Many critical business and societal decisions in areas such as supply chain and healthcare involve numerous potential actions, complex constraints, and goals that can be modeled as objective functions. Mathematical optimization, a core area in Operations Research (OR), provides robust, mathematically grounded methodologies to address such decisions and has shown tremendous benefits in many applications. However, its application requires the creation of accurate and efficient optimization models, necessitating rare expertise and considerable time, creating a barrier to widespread adoption in decision-making. Thus, it is a long-standing goal to make these capabilities widely accessible. The advent of Large Language Models (LLMs) has made advanced Artificial Intelligence (AI) capabilities widely accessible through natural language. LLMs can accelerate expert work in creating formal models like computer programs, and emerging research indicates they can also speed up the development of optimization models by OR experts. We, therefore, propose integrating and advancing LLM and optimization modeling to empower organizational decision-makers to model and solve such complex problems without requiring deep expertise in optimization. In this work, we present our vision for democratizing optimization modeling for organizational decision-making by such a combination of LLMs and optimization modeling. We identify a set of fundamental requirements for the vision's implementation and describe the state of the art through a literature survey and some experimentation. We show that a) LLMs already provide substantial novel capabilities relevant to realizing this vision, but that b) major research challenges remain to be addressed. We also propose possible research directions to overcome these gaps. We would like this work to serve as a call to action to bring together the LLM and OR optimization modeling communities to pursue this vision, thereby enabling much more widespread improved decision-making and increasing by orders of magnitude the benefits AI and OR can bring to enterprises and society.

Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets and optimizes decisions corresponding to each of these subsets. In a general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights, which allows us to train our machine learning tool on a database of resolved branch-and-bound trees and to apply it as is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems as well as in cases when the K-value or the problem size differs from the training ones. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grants OCENW.GROOT.2019.015 and VI.Veni.191E.035]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0314 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0314 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Counterfactual explanations (CEs) play an important role in detecting bias and improving the explainability of data-driven classification models. A CE is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this work, we derive an iterative method to calculate robust CEs (i.e., CEs that remain valid even after the features are slightly perturbed). To this end, our method provides a whole region of CEs, allowing the user to choose a suitable recourse to obtain a desired outcome. We use algorithmic ideas from robust optimization and prove convergence results for the most common machine learning methods, including decision trees, tree ensembles, and neural networks. Our experiments show that our method can efficiently generate globally optimal robust CEs for a variety of common data sets and classification models. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.GROOT.2019.015, Optimization for and with Machine Learning (OPTIMAL)]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.0153 .

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. We propose Bayesian estimation of the regression coefficients, mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version that performs approximate Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.

We propose a new mixed integer linear programming (MILP) formulation of the sparse signal recovery problem in compressed sensing (CS). This formulation is obtained by introduction of an auxiliary binary vector, where ones locate the recovered nonzero indices. Joint optimization for finding this auxiliary vector together with the underlying sparse vector leads to the proposed MILP formulation. By addition of a few appropriate constraints, this problem can be solved by existing MILP solvers. In contrast to other methods, this formulation is not an approximation of the sparse optimization problem, but is its equivalent. Hence, its solution is exactly equal to the optimal solution of the original sparse recovery problem, once it is feasible. We demonstrate this by recovery simulations involving different sparse signal types. The proposed scheme improves recovery over the mainstream CS recovery methods especially when the underlying sparse signals have constant amplitude nonzero elements.

We propose a new generic framework for solving combinatorial optimization problems that can be modeled as a set covering problem. The proposed algorithmic framework combines metaheuristics with exact algorithms through a guiding mechanism based on diversification and intensification decisions. After presenting this generic framework, we extensively demonstrate its application to the vehicle routing problem with time windows. We then conduct a thorough computational study on a set of well-known test problems, where we show that the proposed approach not only finds solutions that are very close to the best-known solutions reported in the literature, but also improves them. We finally set up an experimental design to analyze the effects of different parameters used in the proposed algorithm.