Patient-To-Room Assignment Problem

Airport landside traffic centers connect terminal arrivals with taxis, ride-hailing vehicles, private cars, buses, metro services, parking facilities, and terminal-area roadways. Peak arrivals can create coupled congestion across passenger queues, vehicle queues, pickup berths, storage areas, and access roads. This study proposes a QUBO-inspired computational framework for bottleneck diagnosis and dynamic dispatch in this setting. Shanghai Pudong International Airport and Hangzhou Xiaoshan International Airport serve as case airports. A five-minute state model links passenger arrivals, vehicle supply, pickup berth service, vehicle storage, and road capacity. Bottleneck diagnosis uses service intensity, road demand saturation, bottleneck frequency, queue severity, shadow-price leverage, and a composite congestion severity index. Two dispatch schemes are tested under consistent demand inputs: finite-action model predictive control and quadratic-unconstrained-binary-optimization-inspired simulated annealing. In the strong-peak baseline scenario, the QUBO-inspired method reduces the final passenger queue from 3445 to 2477 passengers at Shanghai Pudong and from 2053 to 1482 passengers at Hangzhou Xiaoshan. Case results indicate different dominant bottlenecks. Shanghai Pudong is more affected by road saturation, whereas Hangzhou Xiaoshan is more affected by pickup berth service. Robustness tests under demand, supply, service, road-capacity, modal-share, and random-noise perturbations show retained queue-reduction benefits under the tested uncertainty levels.

Existing evaluations often reduce agent failures to system-level outcomes, obscuring where the fault originated and which intervention would improve the agent system. This creates a repair-assignment problem: the same visible failure may call for model post-training, harness engineering, environment redesign, or benchmark repair depending on its source. Because agent behavior emerges from interactions among models, harnesses, users, tools, memory, and environments, outcome-level labels are often insufficient for improvement. Most failure taxonomies do little to resolve this problem because they are benchmark-specific and lack a shared structure. We introduce an interaction-centric taxonomy that localizes failures to the interactions in which they originate and identifies the responsible component. It organizes 41 failure modes by assigning each to an edge between two components and a fault side indicating where the repair belongs. This makes the taxonomy actionable: model-side failures identify targets for post-training, harness-side failures point to scaffolding and tool-integration fixes, and environment or grader failures reveal evaluation conditions requiring redesign. The schema applies across agent architectures, from coding assistants to long-horizon personal assistants and multi-agent systems. We ground the taxonomy in worked examples from public benchmarks, model system cards, published reports, and logged agent trajectories, and evaluate its reproducibility using independent reasoning agents as judges. Across four frontier models, the strongest judge reaches Cohen's $κ=0.76$ against human category labels, suggesting that the categories capture shared structure rather than annotator-specific preferences.

Multi-object tracking in dense crowds requires solving a bipartite assignment problem between detections and trajectories at every video frame. The classical Hungarian algorithm solves this in $O(N^3)$ time, which becomes a bottleneck for large scenes with hundreds of people. We propose an \emph{incremental} assignment algorithm that exploits the block-sparse structure of crowd tracking cost matrices --- dense within each crowd cluster, near-zero between clusters. We compute the exact same optimal $N \times N$ assignment as the Hungarian algorithm, but via an incremental strategy: we add one person at a time, exploiting the fact that after step $n-1$ the dual potentials are \emph{exactly optimal} for the $(n-1)\times(n-1)$ subproblem --- a strictly stronger condition than the intermediate feasibility maintained by the Hungarian algorithm during its $N$ outer iterations. Each new step therefore requires only a single augmenting path search from a certified optimal starting point. This avoids repeated full-matrix scans while guaranteeing an identical globally optimal result. A diagonal-reordering invariant keeps the data structure compact and cache-friendly. On realistic crowd benchmarks with $N \in [200, 5000]$ people organised into dense clusters, our algorithm achieves \textbf{3.7--6.5$\times$ speedup} over the Hungarian baseline while producing provably optimal matchings identical to those of Hungarian. The speedup grows with $N$ and remains stable beyond $N=3000$, making the method especially attractive for large-scale crowd scenes such as stadium exits and mass public events.

Autonomous driving requires understanding the road as a graph of drivable lanes and their connectivity, beyond the ego lane alone, to follow routes through intersections and reason about cross- and merging-traffic. Recent perception models infer such lane topology, i.e., lane segments together with their inter-lane connectivity (LCLC), from onboard sensors over a 360-degree BEV view. Due to neural perception's imperfections, their outputs retain structural instabilities such as missed detections, lost or incorrect LCLC, over-detection, and label flicker. This paper presents WASABI, a real-time post-processing pipeline that stabilizes lane topology outputs both within and across frames by treating lane segments and their LCLC connectivity as joint tracking targets, under onboard real-time constraints (10 Hz / 20 ms / up to 200 input lanes). The pipeline integrates segment tracking with connectivity, noise-robust topology-aware refinement, and a resource-constrained real-time design. On internal validation data (16 sequences), WASABI improves LCLC detection F1 from 0.834 to 0.948 (+0.114, +13.6%) and reduces centerline lateral error from 2.50 m to 0.95 m, while reducing detection false-positives by 24.6%. Temporal-stability metrics on the same data show LCLC toggle rate reduced by 63.3% and boundary-label flicker rate by 30.2%, confirming across-frame stabilization beyond per-frame accuracy.

The Vehicle Routing Problem (VRP) and its variants represent some of the most practically consequential optimization challenges in modern logistics and urban mobility. In this study, we address a dynamic, online variant combining elements of the VRP and the Orienteering Problem (OP), in which a fleet of vehicles must maximise cumulative reward collected within a fixed time horizon while continuously replanning as new tasks arrive. We propose and evaluate a reward-density heuristic for dynamic multi-vehicle assignment, referred to as the Efficiency heuristic. We evaluate this formulation across two application domains: autonomous drone task allocation and urban taxi dispatch, across multiple fleet sizes and task scales. The proposed method is compared with four classical construction heuristics and three metaheuristic algorithms (Adaptive Large Neighbourhood Search, Genetic Algorithm, and Simulated Annealing), all evaluated under identical conditions. Across all tested configurations, the Efficiency heuristic matches the solution quality of the best metaheuristic algorithms while requiring two to three orders of magnitude less planning time, establishing Pareto dominance over all competing methods on the reward-versus-compute frontier. These findings suggest a practical design principle for real-time allocation and dispatch systems: in dynamic, time-constrained routing environments, carefully designed greedy heuristics can match the output of sophisticated search procedures at a fraction of the computational cost, making them preferable for online deployment.

The berth allocation and quay crane assignment problem (BACAP) is a representative port-terminal scheduling problem in maritime transportation and freight logistics, where vessel arrivals, berth positions, service durations, and quay?crane availability are tightly coupled. Under uncertainties such as arrival deviations, handling-time fluctuations, and resource disruptions, schedules optimized under nominal assumptions may become fragile during execution, motivating the study of robust metaheuristic optimization for BACAP in port-terminal operations. Although population-based metaheuristics have been widely used for BACAP and related port-scheduling problems, existing studies remain fragmented in their uncertainty repre?sentations, robustness criteria, search mechanisms, and empir?ical evaluation protocols. To the best of our knowledge, this paper provides the first focused review dedicated to robust population-based metaheuristics for BACAP under uncertainty. We first summarize uncertainty sources and information repre?sentations in BACAP, and then organize existing methods from a mechanism-oriented perspective, covering solution representation and decoding, robust evaluation and selection, robustness-guided search dynamics, and feasibility preservation and recovery. We further present a benchmark suite for uncertain BACAP to support controlled empirical comparison and report illustrative baseline results by combining representative metaheuristics with different robustness strategies. Finally, we identify open chal?lenges related to benchmark extension, robustness-aware search design, time-adaptive robustness, and non-stationary uncertainty.

This paper presents a scalable framework for multi-robot task allocation in complex environments where estimating task execution costs is computationally expensive. While combinatorial auction-based approaches offer reliable solutions, the exponential complexity of bundle generation typically renders them intractable for real-time reactive applications, particularly when accurate path planning is required for cost validation. We address this through a distributed, two-stage multi-fidelity bundle generation approach. Agents utilize a local search tree guided by a low-fidelity heuristic (such as euclidean distance) to rapidly explore the bundle space, applying high-fidelity path planning only to the most promising candidates in a best-first manner. These refined bids are then submitted to a central coordinator that solves a set packing problem to ensure global feasibility and maximize the overall utility. Simulation results in multiple environments demonstrate that the framework is able to improve the performance of reactive auction-based task allocation. Overall, the presented framework is shown to enable reactive task allocation with dynamic bundle sizes in multiple settings without exposing the agents' state and internal cost estimation models.

Multi-agent task planning in cluttered, dynamic environments requires assigning tasks to agents while simultaneously determining safe, time-efficient trajectories through the environment. When tasks are dynamic, such as rendezvous objectives, allocation decisions depend not only on which agent is best suited for a task, but also on when and where that task can be reached. This paper presents a solution to this problem, which combines Graphs of Convex Sets (GCS) for trajectory optimization with the Consensus-Based Bundle Algorithm (CBBA) for distributed task allocation. In our approach, GCS finds optimal trajectories through dynamic environments using a time-extended (3D+time) configuration space. At the same time, CBBA coordinates task assignments across agents, enabling informed decision-making in a moving environment. We then connect allocation and planning to allow the agents to avoid collisions in the 3D+time configuration space and provide accurate time estimates for task completion. We demonstrate the effectiveness of our approach in simulated cluttered environments with static and dynamic tasks.

As multi-drone fleets scale, zone assignment rapidly evolves into an intractable NP-hard combinatorial problem that overwhelms classical exhaustive search. While quantum optimization promises to shatter these classical bottlenecks, mapping complex spatial tasks from human intent to restricted quantum hardware remains a severe challenge. To bridge this gap, we present an end-to-end framework integrating a fine-tuned Large Language Model (LLM) front-end with a highly scalable, domain-specific quantum-classical backend. The front-end utilizes Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) to translate free-form natural language instructions into structurally robust Quadratic Unconstrained Binary Optimization (QUBO) constraints without false negatives. To overcome the strict qubit limits of near-term quantum devices, our framework features a novel constraint-preserving graph partitioner and a compressed separator-based dynamic programming (DP) merge. By structurally encoding constraints via W-state initialization and XY-mixers in Conditional Value-at-Risk Quantum Approximate Optimization (CVaR-QAOA), the pipeline stays highly compact. Empirical results demonstrate that this architecture circumvents classical scaling walls, recovering the global optimum on 100% of idealized oracle cases and 96.3% under real QAOA sampling, enabling natural-language-guided task allocation at previously intractable scales.

In distributed optimization, multiple parties collaborate to find an optimal solution to a problem. Privacy-preserving distributed optimization uses techniques, such as secure multi-party computation (MPC), to protect the private inputs of each party. In time-critical settings, the runtime overhead introduced by privacy-preserving computations may prevent the optimization from finishing within the deadline. This paper presents an approach for privacy-preserving distributed optimization in time-critical settings that combines evolutionary algorithms for solution search and MPC for the evaluation of solutions. The approach reduces the impact of privacy-preserving computations on runtime and allows to return solution within the deadline. Obfuscation of evaluation results provides additional protection for private inputs from an honest-but-curious platform provider, but introduces a potential trade-off between protection and solution quality. This trade-off is investigated in experiments using a genetic algorithm for both the single-objective assignment problem and the traveling salesperson problem, as well as NSGA-II for the multi-objective assignment problem.

Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.

Multi-robot systems are integral to modern logistics, but their capabilities are often limited to tasks executable by individual agents. This paper addresses a critical gap in existing frameworks like Multi-Agent Path Finding (MAPF) and Task Allocation and Path Finding (TAPF), which lack true cooperation for transporting large items that require multiple agents. To this end, we formalise the Cooperative Transportation Task Allocation and Path Finding (CT-TAPF) problem, which integrates team formation, task assignment, and collision-free pathfinding. We present an optimal solver, Cooperative Transportation Task Conflict-Based Search (CT-TCBS), which features a novel Incremental Expansion strategy to tackle the combinatorial explosion inherent in team formation. Recognising the computational cost of optimality, we also develop a family of sub-optimal solvers that employ a global, task-centric perspective, selecting the next task to assign based on a global difficulty metric (Best Task or Worst Task). Our comprehensive empirical evaluation demonstrates three key findings: (1) the incremental expansion strategy significantly outperforms the naive combinatorial approach by successfully pruning the dominant task-allocation search space; (2) we identify a task-conflict expansion dilemma, where sophisticated conflict resolvers effective for large-agent pathfinding subproblems can be detrimental in the integrated CT-TAPF setting; and (3) our proposed sub-optimal solvers establish a new, more efficient frontier on the solution quality-runtime spectrum compared to "nn-" agent-centric baselines. This work provides a foundational framework and a set of effective algorithms for a new, practical class of cooperative multi-agent problems.

Token-based transformer world models have shown strong performance in visual reinforcement learning, but often suffer from temporal inconsistency in long-horizon rollouts, including object duplication, disappearance, and transmutation. A key reason is that most existing approaches treat next-frame prediction purely as a token generation problem, without considering the persistence of tokens across time. We introduce Identifiable Token Correspondence (ITC), a decoding step for token-based transformer world models that formulates next-frame prediction as a structured assignment problem with latent token correspondence variables: each next-frame token is explained either by copying a token from the previous frame or by generating a new one. ITC leaves the transformer architecture and training procedure unchanged and can be added on top of existing backbones. Our experiments show state-of-the-art performance on 4 challenging benchmarks. The proposed method achieves a return of 72.5% and a score of 35.6% on the Craftax-classic benchmark, significantly surpassing the previous best of 67.4% and 27.9%. We release our source code on https://github.com/snu-mllab/Identifiable-Token-Correspondence.

A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a logical to physical qubit mapping. Typically in quantum compilers this step is either implemented as a random or a heuristic based assignment that aims to minimize additional (SWAP) gate overhead in the quantum circuit. In this paper, we present an alternative approach to solving the qubit mapping problem. Specifically, we formulate the qubit mapping problem with a combinatorial optimization (CO) objective. We then present a method to find a solution to the CO problem by training a reinforcement learning (RL) policy. We also propose a local search based post-processing algorithm to further reduce the overhead. Our results show a dramatic improvement over conventional techniques in reducing the number of SWAPs. On different real world datasets like MQTBench and Queko circuits, our trained policy achieves a \textbf{65-85%} reduction in SWAP overhead when compared to existing quantum compilers.

Qubit routing is a fundamental problem in quantum compilation, known to be NP-hard. Its dynamic nature makes local routing decisions propagate and compound over time, making global efficient solutions challenging. Existing heuristic methods rely on local rules with limited lookahead, while recent learning-based approaches often treat routing as a generic sequential decision problem without fully exploiting its underlying structure. In this paper, we introduce QAP-Router, framing qubit routing based on a dynamic Quadratic Assignment Problem (QAP) formulation. By modeling logical interactions, or quantum gates, as flow matrices and hardware topology as a distance matrix, our approach captures the interaction-distance coupling in a unified objective, which defines the reward in the reinforcement learning environment. To further exploit this structure, the policy network employs a solution-aware Transformer backbone that encodes the interaction between the flow matrix and the distance matrix into the attention mechanism. We also integrate a lookahead mechanism that blends naturally into the QAP framework, preventing myopic decisions. Extensive experiments on 1,831 real-world quantum circuits from the MQTBench, AgentQ and QUEKO datasets show that our method substantially reduces the CNOT gate count of routed circuits by 15.7%, 30.4% and 12.1%, respectively, relative to existing industry compilers.

The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness. We propose a learning-augmented framework that accelerates exact solvers by predicting dual variables to warm-start the search, backed by a fallback mechanism to preserve worst-case guarantees. Central to our approach is RowDualNet, a lightweight, row-independent architecture that avoids the $\mathcal{O}(N^{2})$ memory bottleneck of graph models, enabling scalable neural warm-starting up to $N=16{,}384$. Feasibility is guaranteed by construction via the Min-Trick mechanism, completely eliminating the need for costly iterative projections. Empirically, our method drastically reduces the search effort of the Jonker-Volgenant (LAPJV) algorithm, yielding robust zero-shot generalization with strict optimality and end-to-end speedups of over 2x on complex synthetic data, 1.25x on real-world tracking, and 1.5x on transportation networks.

Multi-robot systems in automated warehouses must manage continuous streams of pickup-and-delivery tasks while ensuring efficiency and safety. Prior work on Multi-Agent Pickup-and-Delivery (MAPD) has largely focused on the one-to-one variant, where each task has a fixed pickup and delivery location. In contrast, real warehouses often present many-to-many MAPD scenarios, where items, tracked by stock keeping unit (SKU) identifiers, can be retrieved from or stored at multiple locations, resulting in an NP-hard four-dimensional assignment problem. To solve the many-to-many MAPD problem, we contribute our algorithm: Many-to-Many Multi-Agent Pickup and Delivery (M2M). We experiment with two variants of our algorithm: one that minimizes estimated task durations (M2M), and one which incorporates SKU distribution into the objective function (M2M-wSKU). Simulation results over 8-hour warehouse operations show that our method consistently matches or outperforms prior state of the art, with M2M completing up to 22,000 more tasks on average across different environments and warehouse inventory densities.

Coordinating multi-agent systems over spatially distributed areas requires solving a complex hierarchical problem: first distributing areas among agents (allocation) and subsequently determining the optimal visitation order (routing). Existing methods typically decouple these stages ignoring inter-stage dependencies or rely on decentralized heuristics that lack global context. In this work, we propose a centralized, fully end-to-end auto-regressive framework that jointly generates allocation decisions and routing sequences. The core contribution of our approach is a multi-stage decoding mechanism that unifies high-level allocation and low-level routing in a single autoregressive pass while maintaining a centralized global state. This enables the model to implicitly balance workload distribution with routing efficiency, avoiding local optima common in decentralized methods. Extensive experiments demonstrate that our method significantly outperforms diverse baselines, achieving up to a 20% improvement in solution quality over industrial solvers such as Google OR-Tools, IBM CPLEX, and LKH-3, while reducing computation time from hours to seconds.

The quadratic assignment problem (QAP) is a fundamental NP-hard task that poses significant challenges for both traditional heuristics and modern learning-based solvers. Existing QAP solvers still struggle to achieve consistently competitive performance across structurally diverse real-world instances. To bridge this performance gap, we propose PLMA, an innovative permutation learning framework. PLMA features an efficient warm-started MCMC finetuning procedure to enhance deployment-time performance, leveraging short Markov chains to anchor the adaptation to the promising regions previously explored. For rapid exploration via MCMC over the permutation space, we design an additive energy-based model (EBM) that enables an $O(1)$-time 2-swap Metropolis-Hastings sampling step. Moreover, the neural network used to parameterize the EBM incorporates a scalable and flexible cross-graph attention mechanism to model interactions between facilities and locations in the QAP. Extensive experiments demonstrate that PLMA consistently outperforms state-of-the-art baselines across various benchmarks. In particular, PLMA achieves a near-zero average optimality gap on QAPLIB, exhibits remarkably superior robustness on the notoriously difficult Taixxeyy instances, and also serves as an effective QAP solver in bandwidth minimization.

Motivated by the problem of assigning mediators to cases in the Kenyan judicial system, we study an online resource allocation problem where incoming tasks (cases) must be immediately assigned to available, capacity-constrained resources (mediators). The resources differ in their quality, which may need to be learned. In addition, resources can only be assigned to a subset of tasks that overlaps to varying degrees with the subset of tasks other resources can be assigned to. The objective is to maximize task completion while satisfying soft capacity constraints across all the resources. The scale of the real-world problem poses substantial challenges, since there are over 2000 mediators, and a multitude of combinations of geographic locations (87) and case types (12) that each mediator is qualified to work on. Together, these features-unknown quality of new resources (newly onboarded mediators), soft capacity constraints (due to the mandate to assign cases without delay), and high-dimensional state space-make existing scheduling and resource allocation algorithms either inapplicable or inefficient. We formalize the problem in a tractable manner, using a quadratic program formulation for assignment and a multi-agent bandit style framework for learning. We demonstrate the key properties and advantages of our new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on some stylized instances of the mediator allocation problem. We then turn to considering its application to real-world data on cases and mediators from the Kenyan Judiciary. SMaRT outperforms baselines and allows for controlling the tradeoff between the strictness of the capacity constraints and overall case resolution rates, both in situations where mediator quality is known beforehand and when the problem is bandit-like in that learning is part of the problem definition.

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products. We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing. Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions. The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles. We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances. The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining. Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping. Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.

Developing algorithms for real-life problems that perform well in practice depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult, and such data typically cannot be published, which limits reproducibility by other researchers. This is especially true for patient-related problems because of data privacy policies such as the patient-to-room assignment problem. Therefore, artificially generated instances are commonly used. To improve the generation of realistic instances, we develop a configurable instance generator for the patient-to-room assignment problem and other patient-related problems, featuring an easy-to-use graphical user interface. The design of the generator is based on an extensive empirical analysis of real hospital data, which identifies relevant ward-specific patterns such as patients' age and length-of-stay distributions. Moreover, as randomly generated instances are often infeasible, we address this issue in two ways. We implement a dynamic programming approach in the generator to optionally enforce feasibility and extend existing results from the literature to derive new combinatorial insights into patient-to-room feasibility.

The substantial training cost of diffusion models hinders their deployment. Immiscible Diffusion recently showed that reducing diffusion trajectory mixing in the noise space via linear assignment accelerates training by simplifying denoising. To extend immiscible diffusion beyond the inefficient linear assignment under high batch sizes and high dimensions, we refine this concept to a broader miscibility reduction at any layer and by any implementation. Specifically, we empirically demonstrate the bijective nature of the denoising process with respect to immiscible diffusion, ensuring its preservation of generative diversity. Moreover, we provide thorough analysis and show step-by-step how immiscibility eases denoising and improves efficiency. Extending beyond linear assignment, we propose a family of implementations including K-nearest neighbor (KNN) noise selection and image scaling to reduce miscibility, achieving up to >4x faster training across diverse models and tasks including unconditional/conditional generation, image editing, and robotics planning. Furthermore, our analysis of immiscibility offers a novel perspective on how optimal transport (OT) enhances diffusion training. By identifying trajectory miscibility as a fundamental bottleneck, we believe this work establishes a potentially new direction for future research into high-efficiency diffusion training. The code is available at https://github.com/yhli123/Immiscible-Diffusion.

The design and organization of complex robotic systems traditionally requires laborious trial-and-error processes to ensure both hardware and software components are correctly connected with the resources necessary for computation. This paper presents a novel generalization of the quadratic assignment and routing problem, introducing formalisms for selecting components and interconnections to synthesize a complete system capable of providing some user-defined functionality. By introducing mission context, functional requirements, and modularity directly into the assignment problem, we derive a solution where components are automatically selected and then organized into an optimal hardware and software interconnection structure, all while respecting restrictions on component viability and required functionality. The ability to generate complete functional systems directly from individual components reduces manual design effort by allowing for a guided exploration of the design space. Additionally, our formulation increases resiliency by quantifying resource margins and enabling adaptation of system structure in response to changing environments, hardware or software failure. The proposed formulation is cast as an integer linear program which is provably $\mathcal{NP}$-hard. Two case studies are developed and analyzed to highlight the expressiveness and complexity of problems that can be addressed by this approach: the first explores the iterative development of a ground-based search-and-rescue robot in a variety of mission contexts, while the second explores the large-scale, complex design of a humanoid disaster robot for the DARPA Robotics Challenge. Numerical simulations quantify real world performance and demonstrate tractable time complexity for the scale of problems encountered in many modern robotic systems.