Quadratic Optimization with Switching Variables: The Convex Hull for n=2
We consider quadratic optimization in variables (x,y), 0
Month: February 2020
Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound
This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints … Read more
Random-Sampling Multipath Hypothesis Propagation for Cost Approximation in Long-Horizon Optimal Control
In this paper, we develop a Monte-Carlo based heuristic approach to approximate the objective function in long horizon optimal control problems. In this approach, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the weighted average of the costs along all the trajectories. … Read more
Stochastic Last-mile Delivery with Crowd-shipping and Mobile Depots
This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more
Optimal Learning for Structured Bandits
We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision- maker is aware of certain structural information regarding the reward distributions and would … Read more
Two-Stage Facility Location Problems with Restricted Recourse
We introduce a new class of two-stage stochastic uncapacitated facility location problems under system nervousness considerations. The location and allocation decisions are made under uncertainty, while the allocation decisions may be altered in response to the realizations of the uncertain parameters. A practical concern is that the uncertainty-adaptive second-stage allocation decisions might substantially deviate from … Read more
Sparse PSD approximation of the PSD cone
While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller k times k principal submatrices — we call this the sparse SDP relaxation. Surprisingly, … Read more
Quantum Bridge Analytics II: Network Optimization and Combinatorial Chaining for Asset Exchange
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys … Read more
A Simulated Annealing Algorithm for the Directed Steiner Tree Problem
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the … Read more
Economic Interpretation of Demand Curves in Multi-product Electricity Markets
In the absence of direct demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between reliability and cost due to the inelasticity of the fixed requirements. Therefore, ISOs have been … Read more