In this chapter, we pose and analyze a regional evacuation network design problem in order to provide a pre-event strategic planning tool for this purpose. We pro-pose a mixed integer linear program to devise effective and controlled evacuation
Figure 7 Open Shelter Locations with λ = 5 and ξ = 1.2
networks for sending evacuees from their origins to shelters before extreme events such as hurricanes happen. The SEND model determines the optimal evacuation routes based on time and capacity constraints. Also, it selects shelters from a set of potential shelter candidates and decides flow assignments on the optimal routes while minimizing the total evacuation cost.
To solve this model for large scale instances, we develop an efficient solution methodology based on BD approach, which takes advantage of specific characteristics of the SEND problem. We utilize a few techniques to accelerate BD approach: adding surrogate constraints to MsP to improve the lower bound of the objective value of SEND in BD framework, solving MsP with a loose optimality gap in the first several iterations, adding multiple optimality cuts in each iteration by generating multiple feasible solutions of SEND heuristically, and strengthening Benders optimality cuts.
We design and implement an experimental design to test our BD technique us-ing a Texas-based evacuation scenario. The SEND model and BD approach can be efficiently and effectively applied to a large scale evacuation scenario, and we bench-mark the computational performance of our BD technique against the traditional branch-and-cut solution methods, which are implemented by CPLEX 12.2. We also design and implement an experiment to study the effects of parameters T , λ, and ξ on the optimal solution of SEND.
CHAPTER IV
MULTI-AGENT SIMULATION PROBLEM
In the SEND problem, we construct an optimization MIP model to analyze a regional evacuation network design problem in order to provide a pre-event strategic plan-ning tool. The optimization MIP model determines the optimal evacuation network based on time and capacity constraints. It selects shelters from all potential candi-dates, chooses evacuation routes and decides flow assignments while minimizing the total costs. However, a centralized optimization model cannot handle unexpected situations, such as people not following the designated evacuation routes and/or not going to the designated shelters. In this case, evacuees may choose the routes or destinations that look favorable to themselves but not the routes or destinations rec-ommended by the optimal evacuation plan. This may cause traffic jams in some road segments and make evacuees suffer a longer evacuation time. Furthermore, due to the difficulties in communication and coordination, especially for a large population in a chaotic emergency situation, evacuees may fail to follow the evacuation instruc-tions because of misunderstandings and confusion. These situainstruc-tions may cause the optimal evacuation plan to not be achieved smoothly and successfully.
To handle these unexpected situations and to check the robustness of our opti-mization model, we conduct a multi-agent simulation (MAS) model. In the decen-tralized MAS model, every evacuee can make decisions and change those decisions during evacuation. The MAS model simulates the situation in which evacuees have the freedom to choose their own routes and their own destinations after they have been told the designated routes as guidelines. In the MAS problem, we study the effect of probabilities for people following the designated routes and the designated shelters on the total evacuation time, the traffic jam situation and the traveling time
for individuals.
In our optimization model, there is no time component considered. We consider each edge as having a finite capacity on the total flow that it can handle in an evacuation event. This capacity is considered at a macroscopic level rather than with fine granularity as in a dynamic traffic assignment study. As a consequence, we consider a constant traffic speed and a constant traverse time for each edge.
However, it is more complicated in real-world situations. Traffic speed and traverse time are normally not constant, but are related to traffic density on the road. To consider traffic speed as a variant with traffic density, we include traffic speed as a function of traffic density to the MAS model, so traffic speed and traverse time are changed dynamically with traffic density. Moreover, the MAS enables us to model the situation in which evacuees leave in groups at a time sequence. A value is assigned to the range of leaving times for each group. An evacuee may leave at any time in the range of leaving times for his group.
Furthermore, information sharing is an important difference between a central-ized system and a decentralcentral-ized system. In a centralcentral-ized system, information sharing is assumed as perfect for the whole system; however, in a decentralized system, this is not the case. In evacuation problems, the information, which can influence the performance of the system, may or may not be shared perfectly. For example, evac-uees may not know real-time traffic conditions and the status of shelters. In the MAS problem, the interactions between evacuees are considered as a type of approach to sharing information. We consider two types of information shared in the system.
• Information shared among evacuees-If there is slow traffic on a road segment, people who are driving on this road may call their connections (e.g. their friends, their relatives and their colleagues) to inform them the slow traffic.
Then people who receive this message may make a detour.
• Information sent from a radio station to all evacuees-we consider a radio tion broadcast as another approach to sharing information. The radio sta-tion broadcasts the real-time traffic condista-tions and the status of shelters to all drivers (i.e. shelters are full or not). Evacuees may change their routes based on this received information.
We study the effect of the shared information on the evacuation performance.