Neuroscience: Matter and More

Journal of Industrial & Management Optimization, 2016

The very challenging emergency issues because of large scale natural or man-created disasters promote the research on evacuation planning. The earliest arrival contraflow is an important model for evacuation planning that rescue as many evacuees as possible at any point in time by reversing the direction of arcs towards the safe destinations with increased outbound arc capacity. We present efficient algorithms to solve the earliest arrival contraflow problem on multiple sources and on multiple sinks networks separately. We also introduce an approximate-earliest arrival contraflow solution on multi-terminal networks.

Journal of Advanced College of Engineering and Management, 2016

Evacuation planning problem can be considered as a dynamic flow problem on the dynamic network. In a dangerous situation, as many individuals as possible should be rescued from a dangerous zone to a safety zone as quickly and efficiently as possible. The earliest arrival flow problem is to send a maximal amount of dynamic flow reaching the safety zone sink not only for the given time horizon, but also for any earlier moment of the time horizon. In this paper we discuss the optimization formulation of the earliest arrival evacuation planning problem with efficient solution procedure.

Journal of Industrial & Management Optimization, 2017

Dynamic network flow problems have wide applications in evacuation planning. From a given subset of arcs in a directed network, choosing the suitable arcs for facility location is very important in the optimization of flows in emergency cases. Because of the decrease in the capacity of an arc by placing a facility in it, there may be a reduction in the maximum flow or increase in the quickest time. In this work, we consider a problem of identifying the optimal facility locations so that the increase in the quickest time is minimum. Introducing the quickest FlowLoc problem, we give strongly polynomial time algorithms to solve the single facility case. Realizing NP-hardness of the multi-facility case, we develop a mixed integer programming formulation of it and give a polynomial time heuristic for its solution. Because of the growing concerns of arc reversals in evacuation planning, we introduce quickest Con-traFlowLoc problem and present exact algorithms to solve single-facility case and a heuristic to solve the multi-facility case, both of which have polynomial time complexity. The solutions thus obtained here are practically important, particularly in evacuation planning, to systematize traffic flow with facility allocation minimizing evacuation time.

Journal of Combinatorial Optimization, 2017

A dynamic network introduced by Ford and Fulkerson is a directed graph with capacities and transit times on its arcs. The quickest transshipment problem is one of the most fundamental problems in dynamic networks. In this problem, we are given sources and sinks. Then the goal of this problem is to find a minimum time limit such that we can send the right amount of flow from sources to sinks. In this paper, we introduce a variant of this problem called the mixed evacuation problem. This problem models an emergent situation in which people can evacuate on foot or by car. The goal is to organize such a mixed evacuation so that an efficient evacuation can be achieved. In this paper, we study this problem from the theoretical and practical viewpoints. In the first part, we prove the polynomial-time solvability of this problem in

International Journal of Operations Research, 2018

Network flow models have been widely applied for evacuation planning, which involves moving people from risk areas (sources) to safe places (sinks) using some means of transportation, to optimize traffic flow in urban road networks. The decisions related to the locations of the sinks are also important to maximize the number of evacuees or minimize time for the evacuees to reach the safe places. In this work, we consider the problems of identifying the optimal sink node out of a given set of possible sink-nodes in a single source network to maximize the flow value, and that to minimize the time to transfer a given flow value to the sink in minimum time. Designing efficient computational procedures to solve the problems, we prove that the problems can be solved with strongly polynomial time complexity. Corresponding optimal sink location problems along with identification of ideal direction of the flow based on contraflow approach are also solved in strongly polynomial time. Our resu...

Annals of Operations Research, 2012

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.

Lecture Notes in Computer Science, 2008

In this paper, we consider the evacuation problem for a network which consists of a directed graph with capacities and transit times on its arcs. This problem can be solved by the algorithm of Hoppe and Tardos [1] in polynomial time. However their running time is high-order polynomial, and hence is not practical in general. Thus it is necessary to devise a faster algorithm for a tractable and practically useful subclass of this problem. In this paper, we consider a dynamic network with a single sink s such that (i) for each vertex v the sum of transit times of arcs on any path from v to s takes the same value, and (ii) for each vertex v the minimum v-s cut is determined by the arcs incident to s whose tails are reachable from v. We propose an efficient algorithm for this network problem. This class of networks is a generalization of the grid network studied in the paper [2].

American Journal of Applied Mathematics, 2020

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.

Science China Mathematics, 2018

The optimization models and algorithms with their implementations on flow over time problems have been an emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and efficiently as possible, contraflow configuration is one of the highly applicable operations research (OR) models. It increases the outbound road capacities by reversing the direction of arcs towards the safe destinations that not only minimize the congestion and increase the flow but also decrease the evacuation time significantly. In this paper, we sketch the state of quickest flow solutions and solve the quickest contraflow problem with constant transit times on arcs proving that the problem can be solved in strongly polynomial time O(nm 2 (log n) 2), where n and m are number of nodes and number of arcs, respectively in the network. This contraflow solution has the same computational time bound as that of the best min-cost flow solution. Moreover, we also introduce the contraflow approach with load dependent transit times on arcs and present an efficient algorithm to solve the quickest contraflow problem approximately. Supporting the claim, our computational experiments on Kathmandu road network and on randomly generated instances perform very well matching the theoretical results. For sufficiently large number of evacuees, about double flow can be shifted with the same evacuation time and about half time is sufficient to push the given flow value with contraflow reconfiguration.

Prāgyik Prabāha

Flows over time generalize classical network flows by introducing a notion of time. Each arc is equipped with a transit time that specifies how long flow takes to traverse it, while flow rates may vary over time within the given edge capacities. Ford and Fulkerson’s original 1956 max flow/min cut paper formulated max flow in terms of flows on paths. In 1974, Hoffman pointed out that Ford and Fulkerson’s original proof was quite abstract, and applied to a wide range of max flow-like problems. In this abstract model we have capacitated elements and linearly ordered subsets of elements called paths that satisfy switching property. When two paths P and Q cross at an element (node) then there must be a path that is a subset of the first path up to the crossing element and a subset of the second path after the crossing element. Contraflow is a widely accepted solution approach that increases the flow and decreases the evacuation time making the traffic smooth during evacuation by reversin...