16 research outputs found
Submodular Function Maximization for Group Elevator Scheduling
We propose a novel approach for group elevator scheduling by formulating it
as the maximization of submodular function under a matroid constraint. In
particular, we propose to model the total waiting time of passengers using a
quadratic Boolean function. The unary and pairwise terms in the function denote
the waiting time for single and pairwise allocation of passengers to elevators,
respectively. We show that this objective function is submodular. The matroid
constraints ensure that every passenger is allocated to exactly one elevator.
We use a greedy algorithm to maximize the submodular objective function, and
derive provable guarantees on the optimality of the solution. We tested our
algorithm using Elevate 8, a commercial-grade elevator simulator that allows
simulation with a wide range of elevator settings. We achieve significant
improvement over the existing algorithms.Comment: 10 pages; 2017 International Conference on Automated Planning and
Scheduling (ICAPS
Recursive McCormick Linearization of Multilinear Programs
Linear programming (LP) relaxations are widely employed in exact solution
methods for multilinear programs (MLP). One example is the family of Recursive
McCormick Linearization (RML) strategies, where bilinear products are
substituted for artificial variables, which deliver a relaxation of the
original problem when introduced together with concave and convex envelopes. In
this article, we introduce the first systematic approach for identifying RMLs,
in which we focus on the identification of linear relaxation with a small
number of artificial variables and with strong LP bounds. We present a novel
mechanism for representing all the possible RMLs, which we use to design an
exact mixed-integer programming (MIP) formulation for the identification of
minimum-size RMLs; we show that this problem is NP-hard in general, whereas a
special case is fixed-parameter tractable. Moreover, we explore structural
properties of our formulation to derive an exact MIP model that identifies RMLs
of a given size with the best possible relaxation bound is optimal. Our
numerical results on a collection of benchmarks indicate that our algorithms
outperform the RML strategy implemented in state-of-the-art global optimization
solvers.Comment: 22 pages, 11 figures, Under Revie
Semismooth Equation Approach to Network Utility Maximization (NUM)
AbstractPopular approach to solving NUM utilizes dual decomposition and subgradient iterations, which are extremely slow to converge. Recently there has been investigation of barrier methods for the solution of NUM which have been shown to posess second order convergence. However, the question of accelerating dual decomposition based methods is still open. We propose a novel semismooth equation approach to solving the standard dual decomposition formulation of NUM.We show that under fairly mild assumptions that the approach converges locally superlinearly to the solution of the NUM. Globalization of the proposed algorithm using a linesearch is also described. Numerical experiments show that the approach is competitive with a state-of-the-art nonlinear programming solver which solves the NUM without decomposition