Synthesizing mixed-integer linear programming models from natural language descriptions

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice

Transmission of hydrogen detonation across a curtain of dilute inert particles

Transmission of hydrogen detonation wave (DW) in an inert particle curtain is simulated using the Eulerian-Lagrangian approach with gas-particle two-way coupling. A detailed chemical mechanism is used for hydrogen detonative combustion and parametric studies are conducted based on a two-dimensional computational domain. A detonation map of propagation and extinction corresponding to various particle sizes, concentrations, and curtain thicknesses is plotted. It is shown that the critical curtain thickness decreases considerably when the particle concentration is less than the critical value. The effects of curtain thickness on the trajectories of peak pressure, shock front speed, and heat release rate are examined. Three propagation modes of the DW in particle curtain are found: detonation transmission, partial extinction and detonation reinitiation, and detonation extinction. The chemical explosive mode analysis confirms that a detonation re-initiation event is caused by a re-initiation point with high pressure and explosive propensity, resulting from transverse shock focusing. The influence of particle dimeter and concentration, and curtain thickness on the DW are also examined with peak pressure trajectories, shock speed, and interphase exchange rates of energy and momentum. Furthermore, the evolutions of curtain morphologies are analyzed by the particle velocity, volume fraction, Stokes drag and Archimedes force. This analysis confirms the importance of the drag force in influencing the change of curtain morphologies. Different curtain evolution regimes are found: quasi-stationary regime, shrinkage regime, constant-thickness regime, and expansion regime. Finally, the influences of the curtain thickness on the characteristic time of curtain evolutions are studied

Modelling particle collisions in moderately dense curtain impacted by an incident shock wave

The interactions between an incident shock and moderately dense particle curtain are simulated with the Eulerian-Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model, and then validated against two benchmark experiments. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. It is found that smaller particle size and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Different expansion stages of the curtain fronts are also studied in detail. Attention is paid to the particle collision effects on the curtain evolution behaviours. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to faster motion of downstream particles than the upstream ones and hence no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerate large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks due to the local particle accumulations, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and therefore must be modelled

DiactTOD: Learning Generalizable Latent Dialogue Acts for Controllable Task-Oriented Dialogue Systems

Dialogue act annotations are important to improve response generation quality in task-oriented dialogue systems. However, it can be challenging to use dialogue acts to control response generation in a generalizable way because different datasets and tasks may have incompatible annotations. While alternative methods that utilize latent action spaces or reinforcement learning do not require explicit annotations, they may lack interpretability or face difficulties defining task-specific rewards. In this work, we present a novel end-to-end latent dialogue act model (DiactTOD) that represents dialogue acts in a latent space. DiactTOD, when pre-trained on a large corpus, is able to predict and control dialogue acts to generate controllable responses using these latent representations in a zero-shot fashion. Our approach demonstrates state-of-the-art performance across a wide range of experimental settings on the MultiWOZ dataset, including zero-shot, few-shot, and full data fine-tuning with both end-to-end and policy optimization configurations.Comment: SIGDial 202

A case study of the Lunger phenomenon based on multiple algorithms

In this study, we conduct a thorough and meticulous examination of the Runge phenomenon. Initially, we engage in an extensive review of relevant literature, which aids in delineating the genesis and essence of the Runge phenomenon, along with an exploration of both conventional and contemporary algorithmic solutions. Subsequently, the paper delves into a diverse array of resolution methodologies, encompassing classical numerical approaches, regularization techniques, mock-Chebyshev interpolation, the TISI (Three-Interval Interpolation Strategy), external pseudo-constraint interpolation, and interpolation strategies predicated upon Singular Value Decomposition (SVD). For each method, we not only introduce but also innovate a novel algorithm to effectively address the phenomenon. This paper executes detailed numerical computations for each method, employing visualization techniques to vividly illustrate the efficacy of various strategies in mitigating the Runge phenomenon. Our findings reveal that although traditional methods exhibit commendable performance in certain instances, novel approaches such as mock-Chebyshev interpolation and regularization-centric methods demonstrate marked superiority in specific contexts. Moreover, the paper provides a critical analysis of these methodologies, specifically highlighting the constraints and potential avenues for enhancement in SVD decomposition-based interpolation strategies. In conclusion, we propose future research trajectories and underscore the imperative of further exploration into interpolation strategies, with an emphasis on their practical application validation. This article serves not only as a comprehensive resource on the Runge phenomenon for researchers but also offers pragmatic guidance for resolving real-world interpolation challenges.Comment: 13 Figures 9 Pages. After first submission, there was a revision of the authorship order, which was the result of joint discussion

Solving dynamic multi-objective problems with a new prediction-based optimization algorithm

Funding Information: This work is supported by the National Natural Science Foundation of China under Grants 62006103 and 61872168, in part by the Jiangsu national science research of high education under Grand 20KJB110021. The authors express sincerely appreciation to the anonymous reviewers for their helpful opinions.Peer reviewedPublisher PD

Numerical Study on Effects of the Embedded Monopile Foundation on Local Wave-Induced Porous Seabed Response

Effects of the embedded monopile foundation on the local distributions of pore water pressure, soil stresses, and liquefaction are investigated in this study using a three-dimensional integrated numerical model. The model is based on a Reynolds-Averaged Navier-Stokes wave module and a fully dynamic poroelastic seabed module and has been validated with the analytical solution and experimental data. Results show that, compared to the situation without an embedded foundation, the embedded monopile foundation increases and decreases the maximum pore water pressure in the seabed around and below the foundation, respectively. The embedded monopile foundation also significantly modifies the distributions of the maximum effective soil stress around the foundation and causes a local concentration of soil stress below the two lower corners of foundation. A parametric study reveals that the effects of embedded monopile foundation on pore water pressure increase as the degrees of saturation and soil permeability decrease. The embedded monopile foundation tends to decrease the liquefaction depth around the structure, and this effect is relatively more obvious for greater degrees of saturation, greater soil permeabilities, and smaller wave heights