16,600 research outputs found
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
The Traveling Salesman Problem in the Natural Environment
Is it possible for humans to navigate in the natural environment wherein the path taken between various destinations is 'optimal' in some way? In the domain of optimization this challenge is traditionally framed as the "Traveling Salesman Problem" (TSP). What strategies and ecological considerations are plausible for human navigation? When given a two-dimensional map-like presentation of the destinations, participants solve this optimization exceptionally well (only 2-3% longer than optimum)^1, 2^. In the following experiments we investigate the effect of effort and its environmental affordance on navigation decisions when humans solve the TSP in the natural environment. Fifteen locations were marked on two outdoor landscapes with flat and varied terrains respectively. Performance in the flat-field condition was excellent (∼6% error) and was worse but still quite good in the variable-terrain condition (∼20% error), suggesting participants do not globally pre-plan routes but rather develop them on the fly. We suggest that perceived effort guides participant solutions due to the dynamic constraints of effortful locomotion and obstacle avoidance
Stochastic Online Shortest Path Routing: The Value of Feedback
This paper studies online shortest path routing over multi-hop networks. Link
costs or delays are time-varying and modeled by independent and identically
distributed random processes, whose parameters are initially unknown. The
parameters, and hence the optimal path, can only be estimated by routing
packets through the network and observing the realized delays. Our aim is to
find a routing policy that minimizes the regret (the cumulative difference of
expected delay) between the path chosen by the policy and the unknown optimal
path. We formulate the problem as a combinatorial bandit optimization problem
and consider several scenarios that differ in where routing decisions are made
and in the information available when making the decisions. For each scenario,
we derive a tight asymptotic lower bound on the regret that has to be satisfied
by any online routing policy. These bounds help us to understand the
performance improvements we can expect when (i) taking routing decisions at
each hop rather than at the source only, and (ii) observing per-link delays
rather than end-to-end path delays. In particular, we show that (i) is of no
use while (ii) can have a spectacular impact. Three algorithms, with a
trade-off between computational complexity and performance, are proposed. The
regret upper bounds of these algorithms improve over those of the existing
algorithms, and they significantly outperform state-of-the-art algorithms in
numerical experiments.Comment: 18 page
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