The Joint Routing-Assignment (JRA) optimization problem simultaneously determines the assignment of items to placeholders and a Hamiltonian cycle that visits each node pair exactly once, with the objective of minimizing total travel cost. Previous studies introduced an exact mixed-integer programming (MIP) solver, along with datasets and a Gurobi implementation, showing that while the exact approach guarantees optimality, it becomes computationally inefficient for large-scale instances. To overcome this limitation, heuristic methods based on merging algorithms and shaking procedures were proposed, achieving solutions within approximately 1% deviation from the optimum. This work presents a novel and more efficient approach that attains high-accuracy, near-optimal solutions for large-scale JRA problems. The proposed method introduces a Partial Path Reconstructon (PPR) solver that first identifies key item-placeholder pairs to form a reduced subproblem, which is solved efficiently to refine the global solution. Using this PJAR framework, the initial heuristic merging solutions can be further improved, reducing the deviation by half. Moreover, the solution can be iteratively polished with PPR based solver along the optimization path to yield highly accurate tours. Additionally, a global Large-α constraint is incorporated into the JRA model to further enhance solution optimality. Experimental evaluations on benchmark datasets with n = 300, 500, and 1000 demonstrate that the proposed method consistently delivers almost optimal solutions, achieving an average deviation of 0.00% from the ground truth while maintaining high computational efficiency. Beyond the JRA problem, the proposed framework and methodologies exhibit strong potential for broader applications. The Framework can be applied to TSP and related optimization problems.

Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic field topology, which is difficult to detect and characterize in three dimensions. We propose a scalable pipeline for topological data analysis and spatiotemporal graph representation of three-dimensional magnetic vector fields. We demonstrate our methods on simulations of the Earth's magnetosphere produced by Vlasiator, a supercomputer-scale Vlasov theory-based simulation for near-Earth space. The purpose of this work is to challenge the machine learning community to explore graph-based machine learning approaches to address a largely open scientific problem with wide-ranging potential impact.

The growing amount of data produced by simulations and observations of space physics processes encourages the use of methods rooted in Machine Learning for data analysis and physical discovery. We apply a clustering method based on Self-Organizing Maps (SOM) to fully kinetic simulations of plasmoid instability, with the aim of assessing its suitability as a reliable analysis tool for both simulated and observed data. We obtain clusters that map well, a posteriori, to our knowledge of the process: the clusters clearly identify the inflow region, the inner plasmoid region, the separatrices, and regions associated with plasmoid merging. SOM-specific analysis tools, such as feature maps and Unified Distance Matrix, provide one with valuable insights into both the physics at work and specific spatial regions of interest. The method appears as a promising option for the analysis of data, both from simulations and from observations, and could also potentially be used to trigger the switch to different simulation models or resolution in coupled codes for space simulations.