Shabbir Ahmed The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or … Read more
A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more
We consider integer programming (IP) problems consisting of (possibly a large number of) subsystems and a small number of coupling constraints that link variables from different subsystems. Such problems are called loosely coupled or nearly decomposable. Motivated by recent developments in multiobjective programming (MOP), we develop a MOP-based decomposition algorithm to solve loosely coupled IPs. … Read more
We present a parallel large neighborhood search framework for finding high quality primal solutions for generic Mixed Integer Programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary … Read more
Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, such as nested Benders’ decomposition and … Read more
We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of a uniform distribution, and must immediately be matched or discarded. We consider various … Read more
A chance constrained optimization problem over a finite distribution involves a set of scenario constraints from which a small subset can be violated. We consider the setting where all scenario constraints are mixed-integer convex. Existing works typically consider a mixed integer nonlinear programming (MINLP) formulation of this problem by introducing binary variables to indicate which … Read more
Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves upon these bounds by re-enforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into ‘groups’. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve … Read more
In this paper, we extend a recently proposed scenario decomposition algorithm (Ahmed (2013)) for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the … Read more
A recently proposed scenario decomposition algorithm for stochastic 0-1 programs finds an optimal solution by evaluating and removing individual solutions that are discovered by solving scenario subproblems. In this work, we develop an asynchronous, distributed implementation of the algorithm which has computational advantages over existing synchronous implementations of the algorithm. Improvements to both the synchronous … Read more