Integer Linear Programming

Also known as ILP

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Aug 13, 2026cs.CL

From Atomic Evidence to Logical Composition: Structured Compositional Reasoning over Compound Answer Options

Large language models often fail when answer options require combining atomic judgments under explicit logical operators, even when they judge the individual atoms correctly. We study compound options connected by AND, OR, and NEITHER/NOR, introducing a framework that decomposes each option into atomic answers and scores contrastive hypotheses about each one, so the model never sees a compound option. An operator-constrained integer linear program then composes the calibrated scores into a single prediction. We evaluate on LOGICAL-COMMONSENSEQA and introduce LOGICAL-SATA, a reading-comprehension benchmark derived from SATA-Bench. Our framework improves Macro-F1 from 48.3 to 77.0 on the human-validated LOGICAL-COMMONSENSEQA split and from 47.0 to 75.6 on LOGICAL-SATA, with the largest gains on NEITHER/NOR.

Obed Junias, Maria Leonor Pacheco

University of Colorado Boulder

Compositional Reasoning Multiple-Choice Question Answering Question Answering Structured Reasoning LLM Reasoning Integer Linear Programming

Jul 30, 2026cs.AI

The Edge-based Contiguous p-median Problem with Connections to Logistics Districting

This paper introduces the edge-based contiguous p-median (ECpM) problem to partition the roads in a network into a given number of compact and contiguous territories. Two binary programming models are introduced, both of which incorporate a network distance. The first model requires an exponential number of cut set-based constraints to model contiguity; it is paired with a separation scheme that usually generates only a small number of these constraints, namely, a branch-and-cut (B&C) algorithm. The second model utilizes a polynomial number of shortest-path constraints to model contiguity and can be solved with off-the-shelf solvers. The respective solution approaches are tested on road networks with over 2,700 nodes and close to 3,400 edges, yielding models with over 9.6 million binary variables. Solving the model based on shortest path contiguity (SPC) constraints via standard branch and bound attains speedups in computational time of up to 17x relative to the cut set-based B&C implementation. In addition, the SPC constraints are demonstrated to be supervalid inequalities of the edge-based p-median (EpM) model (i.e., for which contiguity is not explicitly required), meaning that they may cut off integer-feasible solutions and some, but not all, of the optimal solutions of this simpler problem. Finally, the paper explores structural insights and connections between ECpM and the edge-based districting (EBD) problem, which enforces an additional work balance criterion. An existing model that utilizes cut set-based contiguity constraints was unable to find a feasible solution within 12 hours for any of the tested instances, while an SPC-based EBD model was able to solve most of these to optimality.

Zeyad Kassem, Adolfo R. Escobedo

School of Computing and Augmented Intelligence, Arizona State University, Tempe, Arizona, 85281 · Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina, 27606

Combinatorial Optimization Integer Linear Programming

Jul 28, 2026cs.AI

Finding Optimal Cost-Bounded Plan Reductions: Refined Model

In some real applications a plan may later become unfeasible due to newly imposed budget constraints, yet, at the same time, using only the original actions of the plan and their order is mandatory. In this paper, we study the problem of extracting, from a precomputed plan, a valid subplan that maximizes utility while respecting a cost bound. Each goal is given a utility value and the plan is reduced by removing actions that support low-utility goals, while preserving both executability and the original action order. We show the decision variant is NP-complete and propose two exact methods to solve it: one via oversubscription planning (OSP) and another via Integer Linear Programming (ILP). This paper extends our previous work published at ICAPS 2026 (Del Toro, Fuentetaja, and García-Olaya 2026b). While the core framework remains as introduced there, we further introduce a refined ILP formulation that significantly decreases the model size and improves computational efficiency.

Martha Del Toro, Raquel Fuentetaja, Angel García-Olaya

Computer Science and Engineering Department, Universidad Carlos III de Madrid, Spain

Combinatorial Optimization Integer Linear Programming

Jul 24, 2026math.OC

Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs

A data-driven inverse optimization problem (DDIOP) is the problem of estimating the objective-function parameters (weights) that explain observed optimal-solution data, and it arises in many applications, including integer linear programming (ILP). It is known that, by applying gradient-based optimization methods to the suboptimality loss, the inverse optimization of ILPs can be solved exactly within finitely many oracle iterations, and that the required number of iterations is bounded as

T=O(1/γ(\ell_{\mathrm{sub}})^2)

in terms of a problem-dependent geometric constant

γ(\ell_{\mathrm{sub}})

. However, no means of bounding

γ(\ell_{\mathrm{sub}})

from below as a function of the problem size has been available, and hence the number of iterations could not be given as an explicit function of the problem size. We therefore give, when the forward problem is an integer linear program (ILP), the number of iterations sufficient for projected subgradient descent applied to the suboptimality loss to achieve exact consistency with the observed data, as a fully explicit function of the number of samples, the dimension of the features, the ranges of the features, and the structure of the constraint coefficient matrix, up to polynomial factors in the basic constants (the diameter of the weight set, the step-size parameter, and the Lipschitz constant of the suboptimality loss).

Akira Kitaoka

Learning to Optimize Integer Linear Programming

Jul 23, 2026cs.AI

SPORD: A Simulation-Propose-then-OR-Dispose Approach for Supply Chain Planning

For years, supply chain planning at e-commerce firms has operated as a collection of isolated projects. Each planning task from static network planning to dynamic warehouse assortment planning requires analysts to spend weeks building models from scratch, calibrating and persuading executives to act on outputs they cannot verify. Three barriers drive this: bespoke models proliferate because standardization is difficult (operational fragmentation); once unified, the combinatorial scale of millions of SKUs, thousands of nodes, and intricate routing logic exceeds what solvers can handle within a tight window (computational intractability); and a mathematically optimal solution still fails to be implemented if the executives do not trust it (implementation hurdle). To bridge this gap, we propose and implement the Simulation-Propose-then-OR-Dispose method, deployed as JD.com's NetSim platform. The central insight is decoupling: simulation proposes by generating and evaluating the full set of operationally valid candidate paths-absorbing all idiosyncratic business logic, while an integer program disposes by selecting the globally optimal subset. Computationally, matrix-vectorized CPU/GPU accelerated simulation achieves a 10-100 times speedup over serial methods, and a list scheduling algorithm reduces coupled-order processing from hours to minutes. Operationally, we establish a closed loop via an intelligent diagnosis engine. Since 2025, NetSim has optimized end to-end services for over 20,000 suppliers, the cross-regional fulfillment rate dropped from 6.1% to 4.9%, and the average monthly carbon reduction is approximately 5,745 tCO2e. SPORD moves simulation from monitoring to active planning. The transparent outputs turn skeptical executives into engaged collaborators, and the modular architecture ensures that the next planning requires just configuration, not reconstruction.

Jiayin He, Yutong Pan, Sen Yang +5

Department of Industrial Engineering, Tsinghua University, Beijing 100084, China · JD.com, Beijing, China, 101111 · College of Engineering, UC Berkeley, Berkeley, CA 94720, USA +1

Combinatorial Optimization Model-Based Planning Supply Chain Management Integer Linear Programming

Jul 13, 2026cs.AI

LP Mining with LP2Graph: A Use Case for Railway Rescheduling

Like many optimization-driven domains, railway rescheduling relies on Mixed-Integer Linear Programming (MILP), yet the field's modeling knowledge is scattered across hundreds of papers in incompatible notations, and narrative surveys organize it subjectively: they classify models by vocabulary rather than by structure, and reproduce neither. We present LP Mining with LP2Graph, a method that mines the structure of published LP and MILP formulations into a reproducible dataset and an induced taxonomy. Its core, LP2Graph, represents each formulation admitted by its canonical grammar as a typed variable--equation graph derived from a single canonical model; once a source is extracted into that model, everything downstream is deterministic. Each source is parsed into this model, homologized, and clustered bottom-up (over variables, then constraints and the objective, then whole-model structure) and, separately, by application domain and solution approach; the resulting groups are labeled by a rule-seeded, self-updating classifier. We validate the representation rather than assume it: per-cluster representatives are regenerated as independent LaTeX and re-solved across CBC, HiGHS and Gurobi against the optimum reported in the source paper. The outcome is an objective, repeatable taxonomy of variables, constraints and model types: the principled foundation on which our raiLPminer line of automated railway-rescheduling model development builds.

Jörn Maurischat, Nikola Bešinović, Michael Färber

aTU Dresden, Chair of Railway Operations,"Friedrich List" Faculty of Transport and Traffic Sciences, Dresden, 01069, Germany · bTU Dresden, ScaDS.AI Dresden/Leipzig, Chair of Scalable Software Architectures for Data Analytics, Dresden, 01069, Germany

Mixed-Integer Linear Programming Integer Linear Programming

Jul 10, 2026cs.MA

Mosaic: Runtime-Efficient Multi-Agent Embodied Planning

LLM-based multi-agent embodied planning remains impractical due to prohibitively high execution latency. We identify failed actions as the dominant bottleneck, stemming from two core challenges: inaccurate state tracking under partial observability and inefficient coordination that produces redundant or conflicting actions. We introduce Mosaic, a runtime-efficient multi-agent planning framework that addresses both challenges. Mosaic maintains accurate yet lightweight state tracking through agent-centric semantic memory that stores objects in relative coordinates, enabling geometric transformations and coordination. It ensures efficient coordination through Integer Linear Programming that allocates actions at every planning step, enforcing physical feasibility and inter-agent coordination constraints. Across AI2-THOR and search-and-rescue benchmarks, Mosaic achieves 27-32% faster execution, 30-33% fewer LLM calls, 25-31% fewer steps, and 4-10% points higher success rates. These results demonstrate that efficient memory and constraint-guided coordination are critical for scalable, low-latency multi-agent planning.

Kunjal Panchal, Saayan Mitra, Sunav Choudhary +3

College of Information and Computer Sciences, University of Massachusetts, Amherst · Adobe, San Jose

Multi-Agent Coordination Large Language Model-Based Robot Planning Multi-Agent Planning Memory-Augmented Agents Integer Linear Programming

Jul 7, 2026cs.LG

GraphBU: MILP Instance Generation with Graph-Native Block Units

Mixed-integer linear programming (MILP) instances used for solver development are hard to obtain when models come from private or application-specific pipelines. A generator must keep the structure that solvers and learned policies rely on. Existing general generators usually choose their generation unit from a formulation template, summary statistics, local graph edits, or blocks found after recombination. These units do not explicitly record how a local part of the MILP is coupled to the rest of the instance. We propose GraphBU, a graph-native generator whose basic unit is a local subproblem plus its interface. The method promotes coupling nodes into master constraints or boundary variables and uses the resulting block units for compatibility-checked replacement. The analysis focuses on the properties needed by this construction: promotion separates interfaces, replacement can preserve feasibility under an interface-slack condition, and the graph construction is invariant to row-column permutations. On MILP instances generation, this unit keeps graph statistics close to the source family, preserves feasibility on most datasets, and improves downstream Predict-and-Search training. Genrated by GraphBU, The average graph-statistical similarity was approximately 0.934, the average feasibility was approximately 96.7%, and the average increase in the main index of downstream PS was approximately 8.0%.

Xiaolei Guo, Chenyu Zhou, Jianghao Lin +1

Shanghai Jiao Tong University

Mixed-Integer Linear Programming Synthetic Benchmark Generation Integer Linear Programming

Jul 6, 2026cs.ET

Optimizing ML Workload Partitioning between CPUs and CIM Accelerators for Heterogeneous Computing

Computing-in-Memory (CIM) accelerators execute Matrix-Vector Multiplications (MVMs) in memory, making them a compelling solution for Machine Learning (ML) workloads. However, existing ML workload partitioning approaches for CIM accelerators do not fully account for Resistive Random Access Memory (RRAM) constraints such as limited memory, high write latency, and limited endurance. They also neglect parallelism, low-level architectural effects, or the Central Processing Unit (CPU) as a complementary compute resource. To address these limitations, we propose an Integer Linear Programming (ILP)-based workload partitioning framework for heterogeneous CPU-CIM systems. It minimizes end-to-end inference latency under RRAM constraints, captures parallelism, and combines empirical profiling with analytical models. Using our framework, heterogeneous CPU-CIM execution achieves speedups of up to 30.9x over CPU-only execution on an edge CPU and 7.3x over a high-performance CPU. A Design Space Exploration (DSE) yields further design insights for future CIM accelerators.

Joel Klein, Rebecca Pelke, Roberto Laudani +2

Institute for Communication Technologies and Embedded Systems, RWTH Aachen University, Germany

Compute-in-Memory Heterogeneous Computing Integer Linear Programming

Jun 28, 2026math.OC

Solver-Verified Formulation Generation and Selection for Multi-Warehouse Inventory Allocation Using Large Language Models

Balance-oriented multi-warehouse inventory allocation is a recurring decision problem in large-scale e-commerce supply chains, in which a fixed replenishment quantity is distributed across warehouses to balance post-allocation inventory coverage while accounting for demand forecasts and heterogeneous allocation constraints. In practice, allocation requirements are often scenario-dependent and expressed in semi-structured or natural-language form rather than as ready-to-solve operations research (OR) formulations. We propose an OR-guided Large Language Model (LLM) for Allocation (ORLA) that uses solver feedback to generate, verify, and select OR formulations. ORLA integrates automatic "Problem-Model-Code (PMC)" generation, learning-based formulation selection, and feasibility restoration. We develop three complementary mixed-integer programming formulation families based on deviation minimization, soft band compliance, and knapsack-inspired allocation, together with solver-ready mixed-integer linear programming reformulations, modular constraint extensions, and a penalty-based relaxation mechanism for infeasible cases. The LLM component generates candidate formulations and executable solver code from textual or semi-structured specifications, while the solver provides verification signals for executability, feasibility, and solution quality. To address instance heterogeneity, ORLA estimates the expected quality of candidate formulations, selects promising candidates, and combines their outputs through score-aware aggregation. Experimental results on 29 production evaluation batches from JD.com show that the best single OR formulation improves allocation accuracy by 3.4 percentage points over the incumbent approach, while the full ORLA framework achieves a 4.5 percentage-point overall improvement and improves allocation accuracy in 26 of the 29 evaluation batches.

Jintao Xu, Yingzheng Ma, Jiong Dong +4

Supply Chain Tech Team Y, JD.com

Inventory Control Mixed-Integer Linear Programming Large Language Model-Guided Optimization Supply Chain Management Natural Language to Optimization Modeling Integer Linear Programming

May 28, 2026cs.LG

Solving Integer Linear Programming with Parallel Tempering

Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have recently shown their effectiveness, they suffer from poor generalization to out-of-distribution instances and inherent dependence on external solvers. In this work, we propose a solver-free, sampling-based optimization framework for ILP that directly explores discrete feasible regions without training or external solvers. Exploiting the linear structure of ILP, we employ a Locally-Balanced Proposal to construct a transition kernel, thereby avoiding the gradient approximation. To overcome the highly multimodal nature of ILP energy landscapes, we integrate Parallel Tempering. In addition to standard temperature tempering, we introduce penalty tempering, which modulates constraint barriers while preserving the objective landscape over feasible solutions. Empirically, our method consistently outperforms SCIP across all four benchmarks, matches or exceeds Gurobi on two of four tasks within a 200-second budget, and is substantially more robust to distribution shift than learning-based methods. Furthermore, on MIPLIB 2017 instances, our framework remains competitive with classical solvers without any problem-specific tuning.

Kyuil Sim, Sanghyeok Choi, Jinkyoo Park

1KAIST · University of Edinburgh

Markov Chain Monte Carlo Mixed-Integer Linear Programming Combinatorial Optimization Parallel Tempering Integer Linear Programming

May 21, 2026cs.CL

Tokenization with Split Trees

We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.

Craig W. Schmidt, Michael Krumdick, Adam Wiemerslage +4

Kensho Technologies · Ben-Gurion University · MIT Cambridge, MA

Token Efficiency Subword Tokenization Integer Linear Programming

May 11, 2026cs.AI

LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs

Efficient branching policies are essential for accelerating Mixed Integer Linear Programming (MILP) solvers. Their design has long relied on hand-crafted heuristics, and now machine learning has emerged as a promising paradigm to automate this process. However, existing learning-based methods are often hindered by their dependence on expensive expert demonstrations and the gap between training objectives and the solver's end-to-end performance. In this work, we propose LLM4Branch, a novel framework that leverages Large Language Models (LLMs) to automate the discovery of efficient branching policies. Specifically, the discovered policy is an executable program with a program skeleton generated by the LLM and a parameter vector, which is optimized via a zeroth-order method over a few instances with their end-to-end performance feedback. Extensive experiments on standard MILP benchmarks demonstrate that LLM4Branch establishes a new state-of-the-art among CPU-based methods and achieves performance competitive with advanced GPU-based models. Codes are available at https://github.com/hzn18/LLM4Branch.

Zhinan Hou, Xingchen Li, Yankai Zhang +2

Department of Automation, BNRist, Tsinghua University, Beijing, China.

Branch and Bound Mixed-Integer Linear Programming Large Language Model-Guided Optimization Learning to Optimize LLM-Based Program Synthesis Integer Linear Programming

Apr 30, 2026stat.ML

A Novel Computational Framework for Causal Inference: Tree-Based Discretization with ILP-Based Matching

Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction between correlation and causation. While recent advances in causal machine learning and matching algorithms have improved estimation accuracy, these methods often face trade-offs between interpretability and computational efficiency. This paper proposes a novel approach that combines a tree-based discretization technique, tailored for causal inference, with an integer linear programming-based matching algorithm. The discretization ensures approximately linear relationships for control datasets within strata, enabling effective matching, while the optimization framework optimizes for global balance. The resulting algorithm yields computational efficiency and less biased ATT estimates compared to state-of-the-art algorithms. Empirical evaluations demonstrate the proposed method's practical advantages over existing techniques in causal inference scenarios.

Tianyu Yang, Md. Noor-E-Alam

Department of Mechanical and Industrial Engineering Northeastern University, Boston, MA 02115, USA

Causal Effect Estimation Causal Inference Integer Linear Programming

Apr 24, 2026math.OC

Relaxation-Informed Training of Neural Network Surrogate Models

ReLU neural networks trained as surrogate models can be embedded exactly in mixed-integer linear programs (MILPs), enabling global optimization over the learned function. The tractability of the resulting MILP depends on structural properties of the network, i.e., the number of binary variables in associated formulations and the tightness of the continuous LP relaxation. These properties are determined during training, yet standard training objectives (prediction loss with classical weight regularization) offer no mechanism to directly control them. This work studies training regularizers that directly target downstream MILP tractability. Specifically, we propose simple bound-based regularizers that penalize the big-M constants of MILP formulations and/or the number of unstable neurons. Moreover, we introduce an LP relaxation gap regularizer that explicitly penalizes the per-sample gap of the continuous relaxation at training points. We derive its associated gradient and provide an implementation from LP dual variables without custom automatic differentiation tools. We show that combining the above regularizers can approximate the full total derivative of the LP gap with respect to the network parameters, capturing both direct and indirect sensitivities. Experiments on non-convex benchmark functions and a two-stage stochastic programming problem with quantile neural network surrogates demonstrate that the proposed regularizers can reduce MILP solve times by up to four orders of magnitude relative to an unregularized baseline, while maintaining competitive surrogate model accuracy.

Calvin Tsay

Department of Computing, Imperial College London, South Kensington, SW7 2AZ, United Kingdom.

Neural Surrogate Modeling Mixed-Integer Linear Programming Neural Network Optimization Constrained Optimization Integer Linear Programming

Jan 8, 2026cs.AI

A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention

Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness. Recent learning-based methods typically model MILP instances as variable-constraint bipartite graphs and use Graph Neural Networks (GNNs) for representation learning, yet their locality limits representation power. We propose an attention-driven neural backbone that adopts an element-centric view of variables and constraints, with dual attention performing parallel intra-type self-attention and inter-type cross-attention. Across three representative tasks at the instance, element, and solving-state levels, our model consistently outperforms conventional GNN-based architectures, highlighting attention-based, element-centric modeling as a powerful foundation for learning-enhanced combinatorial optimization.

Peixin Huang, Yaoxin Wu, Yining Ma +3

Shenzhen Research Institute, Shandong University, China

Graph Neural Networks Mixed-Integer Linear Programming Linear Programming Neural Combinatorial Optimization Integer Linear Programming

Oct 6, 2025math.OC

Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions

Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety of domains, including power systems and scheduling. However, to the best of our knowledge, existing data-driven inverse optimization methods primarily focus on learning objective functions under known constraints, and learning both objective functions and constraints from data for MILPs remains largely unexplored. In this paper, we propose a two-stage approach for a class of inverse optimization problems in which the objective is a linear combination of given feature functions and the constraints are parameterized by unknown functions and thresholds. Our method first learns the constraints and then, conditioned on the learned constraints, estimates the objective-function weights. On the theoretical side, we provide finite-sample guarantees for solving the proposed inverse optimization problem. To this end, we develop statistical learning tools for pseudo-metric spaces under sub-Gaussian assumptions and use them to derive a learning-theoretic framework for inverse optimization with both unknown objectives and constraints. On the experimental side, we demonstrate that our method successfully solves inverse optimization problems on scheduling instances formulated as ILPs with up to 100 decision variables.

Akira Kitaoka

Mixed-Integer Linear Programming Learning to Optimize Inverse Problems Integer Linear Programming

Jul 29, 2024cs.AI

OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce a Large Language Model (LLM)-based system designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. Our system can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve efficiency and correctness of its model and code based on these evaluations. OptiMUS is designed as a productivity tool for optimization practitioners who understand the problem domain and can describe it precisely, but seek to accelerate the modeling and implementation workflow. OptiMUS-0.3 utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS-0.3 outperforms direct-prompting baselines by over 43% on easy and 18% on hard instances. It remains competitive with fine-tuned specialist models on benchmark problems, and outperforms them on real-world case studies (28.6% vs. 0%) where fine-tuned models fail to generalize. Ablation studies show that modular architecture with error correction is central to these gains. A key finding is that system architecture is a stronger driver of performance than model capability. Structured decomposition with targeted error correction enables weaker models to match stronger models under naive prompting, and remains competitive with fine-tuned specialist models without retraining costs.

Ali AhmadiTeshnizi, Wenzhi Gao, Herman Brunborg +3

a School of Management Science and Engineering, Stanford University, Stanford, California 94305 · b Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305

Mixed-Integer Linear Programming Large Language Model-Guided Optimization LLM-Based Program Synthesis Linear Programming Natural Language to Optimization Modeling Integer Linear Programming

Aug 11, 2021cs.AI

Stable Marriage Problems with Ties and Incomplete Preferences: An Empirical Comparison of ASP, SAT, ILP, CP, and Local Search Methods

We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and Incomplete preferences (SMTI). We consider three optimization variants of SMTI, Max Cardinality, Sex-Equal and Egalitarian, and empirically compare the following methods to solve them: Answer Set Programming, Constraint Programming, Integer Linear Programming. For Max Cardinality, we compare these methods with Local Search methods as well. We also empirically compare Answer Set Programming with Propositional Satisfiability, for SMTI instances.

Selin Eyupoglu, Muge Fidan, Yavuz Gulesen +5

Computer Science, Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey · Economics, Faculty of Arts and Social Sciences, Sabanci University, Istanbul, Turkey

Answer Set Programming Constraint Satisfaction Constraint Programming Integer Linear Programming

Jun 14, 2017cs.RO

Context-Aware System Synthesis, Task Assignment, and Routing

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.

Jason Ziglar, Ryan Williams, Alfred Wicks

Combinatorial Optimization Robotics Hardware-Software Co-Design Integer Linear Programming