Recent years have witnessed increasing interest in optimization proxies, i.e., machine learning models that approximate the input-output mapping of parametric optimization problems and return near-optimal feasible solutions. Following recent work by (Nellikkath & Chatzivasileiadis, 2021), this paper reconsiders the optimality verification problem for optimization proxies, i.e., the determination of the worst-case optimality gap over the instance distribution. The paper proposes a compact formulation for optimality verification and a gradient-based primal heuristic that brings substantial computational benefits to the original formulation. The compact formulation is also more general and applies to non-convex optimization problems. The benefits of the compact formulation are demonstrated on large-scale DC Optimal Power Flow and knapsack problems.

This paper introduces Dual Interior Point Learning (DIPL) and Dual Supergradient Learning (DSL) to learn dual feasible solutions to parametric linear programs with bounded variables, which are pervasive across many industries. DIPL mimics a novel dual interior point algorithm while DSL mimics classical dual supergradient ascent. DIPL and DSL ensure dual feasibility by predicting dual variables associated with the constraints then exploiting the flexibility of the duals of the bound constraints. DIPL and DSL complement existing primal learning methods by providing a certificate of quality. They are shown to produce high-fidelity dual-feasible solutions to large-scale optimal power flow problems providing valid dual bounds under 0.5% optimality gap.

Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power grid stability but becomes increasingly complex as systems grow. This paper introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning framework for producing near-optimal solutions to large-scale SCOPF problems in milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised counterparts that rely on training instances with their optimal solutions, which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an Augmented Lagrangian Method (ALM) for training primal and dual networks that learn the primal solutions and the Lagrangian multipliers, respectively, to the unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer to ensure the feasibility of the power balance in the nominal case, and a binary search layer to compute, using the Automatic Primary Response (APR), the generator dispatches in the contingencies. The resulting differentiable program can then be trained end-to-end using the objective function of the SCOPF and the power balance constraints of the contingencies. Experimental results demonstrate that the PDL-SCOPF delivers accurate feasible solutions with minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging the gap between traditional optimization methods and machine learning, highlighting the potential of self-supervised end-to-end primal-dual learning for large-scale optimization tasks.

Many real-world decision processes are modeled by optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. Recent works show that decision quality can be improved in this setting by solving and differentiating the optimization problem in the training loop, enabling end-to-end training with loss functions defined directly on the resulting decisions. However, this approach can be inefficient and requires handcrafted, problem-specific rules for backpropagation through the optimization step. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient, accurate, and flexible solutions to an array of challenging Predict-Then-Optimize problems.

A general overview of current CP courses and instructional methods is presented, with a focus on online and virtually-delivered courses. This is followed by a discussion of the novel approach taken to introductory CP education for engineering students at large scale at the Georgia Institute of Technology (Georgia Tech) in Atlanta, GA, USA. The paper summarizes important takeaways from the Georgia Tech CP course and ends with a discussion on the future of CP education. Some ideas for instructional methods, promotional methods, and organizational changes are proposed to aid in the long-term growth of CP education.

The load planning problem is a critical challenge in service network design for parcel carriers: it decides how many trailers (or loads) to assign for dispatch over time between pairs of terminals. Another key challenge is to determine a flow plan, which specifies how parcel volumes are assigned to planned loads. This paper considers the Dynamic Load Planning Problem (DLPP) that considers both flow and load planning challenges jointly to adjust loads and flows as the demand forecast changes over time before the day of operations. The paper aims at developing a decision-support tool to inform planners making these decisions at terminals across the network. The paper formulates the DLPP as a MIP and shows that it admits a large number of symmetries in a network where each commodity can be routed through primary and alternate paths. As a result, an optimization solver may return fundamentally different solutions to closely related problems, confusing planners and reducing trust in optimization. To remedy this limitation, the paper proposes a Goal-Directed Optimization that eliminates those symmetries by generating optimal solutions staying close to a reference plan. The paper also proposes an optimization proxy to address the computational challenges of the optimization models. The proxy combines a machine learning model and a feasibility restoration model and finds solutions that satisfy real-time constraints imposed by planners-in-the-loop. An extensive computational study on industrial instances shows that the optimization proxy is around 10 times faster than the commercial solver in obtaining the same quality solutions and orders of magnitude faster for generating solutions that are consistent with each other. The proposed approach also demonstrates the benefits of the DLPP for load consolidation, and the significant savings obtained from combining machine learning and optimization.

This article is a short introduction to AI4OPT, the NSF AI Institute for Advances in Optimization. AI4OPT fuses AI and Optimization, inspired by end-use cases in supply chains, energy systems, chip design and manufacturing, and sustainable food systems. AI4OPT also applies its "teaching the teachers" philosophy to provide longitudinal educational pathways in AI for engineering.

Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utilizes heuristic search with mathematical optimization and can optimize a variety of objective functions. We also present the method MIP-LNS-SIM, where we combine agent-based simulation with MIP-LNS to estimate delays due to congestion, as well as, find optimized plans considering such delays. We use Harris County in Houston, Texas, as our study area. We show that, within a given time limit, MIP-LNS finds better solutions than existing methods in terms of three different metrics. However, when congestion dependent delay is considered, MIP-LNS-SIM outperforms MIP-LNS in multiple performance metrics. In addition, MIP-LNS-SIM has a significantly lower percent error in estimated evacuation completion time compared to MIP-LNS.

This paper reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This paper first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes Compact Learning, a new method that learns in a subspace of the principal components before translating the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. Compact Learning is evaluated on a variety of test cases from the PGLib with up to 30,000 buses. The paper also shows that the output of Compact Learning can be used to warm-start an exact AC solver to restore feasibility, while bringing significant speed-ups.

Idle vehicle relocation is crucial for addressing demand-supply imbalance that frequently arises in the ride-hailing system. Current mainstream methodologies - optimization and reinforcement learning - suffer from obvious computational drawbacks. Optimization models need to be solved in real-time and often trade off model fidelity (hence quality of solutions) for computational efficiency. Reinforcement learning is expensive to train and often struggles to achieve coordination among a large fleet. This paper designs a hybrid approach that leverages the strengths of the two while overcoming their drawbacks. Specifically, it trains an optimization proxy, i.e., a machine-learning model that approximates an optimization model, and then refines the proxy with reinforcement learning. This Reinforcement Learning from Optimization Proxy (RLOP) approach is computationally efficient to train and deploy, and achieves better results than RL or optimization alone. Numerical experiments on the New York City dataset show that the RLOP approach reduces both the relocation costs and computation time significantly compared to the optimization model, while pure reinforcement learning fails to converge due to computational complexity.