hierarchical allocation optimization

To address the low computational efficiency of solving mixed-integer bilevel linear programs (MIBLPs), this paper proposes a novel unified modeling approach based on *improving directions*: a single subproblem simultaneously verifies bilevel feasibility and generates strong valid inequalities. Theoretically, we characterize the role of improving directions in encoding the follower’s optimality conditions, establish an optimality-based relaxation hierarchy, and extend the theory of continuous cutting-plane closures to the mixed-integer bilevel setting. Algorithmically, we integrate improving-direction analysis into a branch-and-cut framework, implementing it atop the open-source solver MibS. Computational experiments demonstrate that our method substantially enhances inequality strength and overall solution performance across standard benchmark instances.

This paper studies the student-school assignment problem under capacity constraints and group-level fairness requirements, jointly optimizing individual utilities (e.g., preference rankings), school enrollment caps, and inter-group fairness—such as across ethnicity or geography—formulated either via concave objective functions or explicit group-wise constraints, and supporting arbitrary covering constraints to capture multi-criteria and ordinal optimization needs. We propose, for the first time, a unified algorithmic framework that integrates convex programming modeling with systematic rounding techniques, yielding tunable randomized or deterministic algorithms. These run in polynomial time and provide controlled trade-offs among utility loss, capacity violations, and fairness deviations. Theoretically, our approach achieves provable approximation guarantees and naturally generalizes to covering constraints and ranking-aware settings. It exhibits strong scalability and practical deployability.

This work presents the first systematic evaluation of large language models’ ability to directly generate solutions to optimization problems that are both constraint-satisfying and near-optimal, without solver assistance. To this end, the authors introduce ConstraintBench, a benchmark spanning ten operations research domains, which maps natural language problem descriptions to structured solution outputs. Feasibility and suboptimality are rigorously assessed using Gurobi-computed ground truths and a deterministic verification mechanism. Experiments reveal that the best current model achieves a 65.0% constraint satisfaction rate, with feasible solutions reaching 89–96% of Gurobi’s optimal objective values; however, fewer than 30.5% of solutions are simultaneously feasible and near-optimal (within 0.1% optimality gap). The study also releases a complete evaluation infrastructure, addressing a critical gap in systematic assessment for this emerging capability.

This work addresses the challenge of automatically translating complex business requirements into optimization models for multi-warehouse inventory allocation in e-commerce. To this end, the authors propose ORLA, a novel framework that, for the first time, integrates solver feedback into the generative loop of large language models to automatically construct, validate, and select mixed-integer programming formulations from natural language or semi-structured inputs. ORLA supports dynamic constraints, infeasibility recovery, and modular extensibility, while incorporating modeling paradigms such as deviation minimization, soft bandwidth limits, and knapsack-style formulations. Evaluated on 29 real-world production batches from JD.com, ORLA improves allocation accuracy by 4.5 percentage points overall, significantly outperforming existing approaches.

This study addresses the allocation of multiple heterogeneous resource types in hierarchical organizations, where certain resources can be transformed into one another. The problem is formulated as a market equilibrium model incorporating structural constraints inherent to the hierarchy. To solve it efficiently, the authors propose a novel two-stage approximation algorithm: first solving a tractable instance that respects the hierarchical structure, then iteratively refining the solution to handle general cases. This work introduces, for the first time, a two-stage approximation framework to hierarchical resource allocation with conversion capabilities, establishing both the guaranteed existence of feasible equilibria and computational efficiency. Experiments on real-world Google TPU/GPU allocation datasets demonstrate the algorithm’s effectiveness and rapid convergence.

This work addresses the lack of systematic methodologies in model optimization, which often relies on heuristic choices and struggles to accommodate diverse deployment constraints. It formalizes model compression and acceleration as a constraint-aware multi-objective engineering decision problem, establishing a unified and actionable framework grounded in five key dimensions: data availability, latency, memory footprint, accuracy tolerance, and retraining budget. By integrating techniques such as quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference optimization, the study proposes tailored optimization pipelines for four representative industrial scenarios, delivering a reproducible and quantifiable guide for technology selection.

This paper addresses the two-dimensional hierarchical rectangular packing problem, where the container size is unspecified and items may be either basic rectangles or nested sub-blocks—whose dimensions are determined by lower-level packing optimizations—arising in applications such as VLSI floorplanning, facility layout, and logistics. To overcome the low accuracy and poor scalability of conventional bottom-up approaches, we propose a multi-level logic-based Benders decomposition method that dynamically refines sub-block dimensional constraints without requiring manual enumeration of aspect-ratio candidates. We introduce the first tight integration of recursive structural modeling with Benders decomposition to enable end-to-end joint optimization. On synthetic instances with up to seven hierarchy levels and 80 items per level, our method significantly improves solution quality and scalability over monolithic MILP formulations and bottom-up baselines, while ensuring stable convergence within practical time limits.

This work addresses the high sensitivity of constraint programming solver performance to hyperparameter configurations and the prohibitive cost of manual tuning. The authors propose a resource-aware, two-phase auto-tuning framework that, within a limited time budget, first explores promising configurations and then solves the target problem using the best identified configuration. Innovatively integrating Bayesian optimization with Hamming distance-based search within a unified framework, the approach is implemented using CPMpy. Experimental evaluation on 114 combinatorial optimization instances demonstrates that the method outperforms the default configurations on 25.4% and 38.6% of instances for the ACE and Choco solvers, respectively, significantly surpassing either search strategy in isolation.

Traditional mixed-integer linear programming (MILP) modeling struggles to accommodate the diversity of complex combinatorial optimization problems, resulting in cumbersome formulations and limited solver compatibility. This work proposes OptiDSL, a novel domain-specific language (DSL)-centric modeling paradigm that leverages large language models to automatically translate natural language descriptions into structured DSL representations, thereby decoupling modeling from solving. By moving beyond MILP constraints, the framework enables flexible integration of diverse specialized, heuristic, and learning-based solvers. Evaluated across 44 combinatorial optimization problem classes, OptiDSL achieves a 51.66% improvement in modeling accuracy and reduces modeling time by 91.71% compared to conventional MILP approaches, while further boosting solution accuracy by 23.09% over existing benchmarks.