Evacuation Optimization with Minimum Clearance Time

Abstract

We are under the threats of natural or human-created disasters. Disasters are unavoidable and are mostly uncertain to happen. If occurs, the situation becomes vulnerable, effects badly the society, and its socio-economic status. Its direct impact is on the traffic systems. On the other hand, the increasing number of complex traffic networks brought difficulty in managing the rush hour traffic as well as the large events in urban areas. The optimal use of the vehicles and their assignments to the appropriate shelters from the disastrous zones are highly complicated in emergency situations. The maximum efficiency and effectiveness of the evacuation planning can be achieved by the appropriate assignment of the transit-vehicles during pre- and post-disaster operations. The evacuation planning problem deals with sending the maximum number of evacuees from the danger zones to the safe zones in minimum time, as efficiently as possible. It can be further classified into microscopic and macroscopic planning. The microscopic planning deals with the individual evacuee’s behavior in which some probabilistic laws for individual evacuees movement are presented and mainly based on the simulation approaches. But in macroscopic planning, it is principally based on optimization approaches where the evacuees are treated as the homogeneous group and only the common characteristics are considered. Optimization approaches on such macroscopic evacuation planning can further be classified as a heuristic approach, population optimization, modeling as fluid dynamics, mathematical programmings, traffic management, optimal evacuation destination, and network flow formulation. Among them, the dynamic network flow formulation has been found suitable evacuation optimization approach with the variants of flow maximization and/or time minimization problems. In such formulations, time can be considered as discrete or continuous. Evacuation planning problems are handled with different prospectives, namely, the transit-based, car-based, and pedestrian movements depending upon the movement of the evacuees on the evacuation scenarios. The transit-based planning problems are to vi minimize the duration of evacuation by routing and scheduling a fleet of vehicles, say buses, as the bus-based evacuation planning problem. Such a problem is an important variant of the vehicle routing problem. Traffic route guidance, destination optimization, and optimal route choice are some of the approaches to accelerate the evacuation planning process. Their effectiveness depends upon the evacuee arrival patterns at the pickup locations and their appropriate assignment to the transit-vehicles in the available evacuation network. An embedded network is composed of two constituent sub-networks, namely, the primary and the secondary sub-networks. Evacuees are to be collected at the pickup locations of the primary sub-network from the danger zone(s) and are to be assigned to transit-vehicles in the secondary sub-network. For time minimization evacuation planning problems, evacuees are to be collected in the earliest arrival flow pattern at zero transit times and is to be followed by dominant vehicle assignments. Transit-vehicles are provided from the bus depot in the secondary sub-network. Pickup locations are taken as the sources for the subsequent process to minimize the overall network clearance time from the danger zone to safety. In our work, we have proposed an integrated optimization approach in such an embedding to achieve the minimum clearance time. The earliest arrival pattern respects the partial lane reversal strategy, whereas the better assignments are based on the dominance relations concerning the evacuation duration. 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 prioritized sub-network. By treating such pickup locations as sources, the available set of transit-buses is assigned simultaneously in the secondary sub-network to shift the evacuees finally to the sinks with minimum clearance time. The lane reversal strategy significantly reduces the evacuation time and maximizes the flow of evacuees, 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.