In this paper we propose a generic branch-and-bound algorithm for solving multi-objective integer linear programming problems. % In the recent literature, competitive frameworks has been proposed for bi-objective 0-1 problems, and many of these frameworks rely on the use of the linear relaxation to obtain lower bound sets. When increasing the number of objective functions, … Read more
Allowing drivers to choose which requests to fulfill provides drivers with much-needed autonomy in ridesharing and crowdsourced delivery platforms. While stochastic, a driver’s acceptance of requests in their menu is influenced by the platform’s offered compensation. Therefore, in this work, we create and solve an optimization model to determine personalized menus and incentives to offer … Read more
Problem Definition: While physical (or ‘social’) distancing is an important public health intervention during airborne pandemics, physical distancing dramatically reduces the effective capacity of classrooms. During the COVID-19 pandemic, this presented a unique problem to campus planners who hoped to deliver a meaningful amount of in-person instruction in a way that respected physical distancing. This … Read more
Many states in the U.S. have faced shortages of medical resources because of the surge in the number of patients suffering from COVID-19. As many projections indicate, the situation will be far worse in coming months. The upcoming challenge is not only due to the exponential growth in cases but also because of inherent uncertainty … Read more
Real-world problems are often nonconvex and involve integer variables, representing vexing challenges to be tackled using state-of-the-art solvers. We introduce a mathematical identity-based reformulation of a class of polynomial integer nonlinear optimization (PINLO) problems using a technique that linearizes polynomial functions of separable and bounded integer variables of any degree. We also introduce an alternative … Read more
Since stochastic approximation (SA) based algorithms are easy to implement and need less memory, they are very popular in distributed stochastic optimization problems. Many works have focused on the consistency of the objective values and the iterates returned by the SA based algorithms. It is of fundamental interest to know how to quantify the uncertainty … Read more
The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme … Read more
The nonconvex program plays an important role in the field of optimization and has a lot of applications in practice. However, for general nonconvex programming problems, the lack of verifiable global optimal conditions and the multiple local minimizers make global optimization hard in computation. In this paper, a convex proximal point algorithm (CPPA) is considered … Read more
Airlines face many different planning processes until the day of operation. These include Fleet Assignment, Tail Assignment and the associated control of ground processes between consecutive flights, called Turnaround Handling. All of these planning problems have in common that they often need to be reoptimized on the day of execution due to unplanned events. In … Read more
We present a two-phase methodology to address the problem of optimally deploying indoor wireless local area networks. In the first phase, we use Helmholtz’s equation to simulate electromagnetic fields in a typical environment such as an office floor. The linear system which results from the discretization of this partial differential equation is solved with a … Read more