Progress in understanding expert performance is limited by the scarcity of quantitative data on long-term knowledge acquisition and deployment. Here we use the Rubik's Cube as a cognitive model system existing at the intersection of puzzle solving, skill learning, expert knowledge, cultural transmission, and group theory. By studying competitive cube communities, we find evidence for universality in the collective learning of the Rubik's Cube in both sighted and blindfolded conditions: expert performance follows exponential progress curves whose parameters reflect the delayed acquisition of algorithms that shorten solution paths. Blindfold solves form a distinct problem class from sighted solves and are constrained not only by expert knowledge but also by the skill improvements required to overcome short-term memory bottlenecks, a constraint shared with blindfold chess. Cognitive artifacts such as the Rubik's Cube help solvers navigate an otherwise enormous mathematical state space. In doing so, they sustain collective intelligence by integrating communal knowledge stores with individual expertise and skill, illustrating how expertise can, in practice, continue to deepen over the course of a single lifetime.

Abstract-- In this work, we introduce MO-SeGMan, a Multi-Objective Sequential and Guided Manipulation planner for highly constrained rearrangement problems. MO-SeGMan generates object placement sequences that minimize both re-planning per object and robot travel distance while preserving critical dependency structures with a lazy evaluation method. T o address highly cluttered, non-monotone scenarios, we propose a Selective Guided Forward Search (SGFS) that efficiently relocates only critical obstacles and to feasible relocation points. Furthermore, we adopt a refinement method for adaptive subgoal selection to eliminate unnecessary pick-and-place actions, thereby improving overall solution quality. Extensive evaluations on nine benchmark rearrangement tasks demonstrate that MO-SeGMan generates feasible motion plans in all cases, consistently achieving faster solution times and superior solution quality compared to the baselines. These results highlight the robustness and scalability of the proposed framework for complex rearrangement planning problems. Supplementary videos and code are available at: https: //sites.google.com/view/mo-segman/. Rearrangement planning involves generating a feasible motion plan for a robot to move all goal objects to their designated locations.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

Robots operating in changing environments either predict obstacle changes and/or plan quickly enough to react to them. Predictive approaches require a strong prior about the position and motion of obstacles. Reactive approaches require no assumptions about their environment but must replan quickly and find high-quality paths to navigate effectively. Reactive approaches often reuse information between queries to reduce planning cost. These techniques are conceptually sound but updating dense planning graphs when information changes can be computationally prohibitive. It can also require significant effort to detect the changes in some applications. This paper revisits the long-held assumption that reactive replanning requires updating existing plans. It shows that the incremental planning problem can alternatively be solved more efficiently as a series of independent problems using fast almost-surely asymptotically optimal (ASAO) planning algorithms. These ASAO algorithms quickly find an initial solution and converge towards an optimal solution which allows them to find consistent global plans in the presence of changing obstacles without requiring explicit plan reuse. This is demonstrated with simulated experiments where Effort Informed Trees (EIT*) finds shorter median solution paths than the tested reactive planning algorithms and is further validated using Asymptotically Optimal RRT-Connect (AORRTC) on a real-world planning problem on a robot arm.

Abstract-- Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time and at large scales has remained out of reach due to computational requirements. Recently, GPU-based acceleration has shown promising results, but prior methods achieve limited performance due to CPU-GPU data transfer overhead and complex logic that prevents full hardware utilization. T o this end, we present SPaSM (Sampling Particle optimization for Sequential Manipulation), a fully GPU-parallelized framework that compiles constraint evaluation, sampling, and gradient-based optimization into optimized CUDA kernels for end-to-end trajectory optimization without CPU coordination. The method consists of a two-stage particle optimization strategy: first solving placement constraints through massively parallel sampling, then lifting solutions to full trajectory optimization in joint space. Unlike hierarchical approaches, SPaSM jointly optimizes object placements and robot trajectories to handle scenarios where motion feasibility constrains placement options. Experimental evaluation on challenging benchmarks demonstrates solution times in the realm of milliseconds with a 100% success rate; a 4000 speedup compared to existing approaches. Code and examples are available at commalab.org/papers/spasm.

This paper considers how to fuse Machine Learning (ML) and optimization to solve large-scale Supply Chain Planning (SCP) optimization problems. These problems can be formulated as MIP models which feature both integer (non-binary) and continuous variables, as well as flow balance and capacity constraints. This raises fundamental challenges for existing integrations of ML and optimization that have focused on binary MIPs and graph problems. To address these, the paper proposes PROPEL, a new framework that combines optimization with both supervised and Deep Reinforcement Learning (DRL) to reduce the size of search space significantly. PROPEL uses supervised learning, not to predict the values of all integer variables, but to identify the variables that are fixed to zero in the optimal solution, leveraging the structure of SCP applications. PROPEL includes a DRL component that selects which fixed-at-zero variables must be relaxed to improve solution quality when the supervised learning step does not produce a solution with the desired optimality tolerance. PROPEL has been applied to industrial supply chain planning optimizations with millions of variables. The computational results show dramatic improvements in solution times and quality, including a 60% reduction in primal integral and an 88% primal gap reduction, and improvement factors of up to 13.57 and 15.92, respectively.

This work is original in its use of deep reinforcement learning and graph neural networks to learn novel search control heuristics for SAT solving. While the techniques used are not novel themselves, the application domain is. The authors do a good job of surveying related work in this area and situating their contributions in this landscape. The paper is well-written and I found it very easy to follow the details of the proposed approach and the authors' results. Technically, the work presented is solid, though I have a few comments/suggestions here.

In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of mixed integer programming (MIP) problems. Distinct substantially from existing learning-to-optimize methods, our proposal seeks to train an autoencoder (AE) for binary variables in an unsupervised learning fashion, using data of optimal solutions to historical instances for a parametric family of MIPs. By a deliberate design of AE architecture and exploitation of its statistical implication, we present a simple and straightforward strategy to construct a class of cutting plane constraints from the decoder parameters of an offline-trained AE. These constraints reliably enclose the optimal binary solutions of new problem instances thanks to the representation strength of the AE. More importantly, their integration into the primal MIP problem leads to a tightened MIP with the reduced feasible region, which can be resolved at decision time using off-the-shelf solvers with much higher efficiency. Our method is applied to a benchmark batch process scheduling problem formulated as a mixed integer linear programming (MILP) problem. Comprehensive results demonstrate that our approach significantly reduces the computational cost of off-the-shelf MILP solvers while retaining a high solution quality. The codes of this work are open-sourced at https://github.com/qushiyuan/AE4BV.

Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for efficiently solving mixed-integer MPC motion planning problems using a hybrid zonotope representation of the obstacle-free space. The MPC optimization problem is formulated as a multi-stage mixed-integer quadratic program (MIQP) using a hybrid zonotope representation of the non-convex constraints. Risk-aware planning is supported by assigning costs to different regions of the obstacle-free space within the MPC cost function. A multi-stage MIQP solver is presented that exploits the structure of the hybrid zonotope constraints. For some hybrid zonotope representations, it is shown that the convex relaxation is tight, i.e., equal to the convex hull. In conjunction with logical constraints derived from the AV motion planning context, this property is leveraged to generate tight quadratic program (QP) sub-problems within a branch-and-bound mixed-integer solver. The hybrid zonotope structure is further leveraged to reduce the number of matrix factorizations that need to be computed within the QP sub-problems. Simulation studies are presented for obstacle-avoidance and risk-aware motion planning problems using polytopic maps and occupancy grids. In most cases, the proposed solver finds the optimal solution an order of magnitude faster than a state-of-the-art commercial solver. Processor-in-the-loop studies demonstrate the utility of the solver for real-time implementations on embedded hardware.

Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have exactly two children and where datapoints are assessed on a set of discrete features and (ii) leaf vertices at which datapoints are given a prediction, and can be obtained by solving a biobjective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. Branching vertices are linear combinations of training features and therefore can be thought of as hyperplanes. In this paper, we propose two cut-based mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees (leaf vertices assign discrete classes). Our models leverage on-the-fly identification of minimal infeasible subsystems (MISs) from which we derive cutting planes that hold the form of packing constraints. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available datasets to show our models' ability to scale, strength against traditional branch and bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub.