Neural Pathways to Program Success: Hopfield Networks for PERT Analysis

Project and task scheduling under uncertainty remains a fundamental challenge in program and project management, where accurate estimation of task durations and dependencies is critical for delivering complex, multi project systems. The Program Evaluation and Review Technique provides a probabilistic framework to model task variability and critical paths. In this paper, the author presents a novel formulation of PERT scheduling as an energy minimization problem within a Hopfield neural network architecture. By mapping task start times and precedence constraints into a neural computation framework, the networks inherent optimization dynamics is exploited to approximate globally consistent schedules. The author addresses key theoretical issues related to energy function differentiability, constraint encoding, and convergence, and extends the Hopfield model for structured precedence graphs. Numerical simulations on synthetic project networks comprising up to 1000 tasks demonstrate the viability of this approach, achieving near optimal makespans with minimal constraint violations. The findings suggest that neural optimization models offer a promising direction for scalable and adaptive project tasks scheduling under uncertainty in areas such as the agentic AI workflows, microservice based applications that the modern AI systems are being built upon.

A Time-dependent Risk-aware distributed Multi-Agent Path Finder based on A*

Multi-Agent Path-Finding (MAPF) focuses on the collaborative planning of paths for multiple agents within shared spaces, aiming for collision-free navigation. Conventional planning methods often overlook the presence of other agents, which can result in conflicts. In response, this article introduces the A$^*_+$T algorithm, a distributed approach that improves coordination among agents by anticipating their positions based on their movement speeds. The algorithm also considers dynamic obstacles, assessing potential collisions with respect to observed speeds and trajectories, thereby facilitating collision-free path planning in environments populated by other agents and moving objects. It incorporates a risk layer surrounding both dynamic and static entities, enhancing its utility in real-world applications. Each agent functions autonomously while being mindful of the paths chosen by others, effectively addressing the complexities inherent in multi-agent situations. The performance of A$^*_+$T has been rigorously tested in the Gazebo simulation environment and benchmarked against established approaches such as CBS, ECBS, and SIPP. Furthermore, the algorithm has shown competence in single-agent experiments, with results demonstrating its effectiveness in managing dynamic obstacles and affirming its practical relevance across various scenarios.

Collaborative Multi-Agent Reinforcement Learning for Automated Feature Transformation with Graph-Driven Path Optimization

Feature transformation methods aim to find an optimal mathematical feature-feature crossing process that generates high-value features and improves the performance of downstream machine learning tasks. Existing frameworks, though designed to mitigate manual costs, often treat feature transformations as isolated operations, ignoring dynamic dependencies between transformation steps. To address the limitations, we propose TCTO, a collaborative multi-agent reinforcement learning framework that automates feature engineering through graph-driven path optimization. The framework's core innovation lies in an evolving interaction graph that models features as nodes and transformations as edges. Through graph pruning and backtracking, it dynamically eliminates low-impact edges, reduces redundant operations, and enhances exploration stability. This graph also provides full traceability to empower TCTO to reuse high-utility subgraphs from historical transformations. To demonstrate the efficacy and adaptability of our approach, we conduct comprehensive experiments and case studies, which show superior performance across a range of datasets.

Anytime Single-Step MAPF Planning with Anytime PIBT

PIBT is a popular Multi-Agent Path Finding (MAPF) method at the core of many state-of-the-art MAPF methods including LaCAM, CS-PIBT, and WPPL. The main utility of PIBT is that it is a very fast and effective single-step MAPF solver and can return a collision-free single-step solution for hundreds of agents in less than a millisecond. However, the main drawback of PIBT is that it is extremely greedy in respect to its priorities and thus leads to poor solution quality. Additionally, PIBT cannot use all the planning time that might be available to it and returns the first solution it finds. We thus develop Anytime PIBT, which quickly finds a one-step solution identically to PIBT but then continuously improves the solution in an anytime manner. We prove that Anytime PIBT converges to the optimal solution given sufficient time. We experimentally validate that Anytime PIBT can rapidly improve single-step solution quality within milliseconds and even find the optimal single-step action. However, we interestingly find that improving the single-step solution quality does not have a significant effect on full-horizon solution costs.

Real-Time LaCAM

The vast majority of Multi-Agent Path Finding (MAPF) methods with completeness guarantees require planning full horizon paths. However, planning full horizon paths can take too long and be impractical in real-world applications. Instead, real-time planning and execution, which only allows the planner a finite amount of time before executing and replanning, is more practical for real world multi-agent systems. Several methods utilize real-time planning schemes but none are provably complete, which leads to livelock or deadlock. Our main contribution is to show the first Real-Time MAPF method with provable completeness guarantees. We do this by leveraging LaCAM (Okumura 2023) in an incremental fashion. Our results show how we can iteratively plan for congested environments with a cutoff time of milliseconds while still maintaining the same success rate as full horizon LaCAM. We also show how it can be used with a single-step learned MAPF policy. The proposed Real-Time LaCAM also provides us with a general mechanism for using iterative constraints for completeness in future real-time MAPF algorithms.

CTS-CBS: A New Approach for Multi-Agent Collaborative Task Sequencing and Path Finding

This paper addresses a generalization problem of Multi-Agent Pathfinding (MAPF), called Collaborative Task Sequencing - Multi-Agent Pathfinding (CTS-MAPF), where agents must plan collision-free paths and visit a series of intermediate task locations in a specific order before reaching their final destinations. To address this problem, we propose a new approach, Collaborative Task Sequencing - Conflict-Based Search (CTS-CBS), which conducts a two-level search. In the high level, it generates a search forest, where each tree corresponds to a joint task sequence derived from the jTSP solution. In the low level, CTS-CBS performs constrained single-agent path planning to generate paths for each agent while adhering to high-level constraints. We also provide heoretical guarantees of its completeness and optimality (or sub-optimality with a bounded parameter). To evaluate the performance of CTS-CBS, we create two datasets, CTS-MAPF and MG-MAPF, and conduct comprehensive experiments. The results show that CTS-CBS adaptations for MG-MAPF outperform baseline algorithms in terms of success rate (up to 20 times larger) and runtime (up to 100 times faster), with less than a 10% sacrifice in solution quality. Furthermore, CTS-CBS offers flexibility by allowing users to adjust the sub-optimality bound omega to balance between solution quality and efficiency. Finally, practical robot tests demonstrate the algorithm's applicability in real-world scenarios.

RAILGUN: A Unified Convolutional Policy for Multi-Agent Path Finding Across Different Environments and Tasks

Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community's continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.

Accelerating Focal Search in Multi-Agent Path Finding with Tighter Lower Bounds

Multi-Agent Path Finding (MAPF) involves finding collision-free paths for multiple agents while minimizing a cost function--an NP-hard problem. Bounded suboptimal methods like Enhanced Conflict-Based Search (ECBS) and Explicit Estimation CBS (EECBS) balance solution quality with computational efficiency using focal search mechanisms. While effective, traditional focal search faces a limitation: the lower bound (LB) value determining which nodes enter the FOCAL list often increases slowly in early search stages, resulting in a constrained search space that delays finding valid solutions. In this paper, we propose a novel bounded suboptimal algorithm, double-ECBS (DECBS), to address this issue by first determining the maximum LB value and then employing a best-first search guided by this LB to find a collision-free path. Experimental results demonstrate that DECBS outperforms ECBS in most test cases and is compatible with existing optimization techniques. DECBS can reduce nearly 30% high-level CT nodes and 50% low-level focal search nodes. When agent density is moderate to high, DECBS achieves a 23.5% average runtime improvement over ECBS with identical suboptimality bounds and optimizations.

Multi-agent coordination for data gathering with periodic requests and deliveries

In this demo work we develop a method to plan and coordinate a multi-agent team to gather information on demand. The data is periodically requested by a static Operation Center (OC) from changeable goals locations. The mission of the team is to reach these locations, taking measurements and delivering the data to the OC. Due to the limited communication range as well as signal attenuation because of the obstacles, the agents must travel to the OC, to upload the data. The agents can play two roles: ones as workers gathering data, the others as collectors traveling invariant paths for collecting the data of the workers to re-transmit it to the OC. The refreshing time of the delivered information depends on the number of available agents as well as of the scenario. The proposed algorithm finds out the best balance between the number of collectors-workers and the partition of the scenario into working areas in the planning phase, which provides the minimum refreshing time and will be the one executed by the agents.

Multi-Agent Path Planning in Complex Environments using Gaussian Belief Propagation with Global Path Finding

Multi-agent path planning is a critical challenge in robotics, requiring agents to navigate complex environments while avoiding collisions and optimizing travel efficiency. This work addresses the limitations of existing approaches by combining Gaussian belief propagation with path integration and introducing a novel tracking factor to ensure strict adherence to global paths. The proposed method is tested with two different global path-planning approaches: rapidly exploring random trees and a structured planner, which leverages predefined lane structures to improve coordination. A simulation environment was developed to validate the proposed method across diverse scenarios, each posing unique challenges in navigation and communication. Simulation results demonstrate that the tracking factor reduces path deviation by 28% in single-agent and 16% in multi-agent scenarios, highlighting its effectiveness in improving multi-agent coordination, especially when combined with structured global planning.