One goal of multiobjective optimization is to approximate the nondominated set in the image space. One widely used approximation concept is that of enclosures. These are unions of closed boxes that cover the nondominated set. The bounds of these boxes form the lower and upper bound sets of the enclosure. The quality of an enclosure … Read more
We systematically investigate the potentials of improving the lower bound obtained with a linear relaxation of the Quadratic Unconstrained Binary Optimization problem by integrating curvature information from an accompanying quadratic convex underestimator via gradient inequalities. On the one hand, we exemplify to which extent this hybrid approach may provide a lower bound that is strictly … Read more
We study mixed-integer quadratic optimization (MIQO) problems with indicator variables. We propose a unified framework, based on decision diagrams, that serves both to solve the associated optimization problems and to construct ideal conic quadratic extended formulations of the closure of the convex hull of the underlying mixed-integer set. The construction applies to arbitrary quadratics and … Read more
Georeferenced synthetic populations are essential inputs for agent-based simulations in epidemiology, transportation, and urban planning, yet existing methods for spatial allocation of households to residences lack formal optimality guarantees. We present a two-stage mathematical framework for generating such populations from publicly available census data. The first stage combines Iterative Proportional Fitting (IPF) with a mixed-integer … Read more
We consider optimization applications with unknown parameters where the decision maker believes that the optimal value of the nominal problem—the optimization problem they would have solved if the true parameters were known—is unlikely to be large. This belief derives from information that humans have that is not captured in datasets, obtained from domain knowledge and … Read more
Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more
This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distributions in Sinkhorn discrepancy-based ambiguity sets centered at the empirical distributions. Existing approaches solve this problem by solving large-scale conic programs, which are not scalable. To overcome this, we propose a generative framework that learns least-favorable distributions and … Read more
This paper proposes a new arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc stays in the interior set longer than any straight line, it is expected that the scheme will generate a better new iterate … Read more
Many retail distribution networks use a hierarchical structure in which regional distribution centers replenish local distribution centers that are closer to customers. In such networks, products are often shipped in large quantities, as case packs, cases or pallets, to the regional distribution center, whereas local distribution centers may require quantities at the individual-unit level. Case … Read more
The Ramsey number R(m,n) is the smallest order at which every red-blue edge coloring of a complete graph must contain a blue clique (a complete subgraph) of size m or a red clique of size n. Determining these numbers exactly is extremely hard, and even certifying a lower bound requires exhibiting an explicit coloring that … Read more