A Novel Cooperative Multi-search Benders Decomposition for Solving the Hydrothermal Unit-Commitment Problem

Categories Applications - Science and Engineering, Parallel Algorithms, Scheduling

Renewable energy and modernization of power operation demand Independent System Operators (ISOs) to solve ever more complex and larger programming problems to securely and economically schedule power resources. A key step in the scheduling process is the unit commitment (UC). In a hydro-dominated system, this process also involves managing reservoirs and is called hydrothermal UC … Read more

Decomposing Optimization-Based Bounds Tightening Problems Via Graph Partitioning

Categories Global Optimization

Bounds tightening or domain reduction is a critical refinement technique used in global optimization algorithms for nonlinear and mixed-integer nonlinear programming problems. Bounds tightening can strengthen convex relaxations and reduce the size of branch and bounds trees. An effective but computationally intensive bounds tightening technique is optimization-based bounds tightening (OBBT). In OBBT, each variable is … Read more

UAV Formation Shape Control via Decentralized Markov Decision Processes

Categories Applications - Science and Engineering

In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region … Read more

A Framework for Multi-stage Bonus Allocation in Meal-Delivery Platform

Categories Applications - OR and Management Sciences, Dynamic Programming Tags , , , ,

Online meal delivery is undergoing explosive growth, as this service is becoming increasingly fashionable. A meal delivery platform aims to provide efficient services for customers and restaurants. However, in reality, several hundred thousand orders are canceled per day in the Meituan meal delivery platform since they are not accepted by the crowdsoucing drivers, which is … Read more

Optimal Transport in the Face of Noisy Data

Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming Tags , ,

Optimal transport distances are popular and theoretically well understood in the context of data-driven prediction. A flurry of recent work has popularized these distances for data-driven decision-making as well although their merits in this context are far less well understood. This in contrast to the more classical entropic distances which are known to enjoy optimal … Read more

Implicit Regularization of Sub-Gradient Method in Robust Matrix Recovery: Don’t be Afraid of Outliers

Categories Nonlinear Optimization, Nonsmooth Optimization, Statistics Tags , ,

It is well-known that simple short-sighted algorithms, such as gradient descent, generalize well in the over-parameterized learning tasks, due to their implicit regularization. However, it is unknown whether the implicit regularization of these algorithms can be extended to robust learning tasks, where a subset of samples may be grossly corrupted with noise. In this work, … Read more

Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees

Categories Combinatorial Optimization, Statistics Tags , ,

In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying MRFs rely on the regularized maximum likelihood estimation (MLE), that typically suffer from weak statistical guarantees and high … Read more

Solving set-valued optimization problems using a multiobjective approach

Categories Multi-Criteria Optimization, Robust Optimization Tags , , ,

Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimzation problems even for specific cases. In this paper we study set-valued optimization problems and develop a multiobjective optimization … Read more

Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methods

Categories Convex and Nonsmooth Optimization Tags , , , , , , ,

For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove \emph{linear} and the \emph{superlinear} $\mathcal{O}\left(k^{\,-k\left(\frac{p-1}{p+1}\right)}\right)$ global rates for the proposed variants of the A-HPE and large-step A-HPE methods, respectively. The parameter $p\geq 2$ appears in the (high-order) … Read more

Minimizing delays of patient transports with incomplete information: A modeling approach based on the Vehicle Routing Problem

Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

We investigate a challenging task in ambulatory care, the minimizing of delays of patient transports. In practice, a limited number of vehicles is available for non-rescue transports. Furthermore, the dispatcher rarely has access to complete information when establishing a transport plan for dispatching the vehicles. If additional transport is requested on demand then schedules need … Read more