Fast and Memory-Efficient Algorithms for Evacuation Problems

Schlöter, Miriam; Skutella, Martin

doi:10.1137/1.9781611974782.52

Cited by 19 publications

(24 citation statements)

References 33 publications

(70 reference statements)

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“…Such chain flows in a nonstandard chain decomposition may use a backwards arc with negative transit time. Based on this landmark paper [18], authors in [21] have also presented the quickest transshipment algorithm to determine the quickest transshipment as a convex combination of simple lex-max dynamic flows. Now, we are presenting the quickest partial arc reversal transshipment algorithm to get the quickest arrival of evacuees at in corresponding to the arc reversal capability.…”

Section: Arrival Of Evacueesmentioning

confidence: 99%

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

Adhikari¹,

Dhamala²

2020

AJAM

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The evacuation planning problem can be viewed as different variants of dynamic flow maximization and time minimization problems. An optimal solution to the latter problem sends a given amount of flow from disaster zones to safe zones in minimum time. We solve this problem on an embedded integrated network of a prioritized primary and a bus-routed secondary sub-networks. For a lexicographically maximum (lex-max) dynamic flow problem, we are given a time horizon and a prioritized network, where we need a feasible dynamic flow that lexicographically maximizes the flow amount leaving each terminal respecting the priority. Here, we use the quickest transshipment partial arc reversal strategy to collect the evacuees in minimum time from the disaster zones to the pickup locations of the primary sub-network. By treating such pickup locations as sources, the available set of transit-buses is assigned in the secondary sub-network to shift the evacuees finally to the sinks on the first-come-first-serve basis. This novel approach proposed here is better suited for the simultaneous flow of evacuees with minimum waiting delay at such pickup locations in the integrated evacuation network topology. The lane reversal strategy significantly reduces the evacuation time, whereas reversing them only partially has an additional benefit that the unused road capacities can be used for supplying emergency logistics and allocating facilities as well.

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Section: Arrival Of Evacueesmentioning

confidence: 99%

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

Adhikari¹,

Dhamala²

2020

AJAM

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“…Roughly speaking, the evacuation problem is the problem of sending all the supplies to the sinks as quickly as possible. Hoppe and Tardos proved that this problem can be solved in polynomial time (see also for another polynomial‐time algorithm). Notice that although the bit length of Θ (i.e., ⌈log 2 Θ⌉) is bounded by a polynomial in the input size, Θ may not be bounded by a polynomial in the input size (more precisely, Θ has pseudo‐polynomial size).…”

Section: Dynamic Flowsmentioning

confidence: 99%

“…The goal of this problem is to find the minimum time limit Θ such that we can send all the supplies to the sinks within time Θ. It is known [17] that we can solve the evacuation problem in polynomial time (see also [23] for another polynomial-time algorithm).…”

Section: Introductionmentioning

confidence: 99%

“…Baumann and Skutella [1] proved that an earliest arrival flow can be found in time bounded by a polynomial in the input size plus the number of breakpoints of the earliest arrival pattern. Furthermore, Schlöter and Skutella [23] proposed a polynomial-space algorithm for finding an earliest arrival flow. On the negative side, Disser and Skutella [2] showed that the problem of determining the average arrival time of an earliest arrival flow is NP-hard.…”

Section: Introductionmentioning

confidence: 99%

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Lexicographically optimal earliest arrival flows

Kamiyama

2019

Networks

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A dynamic network introduced by Ford and Fulkerson is a directed graph in which each arc has a capacity and a transit time. The evacuation problem is one of the fundamental problems in a dynamic network. The goal of this problem is to find the minimum time limit Θ such that we can send all the supplies to the sinks within time Θ. An earliest arrival flow is an optimal flow for the evacuation problem such that the amount of supplies which have reached the sinks is maximized at every time step. It is known that in a dynamic network with multiple sinks, if the sinks have capacities, then an earliest arrival flow does not necessarily exist. In this paper, to cope with this issue, we first introduce a lexicographically optimal earliest arrival flow in a dynamic network with multiple sinks. Then we propose a pseudo-polynomial-time algorithm for finding a lexicographically optimal earliest arrival flow. Furthermore, we prove that if the transit time of every arc is zero, then we can find a lexicographically optimal earliest arrival flow in polynomial time. KEYWORDS dynamic network, earliest arrival flow, evacuation problem, lexicographically optimal flow, submodular function, time-expanded network 1 This result was cited as personal communication (2002) in [7].Networks. 2020;75:18-33.wileyonlinelibrary.com/journal/net

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“…The same authors have shown how to efficiently construct a Maximum Dynamic s-t flow: a path decomposition is first applied to the solution of a static minimum cost flow obtained in the original network, then temporally repeated flows are sent among the decomposed paths as long as there is enough time left to reach the destination t within the time horizon. Novel problems find their roots right in the dynamic environment, for instance the Quickest Transshipment Problem and the Earliest Arrival Flow Problem where the exact time horizon of the process is not known a priori [15,16,17]. For a complete overview of dynamic problems we refer to Aronson [3], Kotnyek [18], Köhler et al [4], Skutella [19].…”

Section: Introductionmentioning

confidence: 99%

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

Melchiori

Sgalambro

2018

Computers & Operations Research

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The literature on k-splittable flows, see Baier et al. (2002) [1], provides evidence on how controlling the number of used paths enables practical applications of flows optimization in many real-world contexts. Such a modeling feature has never been integrated so far in Quickest Flows, a class of optimization problems suitable to cope with situations such as emergency evacuations, transportation planning and telecommunication systems, where one aims to minimize the makespan, i.e. the overall time needed to complete all the operations, see Pascoal et al. (2006) [2]. In order to bridge this gap, a novel optimization problem, the Quickest Multicommodity k-Splittable Flow Problem (QM CkSF P) is introduced in this paper. The problem seeks to minimize the makespan of transshipment operations for given demands of multiple commodities, while imposing restrictions on the maximum number of paths for each single commodity. The computational complexity of this problem is analyzed, showing its N P-hardness in the strong sense, and an original Mixed-Integer Programming formulation is detailed. We propose a matheuristic algorithm based on a hybridized Very Large-Scale Neighborhood Search that, utilizing the presented mathematical formulation, explores multiple search spaces to solve efficiently large instances of the QM CkSF P. High quality computational results obtained on benchmark test sets are presented and discussed, showing how the proposed matheuristic largely outperforms a state-of-the-art heuristic scheme frequently adopted in path-restricted flow problems.

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Fast and Memory-Efficient Algorithms for Evacuation Problems

Cited by 19 publications

References 33 publications

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

Minimum Clearance Time on the Prioritized Integrated Evacuation Network

Lexicographically optimal earliest arrival flows

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

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