Nonlinear mixed integer programming models and algorithms for fair and efficient large scale evacuation planning
Author
Bayram, Vedat
Advisor
Yaman, Hande
Date
2015-07Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Show full item recordAbstract
Shelters are safe facilities that protect a population from possible damaging
effects of a disaster. Traffic management during an evacuation and the decision
of where to locate the shelters are of critical importance to the performance of an
evacuation plan. From the evacuation management authority's point of view, the
desirable goal is to minimize the total evacuation time by computing a system
optimum (SO). However, evacuees may not be willing to take long routes enforced
on them by a SO solution; but they may consent to taking routes with lengths
not longer than the shortest path to the nearest shelter site by more than a
tolerable factor. We develop a model that optimally locates shelters and assigns
evacuees to the nearest shelter sites by assigning them to shortest paths, shortest
and nearest with a given degree of tolerance, so that the total evacuation time is
minimized. As the travel time on a road segment is often modeled as a nonlinear
function of the
ow on the segment, the resulting model is a nonlinear mixed
integer programming model. We develop a solution method that can handle
practical size problems using second order cone programming techniques. Using
our model, we investigate the trade-of between efficiency and fairness.
Disasters are uncertain events. Related studies and real-life practices show
that a significant uncertainty regarding the evacuation demand and the impact
of the disaster on the infrastructure exists. The second model we propose is
a scenario-based two-stage stochastic evacuation planning model that optimally
locates shelter sites and that assigns evacuees to shelters and paths to minimize
the expected total evacuation time, under uncertainty. The model considers the
uncertainty in the evacuation demand and the disruption in the road network and
shelter sites. We present a case study for an impending earthquake in Istanbul,
Turkey. We compare the performance of the stochastic programming solutions
to solutions based on single scenarios and mean values.
We also propose an exact algorithm based on Benders decomposition to solve the stochastic problem. To the best of our knowledge, ours is the first algorithm
that uses duality results for second order cone programming in a Benders decomposition
setting. We solve practical size problems with up to 1000 scenarios
in moderate CPU times. We investigate methods such as employing a multi-cut
strategy, deriving pareto-optimal cuts, using a reduced primal subproblem and
preemptive priority multiobjective program to enhance the proposed algorithm.
Computational results confirm the efficiency of our algorithm.
This research is supported by TUBITAK, The Scientific and Technological
Research Council of Turkey with project number 213M434.
Keywords
Disaster managementEvacuation tra c management
Shelter location
System optimal
Constrained system optimal
User equilibrium
Nearest allocation
Two-stage stochastic programming
Second order cone programming
Benders decomposition
Pareto-optimal cuts