12,121 research outputs found
An Active Set Algorithm for Robust Combinatorial Optimization Based on Separation Oracles
We address combinatorial optimization problems with uncertain coefficients
varying over ellipsoidal uncertainty sets. The robust counterpart of such a
problem can be rewritten as a second-oder cone program (SOCP) with integrality
constraints. We propose a branch-and-bound algorithm where dual bounds are
computed by means of an active set algorithm. The latter is applied to the
Lagrangian dual of the continuous relaxation, where the feasible set of the
combinatorial problem is supposed to be given by a separation oracle. The
method benefits from the closed form solution of the active set subproblems and
from a smart update of pseudo-inverse matrices. We present numerical
experiments on randomly generated instances and on instances from different
combinatorial problems, including the shortest path and the traveling salesman
problem, showing that our new algorithm consistently outperforms the
state-of-the art mixed-integer SOCP solver of Gurobi
Fault-Tolerant, but Paradoxical Path-Finding in Physical and Conceptual Systems
We report our initial investigations into reliability and path-finding based
models and propose future areas of interest. Inspired by broken sidewalks
during on-campus construction projects, we develop two models for navigating
this "unreliable network." These are based on a concept of "accumulating risk"
backward from the destination, and both operate on directed acyclic graphs with
a probability of failure associated with each edge. The first serves to
introduce and has faults addressed by the second, more conservative model.
Next, we show a paradox when these models are used to construct polynomials on
conceptual networks, such as design processes and software development life
cycles. When the risk of a network increases uniformly, the most reliable path
changes from wider and longer to shorter and narrower. If we let professional
inexperience--such as with entry level cooks and software developers--represent
probability of edge failure, does this change in path imply that the novice
should follow instructions with fewer "back-up" plans, yet those with
alternative routes should be followed by the expert?Comment: 8 page
Cautious Weight Tuning for Link State Routing Protocols
Link state routing protocols are widely used for intradomain routing in the Internet. These protocols are simple to administer and automatically update paths between sources and destinations when the topology changes. However, finding link weights that optimize network performance for a given traffic scenario is computationally hard. The situation is even more complex when the traffic is uncertain or time-varying. We present an efficient heuristic for finding link settings that give uniformly good performance also under large changes in the traffic. The heuristic combines efficient search techniques with a novel objective function. The objective function combines network performance with a cost of deviating from desirable features of robust link weight settings. Furthermore, we discuss why link weight optimization is insensitive to errors in estimated traffic data from link load measurements. We assess performance of our method using traffic data from an operational IP backbone
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