This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available alternative that maximizes a random utility function. We introduce a deterministic equivalent reformulation of this stochastic problem as a maximum covering location problem with an exponential number of demand points, each of which is covered by a different set of candidate locations. Estimating the prevalence of these preference profiles through simulation generalizes a sample average approximation method from the literature and results in a maximum covering location problem of manageable size. To solve it, we develop a partial Benders reformulation in which the contribution to the objective of the least influential preference profiles is aggregated and bounded by submodular cuts. This set of profiles is selected by a knee detection method that seeks to identify the best tradeoff between the fraction of the demand that is retained in the master problem and the size of the model. We develop a theoretical analysis of our approach and show that the solution quality it provides for the original stochastic problem, its computational performance, and the automatic profile-retention strategy it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances of the competitive facility location problem, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model. We characterize a broader class of problems, which includes assortment optimization, to which the solving methodology and the analyses developed in this paper can be extended. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported by Fonds de Recherche du Québec-Nature et Technologies and Institut de Valorisation des Données through scholarships to R. Legault. E. Frejinger was partially supported by the Canada Research Chair program [Grant 950-232244]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.0280 .

Generative Flow Networks (GFNs) have emerged as a powerful tool for sampling discrete objects from unnormalized distributions, offering a scalable alternative to Markov Chain Monte Carlo (MCMC) methods. While GFNs draw inspiration from maximum entropy reinforcement learning (RL), the connection between the two has largely been unclear and seemingly applicable only in specific cases. This paper addresses the connection by constructing an appropriate reward function, thereby establishing an exact relationship between GFNs and maximum entropy RL. This construction allows us to introduce maximum entropy GFNs, which achieve the maximum entropy attainable by GFNs without constraints on the state space, in contrast to GFNs with uniform backward policy.

Regularized reinforcement learning (RL), particularly the entropy-regularized kind, has gained traction in optimal control and inverse RL. While standard unregularized RL methods remain unaffected by changes in the number of actions, we show that it can severely impact their regularized counterparts. This paper demonstrates the importance of decoupling the regularizer from the action space: that is, to maintain a consistent level of regularization regardless of how many actions are involved to avoid over-regularization. Whereas the problem can be avoided by introducing a task-specific temperature parameter, it is often undesirable and cannot solve the problem when action spaces are state-dependent. In the state-dependent action context, different states with varying action spaces are regularized inconsistently. We introduce two solutions: a static temperature selection approach and a dynamic counterpart, universally applicable where this problem arises. Implementing these changes improves performance on the DeepMind control suite in static and dynamic temperature regimes and a biological design task.

We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving problems where the second stage is demanding. Our core idea is to gain large reductions in online solution time, while incurring small reductions in first-stage solution accuracy by substituting the exact second-stage solutions with fast, yet accurate, supervised ML predictions. This upfront investment in ML would be justified when similar problems are solved repeatedly over time—for example, in transport planning related to fleet management, routing, and container yard management. Our numerical results focus on the problem class seminally addressed with the integer and continuous L-shaped cuts. Our extensive empirical analysis is grounded in standardized families of problems derived from stochastic server location (SSLP) and stochastic multi-knapsack (SMKP) problems available in the literature. The proposed method can solve the hardest instances of SSLP in less than 9% of the time it takes the state-of-the-art exact method, and in the case of SMKP, the same figure is 20%. Average optimality gaps are, in most cases, less than 0.1%. History: Accepted by Alice Smith, Area Editor (for this paper) for Design and Analysis of Algorithms–Discrete. Funding: Financial support from the Institut de Valorisation des Données (IVADO) Fundamental Research Project Grants [project entitled “Machine Learning for (Discrete) Optimization”]; Canada Research Chairs; the Natural Sciences and Engineering Research Council of Canada [Collaborative Research and Development Grant CRD-477938-14]; and the Canadian National Railway Company Chair in Optimization of Railway Operations at Université de Montréal is gratefully acknowledged. E. Frejinger holds a Canada Research Chair. Computations were made on the supercomputer Béluga, managed by Calcul Québec and Digital Research Alliance of Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation; the Ministère de l’Économie, de la Science et de l’Innovation du Québec; and the Fonds de Recherche du Québec – Nature et Technologies.

We present a new model for finding the optimal placement of electric vehicle charging stations across a multiperiod time frame so as to maximise electric vehicle adoption. Via the use of stochastic discrete choice models and user classes, this work allows for a granular modelling of user attributes and their preferences in regard to charging station characteristics. We adopt a simulation approach and precompute error terms for each option available to users for a given number of scenarios. This results in a bilevel optimisation model that is, however, intractable for all but the simplest instances. Our major contribution is a reformulation into a maximum covering model, which uses the precomputed error terms to calculate the users covered by each charging station. This allows solutions to be found more efficiently than for the bilevel formulation. The maximum covering formulation remains intractable in some instances, so we propose rolling horizon, greedy, and greedy randomised adaptive search procedure heuristics to obtain good-quality solutions more efficiently. Extensive computational results are provided, and they compare the maximum covering formulation with the current state of the art for both exact solutions and the heuristic methods. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Hydro-Québec and the Natural Sciences and Engineering Research Council of Canada [Discovery Grant 2017-06054; Collaborative Research and Development Grant CRDPJ 536757–19]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0185 .

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming, where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second-stage problem, conditionally on the first-stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second-stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training data set consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.