Dynamic Traveling Salesman Problem in Stochastic-State Network Setting for Search-and-Rescue Application

David Fajardo, S. Travis Waller
2012 Transportation Research Record  
the appropriate number of search-and-rescue units, the necessary resources to allow the timely rescue of victims, and an efficient and flexible plan for units to follow. The focus of this paper is the development and determination of the solution to a simplified network-based mathematical model of the search-and-rescue problem that allows description of the characteristics of the problem that have not been explored in the past, namely, the way in which information affects the dynamics of a
more » ... e operation. The two main features that are included in this model are referred to in the literature as "online information" and "late information." Under an online information setting, problem information is assumed to be disclosed throughout the problem and thereby affects the decisions that are made. The first, key aspect of a problem formulation that allows consideration of online information is the ability of the decision-making process to account not only for information gathered en route but also for the possibility of gathering information in the future. When one explicitly accounts for information that is known to be obtained in the future, better decisions can be made in the present. The second feature, which is not mutually exclusive to the concept of online information, is the late information setting (2). In this setting, some problem variables are assumed to be unknown until they are directly observed or until variables have been observed indirectly as part of the decision-making process. In the case of this problem, the late information assumption refers to the node demands; that is, the number of units to be rescued at each node is not known until a routing unit visits the node itself or the scenario set is reduced to reveal that number. In contrast, a problem that does not account for this late information feature would be one in which the information is revealed at preestablished points that are not affected by the intermediate decisions. The problem is framed as a traveling salesman problem (TSP), in which the presence of victims at each node can be modeled as part of what is referred to here as a stochastic-state network (SSN). This modeling choice creates an implicit correlation between these demand variables that will affect the routing policies developed. The problem is formulated as a Markovian decision process (MDP). Because of the complexity of the problem, a heuristic based on a two-stage stochastic programming approximation of the problem solved on an aggregated set of network states is provided. The following problem is addressed in this paper: given a single vehicle and an SSN, determine the optimal online routing policy to minimize the total expected routing costs. An "online policy" is defined to be the set of routing decisions conditional on the information acquired at each stage of the problem. The problem presented in this paper was motivated by the need for a solution to be used in a search-and-rescue application and is formulated as a dynamic traveling salesman problem in a stochastic-state network setting. This problem formulation features a full-recourse decision framework and stochastic demands that are revealed only through direct observation. This problem is defined in a stochastic-state network setting, which allows the modeling of implicitly correlated demand stochasticity. The problem is then formulated as a Markovian decision process, and, finally, a heuristic solution is provided. The heuristic solution is based on a two-stage stochastic program with recourse solved on a set of aggregated networks generated by the use of an aggregating function. Subsets of the feasible solutions obtained at each stage are fixed, and the heuristic is used iteratively to further refine the routing policy. Recent natural disasters have highlighted the need for efficient emergency response operations. Hurricanes Katrina and Rita exposed many flaws in U.S. emergency response plans, and no aspect received more attention than the delays of response to search-and-rescue missions. Soon after the hurricanes, U.S. military leaders requested the creation of a national search-and-rescue plan, recognizing that both natural disasters and terrorist attacks may occur at any moment, leaving search-and-rescue task forces with little time to react (1). An emergency response plan consists of many different operations, which can be analyzed at various levels. Evacuation, search, rescue, delivery of goods, and rebuilding are all critical parts of an emergency response action. An optimal emergency response plan would allocate resources to each of these operations to minimize the impact of an emergency on society. However, because of the large amount of uncertainty and the large number of variables involved in an emergency operation, modeling and determination of the solution to such an allocation problem becomes difficult. As a result, a way to solve the related subproblems as efficiently and accurately as possible must be found. Search and rescue is one of the subproblems of an emergency response operation. The search-and-rescue problem consists of the detection and rescue of victims whose locations may or may not be known a priori. A proper search-and-rescue plan will assign
doi:10.3141/2283-13 fatcat:jd3fhsvv3jas7b7apobude4iti