870 research outputs found
Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition
Mixed integer Model Predictive Control (MPC) problems arise in the operation
of systems where discrete and continuous decisions must be taken simultaneously
to compensate for disturbances. The efficient solution of mixed integer MPC
problems requires the computationally efficient and robust online solution of
mixed integer optimization problems, which are generally difficult to solve. In
this paper, we propose a machine learning-based branch and check Generalized
Benders Decomposition algorithm for the efficient solution of such problems. We
use machine learning to approximate the effect of the complicating variables on
the subproblem by approximating the Benders cuts without solving the
subproblem, therefore, alleviating the need to solve the subproblem multiple
times. The proposed approach is applied to a mixed integer economic MPC case
study on the operation of chemical processes. We show that the proposed
algorithm always finds feasible solutions to the optimization problem, given
that the mixed integer MPC problem is feasible, and leads to a significant
reduction in solution time (up to 97% or 50x) while incurring small error (in
the order of 1%) compared to the application of standard and accelerated
Generalized Benders Decomposition
Evaluating Resilience of Electricity Distribution Networks via A Modification of Generalized Benders Decomposition Method
This paper presents a computational approach to evaluate the resilience of
electricity Distribution Networks (DNs) to cyber-physical failures. In our
model, we consider an attacker who targets multiple DN components to maximize
the loss of the DN operator. We consider two types of operator response: (i)
Coordinated emergency response; (ii) Uncoordinated autonomous disconnects,
which may lead to cascading failures. To evaluate resilience under response
(i), we solve a Bilevel Mixed-Integer Second-Order Cone Program which is
computationally challenging due to mixed-integer variables in the inner problem
and non-convex constraints. Our solution approach is based on the Generalized
Benders Decomposition method, which achieves a reasonable tradeoff between
computational time and solution accuracy. Our approach involves modifying the
Benders cut based on structural insights on power flow over radial DNs. We
evaluate DN resilience under response (ii) by sequentially computing autonomous
component disconnects due to operating bound violations resulting from the
initial attack and the potential cascading failures. Our approach helps
estimate the gain in resilience under response (i), relative to (ii)
Partitioning Procedure for Polynomial Optimization: Application to Portfolio Decisions with Higher Order Moments
We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition. Towards this goal we introduce a partitioning procedure. The problem manipulations are in line with the pattern used in the Benders decomposition [1], namely relaxation preceded by projection. Stengle’s and Putinar’s Positivstellensatz are employed to derive the so-called feasibility and optimality constraints, respectively. We test the performance of the proposed method on a collection of benchmark problems and we present the numerical results. As an application, we consider the problem of selecting an investment portfolio optimizing the mean, variance, skewness and kurtosis of the portfolio.Polynomial optimization, Semidefinite relaxations, Positivstellensatz, Sum of squares, Benders decomposition, Portfolio optimization
Scheduling of EV Battery Swapping, I: Centralized Solution
We formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best battery station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize a weighted sum of EVs’ travel distance and electricity generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints, and ac power flow equations. To deal with the nonconvexity of power flow equations and the binary nature of station assignments, we propose a solution based on second-order cone programming (SOCP) relaxation of optimal power flow and generalized Benders decomposition. When the SOCP relaxation is exact, this approach computes a global optimum. We evaluate the performance of the proposed algorithm through simulations. The algorithm requires global information and is suitable for cases where the distribution grid, battery stations, and EVs are managed centrally by the same operator. In Part II of this paper, we develop distributed solutions for cases where they are operated by different organizations that do not share private information
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