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This article is a short introduction toAI4OPT, the NSF AI Institute for Advances in Optimization.AI4OPTfuses AI and optimization, inspired by societal challenges in supply chains, energy systems, chip design and manufacturing, and sustainable food systems. By combining machine learning and mathematical optimization,AI4OPTstrives to develop AI‐assisted optimization systems that bring orders of magnitude improvements in efficiency, perform accurate uncertainty quantification, and address challenges in resiliency and sustainability.AI4OPTalso applies its “teaching the teachers” philosophy to provide longitudinal educational pathways in AI for engineering.

 

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches. 

This paper studies how to integrate rider mode preferences into the design of on-demand multimodal transit systems (ODMTSs). It is motivated by a common worry in transit agencies that an ODMTS may be poorly designed if the latent demand, that is, new riders adopting the system, is not captured. This paper proposes a bilevel optimization model to address this challenge, in which the leader problem determines the ODMTS design, and the follower problems identify the most cost efficient and convenient route for riders under the chosen design. The leader model contains a choice model for every potential rider that determines whether the rider adopts the ODMTS given her proposed route. To solve the bilevel optimization model, the paper proposes an exact decomposition method that includes Benders optimal cuts and no-good cuts to ensure the consistency of the rider choices in the leader and follower problems. Moreover, to improve computational efficiency, the paper proposes upper and lower bounds on trip durations for the follower problems, valid inequalities that strengthen the no-good cuts, and approaches to reduce the problem size with problem-specific preprocessing techniques. The proposed method is validated using an extensive computational study on a real data set from the Ann Arbor Area Transportation Authority, the transit agency for the broader Ann Arbor and Ypsilanti region in Michigan. The study considers the impact of a number of factors, including the price of on-demand shuttles, the number of hubs, and access to transit systems criteria. The designed ODMTSs feature high adoption rates and significantly shorter trip durations compared with the existing transit system and highlight the benefits of ensuring access for low-income riders. Finally, the computational study demonstrates the efficiency of the decomposition method for the case study and the benefits of computational enhancements that improve the baseline method by several orders of magnitude. Funding: This research was partly supported by National Science Foundation [Leap HI Proposal NSF-1854684] and the Department of Energy [Research Award 7F-30154]. 

AC Optimal Power Flow (AC-OPF) is a fundamental building block in power system optimization. It is often solved repeatedly, especially in regions with large penetration of renewable generation, to avoid violating operational limits. Recent work has shown that deep learning can be effective in providing highly accurate approximations of AC-OPF. However, deep learning approaches may suffer from scalability issues, especially when applied to large realistic grids. This paper addresses these scalability limitations and proposes a load embedding scheme using a 3-step approach. The first step formulates the load embedding problem as a bilevel optimization model that can be solved using a penalty method. The second step learns the encoding optimization to quickly produce load embeddings for new OPF instances. The third step is a deep learning model that uses load embeddings to produce accurate AC-OPF approximations. The approach is evaluated experimentally on large-scale test cases from the NESTA library. The results demonstrate that the proposed approach produces an order of magnitude improvements in training convergence and prediction accuracy.