV movement is an important area in many applied domains like robotics, the development of drones, autopilots, and self-learnable platforms, we propose and study a promising approach based on the algorithm of swarm AI. Given the 2D environment with multiple obstacles of rectangular shape, the task is to dynamically calculate a suboptimal path from the starting point to the target. The agent has been represented as UV in 2D space and should find the next optimal movement point from the current position only within a small neighborhood area. This area has been defined as a square region around the current agent’s position. The size of the region has been determined by the attainability of the agent's scanning sensors. If the obstacle is detected by the agent, the latter should be taken into consideration while calculating the next trajectory point. To perform these calculations, the ABC metaheuristic, one of the best representatives of swarm AI, has been used. The validation of the proposed approach has been performed on several 2D maps with different complexity and number of obstacles. Also, to obtain the proper configuration, an inverse problem of identification of guided function weights has been formulated and solved. The outlined results show the perspective of the proposed approach and can complement the existing solutions to the pathfinding problem.

Constrained Motion Planning and Multi-Agent Path Finding on directed graphs

We discuss C-MP and C-MAPF, generalizations of the classical Motion Planning (MP) and Multi-Agent Path Finding (MAPF) problems on a directed graph G. Namely, we enforce an upper bound on the number of agents that occupy each member of a family of vertex subsets. For instance, this constraint allows maintaining a safety distance between agents. We prove that finding a feasible solution of C-MP and C-MAPF is NP-hard. Also, we propose a method to convert these problems to standard MP and MAPF by strengthening the constraints. The method consists in finding a subset of vertices W and a reduced graph GW, such that a feasible solution of MP and MAPF on GW provides, in polynomial time, a feasible solution of C-MP and C-MAPF on G. However, since the conversion into standard MP and MAPF is obtained by strengthening constraints, feasible solutions of C-MP and C-MAPF on G may exist even if MP and MAPF on GW do not admit any feasible solution. We also study the problem of finding W of maximum cardinality. First, we show that such problem is strongly NP-hard. Then, we propose a heuristic approach for its solution.

Generally Applicable Q-Table Compression Method and Its Application for Constrained Stochastic Graph Traversal Optimization Problems

We analyzed a special class of graph traversal problems, where the distances are stochastic, and the agent is restricted to take a limited range in one go. We showed that both constrained shortest Hamiltonian pathfinding problems and disassembly line balancing problems belong to the class of constrained shortest pathfinding problems, which can be represented as mixed-integer optimization problems. Reinforcement learning (RL) methods have proven their efficiency in multiple complex problems. However, researchers concluded that the learning time increases radically by growing the state- and action spaces. In continuous cases, approximation techniques are used, but these methods have several limitations in mixed-integer searching spaces. We present the Q-table compression method as a multistep method with dimension reduction, state fusion, and space compression techniques that project a mixed-integer optimization problem into a discrete one. The RL agent is then trained using an extended Q-value-based method to deliver a human-interpretable model for optimal action selection. Our approach was tested in selected constrained stochastic graph traversal use cases, and comparative results are shown to the simple grid-based discretization method.

Integration of Efficient Techniques Based on Endpoints in Solution Method for Lifelong Multiagent Pickup and Delivery Problem

We investigate the integration of several additional efficient techniques that improve a solution method for the lifelong multiagent pickup-and-delivery (MAPD) problem to reduce the redundancy in the concurrent task execution and space usage of a warehouse map. The lifelong MAPD problem is an extended class of iterative multiagent pathfinding problems where a set of shortest collision-free travel paths of multiple agents is iteratively planned. This problem models a system in automated warehouses with robot-carrier agents that are allocated to pickup-and-delivery tasks generated on demand. In the task allocation to agents, several solution methods for lifelong MAPD problems consider the endpoints of the agents’ travel paths to avoid the deadlock situations among the paths due to the conflict of the endpoints. Since redundancies are found in the problem settings themselves and the concurrency of allocated tasks, several additional techniques have been proposed to reduce them in solution methods. However, there should be opportunities to investigate the integration of additional techniques with improvements for more practical solution methods. As analysis and an improved understanding of the additional solution techniques based on endpoints, we incrementally integrate the techniques and experimentally investigate their contributions to the quality of task allocation and the paths of the agents. Our result reveals significant complementary effects of the additionally integrated techniques and trade-offs among them in several different problem settings.

Bidirectional Temporal Plan Graph: Enabling Switchable Passing Orders for More Efficient Multi-Agent Path Finding Plan Execution

The Multi-Agent Path Finding (MAPF) problem involves planning collision-free paths for multiple agents in a shared environment. The majority of MAPF solvers rely on the assumption that an agent can arrive at a specific location at a specific timestep. However, real-world execution uncertainties can cause agents to deviate from this assumption, leading to collisions and deadlocks. Prior research solves this problem by having agents follow a Temporal Plan Graph (TPG), enforcing a consistent passing order at every location as defined in the MAPF plan. However, we show that TPGs are overly strict because, in some circumstances, satisfying the passing order requires agents to wait unnecessarily, leading to longer execution time. To overcome this issue, we introduce a new graphical representation called a Bidirectional Temporal Plan Graph (BTPG), which allows switching passing orders during execution to avoid unnecessary waiting time. We design two anytime algorithms for constructing a BTPG: BTPG-naïve and BTPG-optimized. Experimental results show that following BTPGs consistently outperforms following TPGs, reducing unnecessary waits by 8-20%.

Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology

In the Multiagent Path Finding (MAPF for short) problem, we focus on efficiently finding non-colliding paths for a set of k agents on a given graph G, where each agent seeks a path from its source vertex to a target. An important measure of the quality of the solution is the length of the proposed schedule l, that is, the length of a longest path (including the waiting time). In this work, we propose a systematic study under the parameterized complexity framework. The hardness results we provide align with many heuristics used for this problem, whose running time could potentially be improved based on our Fixed-Parameter Tractability (FPT) results. We show that MAPF is W[1]-hard with respect to k (even if k is combined with the maximum degree of the input graph). The problem remains NP-hard in planar graphs even if the maximum degree and the makespan l are fixed constants. On the positive side, we show an FPT algorithm for k+l. As we continue, the structure of G comes into play. We give an FPT algorithm for parameter k plus the diameter of the graph G. The MAPF problem is W[1]-hard for cliquewidth of G plus l while it is FPT for treewidth of G plus l.

Decentralized Monte Carlo Tree Search for Partially Observable Multi-Agent Pathfinding

The Multi-Agent Pathfinding (MAPF) problem involves finding a set of conflict-free paths for a group of agents confined to a graph. In typical MAPF scenarios, the graph and the agents' starting and ending vertices are known beforehand, allowing the use of centralized planning algorithms. However, in this study, we focus on the decentralized MAPF setting, where the agents may observe the other agents only locally and are restricted in communications with each other. Specifically, we investigate the lifelong variant of MAPF, where new goals are continually assigned to the agents upon completion of previous ones. Drawing inspiration from the successful AlphaZero approach, we propose a decentralized multi-agent Monte Carlo Tree Search (MCTS) method for MAPF tasks. Our approach utilizes the agent's observations to recreate the intrinsic Markov decision process, which is then used for planning with a tailored for multi-agent tasks version of neural MCTS. The experimental results show that our approach outperforms state-of-the-art learnable MAPF solvers. The source code is available at https://github.com/AIRI-Institute/mats-lp.

Improved Anonymous Multi-Agent Path Finding Algorithm

We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we are interested in finding the solution with the optimal makespan. A well-established approach to solve this problem is to reduce it to a special type of a graph search problem, i.e. to the problem of finding a maximum flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck. To this end, we suggest a specific search algorithm that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store and expand bulks of the search states as single states, which results in high reduction in runtime and memory. Empirically, the resultant AMAPF solver demonstrates superior performance compared to the state-of-the-art competitor and is able to solve all publicly available MAPF instances from the well-known MovingAI benchmark in less than 30 seconds.

Learn to Follow: Decentralized Lifelong Multi-Agent Pathfinding via Planning and Learning

Multi-agent Pathfinding (MAPF) problem generally asks to find a set of conflict-free paths for a set of agents confined to a graph and is typically solved in a centralized fashion. Conversely, in this work, we investigate the decentralized MAPF setting, when the central controller that possesses all the information on the agents' locations and goals is absent and the agents have to sequentially decide the actions on their own without having access to the full state of the environment. We focus on the practically important lifelong variant of MAPF, which involves continuously assigning new goals to the agents upon arrival to the previous ones. To address this complex problem, we propose a method that integrates two complementary approaches: planning with heuristic search and reinforcement learning through policy optimization. Planning is utilized to construct and re-plan individual paths. We enhance our planning algorithm with a dedicated technique tailored to avoid congestion and increase the throughput of the system. We employ reinforcement learning to discover the collision avoidance policies that effectively guide the agents along the paths. The policy is implemented as a neural network and is effectively trained without any reward-shaping or external guidance. We evaluate our method on a wide range of setups comparing it to the state-of-the-art solvers. The results show that our method consistently outperforms the learnable competitors, showing higher throughput and better ability to generalize to the maps that were unseen at the training stage. Moreover our solver outperforms a rule-based one in terms of throughput and is an order of magnitude faster than a state-of-the-art search-based solver. The code is available at https://github.com/AIRI-Institute/learn-to-follow.

Decentralized multi-agent path finding framework and strategies based on automated negotiation

This paper introduces a negotiation framework to solve the Multi-Agent Path Finding (MAPF) Problem for self-interested agents in a decentralized fashion. The framework aims to achieve a good trade-off between the privacy of the agents and the effectiveness of solutions. Accordingly, a token-based bilateral negotiation protocol and two negotiation strategies are presented. The experimental results over four different settings of the MAPF problem show that the proposed approach could find conflict-free path solutions albeit suboptimally, especially when the search space is large and high-density. In contrast, Explicit Estimation Conflict-Based Search (EECBS) struggles to find optimal solutions. Besides, deploying a sophisticated negotiation strategy that utilizes information about local density for generating alternative paths can yield remarkably better solution performance in this negotiation framework.

An Algorithm with Improved Complexity for Pebble Motion/Multi-Agent Path Finding on Trees

The pebble motion on trees (PMT) problem consists in finding a feasible sequence of moves that repositions a set of pebbles to assigned target vertices. This problem has been widely studied because, in many cases, the more general Multi-Agent path finding (MAPF) problem on graphs can be reduced to PMT. We propose a simple and easy to implement procedure, which finds solutions of length O(|P|nc + n2), where n is the number of nodes, P is the set of pebbles, and c the maximum length of corridors in the tree. This complexity result is more detailed than the current best known result O(n3), which is equal to our result in the worst case, but does not capture the dependency on c and |P|.

Combining Optimal Path Search With Task-Dependent Learning in a Neural Network.

Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms, where, usually, costs are predefined for all edges. Conventional planning methods can, thus, normally not be used when wanting to change costs in an adaptive way following the requirements of some task. Here, we show that one can define a neural network representation of path-finding problems by transforming cost values into synaptic weights, which allows for online weight adaptation using network learning mechanisms. When starting with an initial activity value of one, activity propagation in this network will lead to solutions, which are identical to those found by the Bellman-Ford (BF) algorithm. The neural network has the same algorithmic complexity as BF, and, in addition, we can show that network learning mechanisms (such as Hebbian learning) can adapt the weights in the network augmenting the resulting paths according to some task at hand. We demonstrate this by learning to navigate in an environment with obstacles as well as by learning to follow certain sequences of path nodes. Hence, the here-presented novel algorithm may open up a different regime of applications where path augmentation (by learning) is directly coupled with path finding in a natural way.

A supervised parallel optimisation framework for metaheuristic algorithms

A Supervised Parallel Optimisation (SPO) is presented. The proposed framework couples different optimisation algorithms to solve single-objective optimisation problems. The supervision balances the exploration and exploitation capabilities of the distinct optimisers included, providing a general framework to solve problems with diverse characteristics. In this work, five optimisation algorithms are included in the ensemble: Particle Swarm Optimisation (PSO), Genetic Algorithm (GA), Covariance Matrix Adaption-Evolution Strategy (CMA-ES), Differential Evolution (DE), and Modified Cuckoo Search (MCS). A geometric path-finding problem with numerous local minima is used to demonstrate the advantage of SPO. The effectiveness of the approach is compared with that of stand-alone incidences of the integrated optimisation strategies and with state-of-the-art algorithms. In addition, a benchmark test suit composed of engineering applications is utilised to validate the general applicability of SPO with respect to a variety of problems. The good solutions generated by SPO are shown to be generally reproducible, while isolated algorithms, at best, render good solutions only occasionally.

Non-Crossing Anonymous MAPF for Tethered Robots

This paper deals with the anonymous multi-agent path finding (MAPF) problem for a team of tethered robots. The goal is to find a set of non-crossing paths such that the makespan is minimal. A difficulty comes from the fact that a safety distance must be maintained between two robots when they pass through the same subpath, to avoid collisions and cable entanglements. Hence, robots must be synchronized and waiting times must be added when computing the makespan. We show that bounds can be efficiently computed by solving linear assignment problems. We introduce a variable neighborhood search method to improve upper bounds, and a Constraint Programming model to compute optimal solutions. We experimentally evaluate our approach on three different kinds of instances.

Left Ventricle Contouring in Cardiac Images in the Internet of Medical Things via Deep Reinforcement Learning

Assessment of the left ventricle segmentation in cardiac magnetic resonance imaging (MRI) is of crucial importance for cardiac disease diagnosis. However, conventional manual segmentation is a tedious task that requires excessive human effort, which makes automated segmentation highly desirable in practice to facilitate the process of clinical diagnosis. The internet of medical things (IoMT) and artificial intelligence (AI) for efficient medical data collection and analysis have been deemed effective approaches to remote and automatic diagnosis. In this paper, we propose a novel reinforcement-learning-based framework for left ventricle contouring, which mimics how a cardiologist outlines the left ventricle in a cardiac image. Since such a contour drawing process is simply moving a paintbrush along a specific trajectory, it is thus analogized to a path finding problem. Following the algorithm of proximal policy optimization (PPO), we train a policy network, which makes a stochastic decision on the agents movement according to its local observation such that the generated trajectory matches the true contour of the left ventricle as much as possible. Moreover, we design a deep learning model with a customized loss function to generate the agents landing spot (or coordinate of its initial position on a cardiac image). We further propose an alternative approach for generating the landing spot based on interventricular septum detection, which is more efficient since no extra effort in data preprocessing and model training are involved. The experiment results show that the coordinates of the generated landing spots with both of the two approaches are sufficiently close to the true contour and the proposed reinforcement-learning-based approach outperforms the existing U-net model and its improved version, even with limited training set.