Path Optimization for the Resource-Constrained Searcher

Naval Research LogisticsWe formulate and solve a discrete-time path-optimization problem where a single searcher, operating in a discretized 3-dimensional airspace, looks for a moving target in a finite set of cells. The searcher is constrained by maximum limits on the consumption of several resources such as time, fuel, and risk along any path. We develop a special- ized branch-and-bound algorithm for this problem that utilizes several network reduction procedures as well as a new bounding technique based on Lagrangian relaxation and net- work expansion. The resulting algorithm outperforms a state-of-the-art algorithm for solving time-constrained problems and also is the first algorithm to solve multi-constrained problems

Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems --- including multi-constraint variants --- by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. As opposed to our method, which provides strong models, conventional models are usually highly symmetric and provide very weak lower bounds. Our formulation is equivalent to Gilmore and Gomory's, thus providing a very strong linear relaxation. However, instead of using column-generation in an iterative process, the method constructs a graph, where paths from the source to the target node represent every valid packing pattern. The same method, without any problem-specific parameterization, was used to solve a large variety of instances from several different cutting and packing problems. In this paper, we deal with vector packing, graph coloring, bin packing, cutting stock, cardinality constrained bin packing, cutting stock with cutting knife limitation, cutting stock with binary patterns, bin packing with conflicts, and cutting stock with binary patterns and forbidden pairs. We report computational results obtained with many benchmark test data sets, all of them showing a large advantage of this formulation with respect to the traditional ones

Utilizing Dual Information for Moving Target Search Trajectory Optimization

Various recent events have shown the enormous importance of maritime search-and-rescue missions. By reducing the time to find floating victims at sea, the number of casualties can be reduced. A major improvement can be achieved by employing autonomous aerial systems for autonomous search missions, allowed by the recent rise in technological development. In this context, the need for efficient search trajectory planning methods arises. The objective is to maximize the probability of detecting the target at a certain time k, which depends on the estimation of the position of the target. For stationary target search, this is a function of the observation at time k. When considering the target movement, this is a function of all previous observations up until time k. This is the main difficulty arising in solving moving target search problems when the duration of the search mission increases. We present an intermediate result for the single searcher single target case towards an efficient algorithm for longer missions with multiple aerial vehicles. Our primary aim in the development of this algorithm is to disconnect the networks of the target and platform, which we have achieved by applying Benders decomposition. Consequently, we solve two much smaller problems sequentially in iterations. Between the problems, primal and dual information is exchanged. To the best of our knowledge, this is the first approach utilizing dual information within the category of moving target search problems. We show the applicability in computational experiments and provide an analysis of the results. Furthermore, we propose well-founded improvements for further research towards solving real-life instances with multiple searchers

An approximate solution technique for the constrained search path moving target search problem

A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set of cells from which he can choose is a function of the cell chosen in the previous time period. The problem is to find a searcher path, i.e., a sequence of search cells, that minimizes the probability of not detecting the target in a fixed number of time periods. The problem is formulated as a nonlinear program and solved for a local optimum by a simple implementation of the convex simplex methodNaval Postgraduate School, Monterey, CA.http://archive.org/details/approximatesolut15eaglNaval Postgraduate School, Monterey, CA.NAApproved for public release; distribution is unlimited

An ant system algorithm for automated trajectory planning

The paper presents an Ant System based algorithm to optimally plan multi-gravity assist trajectories. The algorithm is designed to solve planning problems in which there is a strong dependency of one decision one all the previously made decisions. In the case of multi-gravity assist trajectories planning, the number of possible paths grows exponentially with the number of planetary encounters. The proposed algorithm avoids scanning all the possible paths and provides good results at a low computational cost. The algorithm builds the solution incrementally, according to Ant System paradigms. Unlike standard ACO, at every planetary encounter, each ant makes a decision based on the information stored in a tabu and feasible list. The approach demonstrated to be competitive, on a number of instances of a real trajectory design problem, against known GA and PSO algorithms