We introduce a novel technique to generate Benders’ cuts from a conic relaxation (“corner”) derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation … Read more
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We show how to extract alternative solutions for optimization problems solved by Benders Decom- position. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative solutions but none appear to support such generation when using Benders Decomposition. We propose a new post-processing method that extracts multiple optimal and … Read more
In mathematical optimization, we want to find the best possible solution for a decision-making problem. Curiously, these problems are harder to solve if they have discrete decisions. Imagine that you would like to buy chocolate: you can buy no chocolate or one chocolate bar, but typically you cannot buy just half of a bar. Now … Read more
This paper introduces a generalized isotonic optimization framework over an arborescence graph, where each node incurs state-dependent convex costs and a fixed cost upon strict increases. We begin with the special case in which the arborescence is a path and develop a dynamic programming (DP) algorithm with an initial complexity of $O(n^3)$, which we improve … Read more
To meet sustainability goals and regulatory requirements, transit agencies worldwide are planning partial and complete transitions to electric bus fleets. This paper presents the first comprehensive and computationally efficient multi-period optimization framework integrating the key planning decisions necessary to support such electrification initiatives. Our model, formulated as a two-stage integer program with integer subproblems, jointly … Read more
We consider the problem of minimizing a sparse nonconvex quadratic function over the unit hypercube. By developing an extension of the Reformulation Linearization Technique (RLT) to continuous quadratic sets, we propose a novel second-order cone (SOC) representable relaxation for this problem. By exploiting the sparsity of the quadratic function, we establish a sufficient condition under … Read more
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Problem definition. The opioid crisis has remained a major public health challenge in the United States for many years. This study develops a data-driven decision support framework to guide policymakers in allocating county-level budgets across multiple expenditure categories in order to address the opioid crisis. Methodology/results. We compile and curate a detailed dataset on fiscal … Read more
In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more