Toward optimizing static target search path planning

Discrete search and rescue path planning is known to be hard, and problem-solving techniques proposed so far mainly fail to properly assess optimality gap for practical size problems. A new mixed-integer linear programming (MIP) formulation is proposed to optimally solve the single agent discrete search and rescue (SAR) path planning problem. The approach lies on a compact open-loop SAR with anticipated feedback problem model to efficiently maximize cumulative probability of success in detecting a target. Anticipated feedback information resulting from possible observations outcomes along the path is exploited to update target occupancy beliefs. A network representation is utilized to simplify modeling, facilitate constraint specification and speed-up problem-solving. The proposed MIP approach rapidly yields optimal solutions for realistic problems using parallel processing CPLEX technology, while providing for the first time a robust upper bound on solution quality through Lagrangean integrality constraint relaxation. Fast computation naturally allows extending open-loop modeling to a closed-loop environment to progressively integrate real-time action outcomes as they occur on a rolling time horizon. Comparative performance results clearly show the value of the approach Index Terms-search path planning, search and rescue, linear programming.

Zenodo (CERN European Organization for Nuclear Research), 2014

Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multiagent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problemsolving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Computers & Operations Research, 2015

Search and rescue path planning is known to be computationally hard, and most techniques developed to solve practical size problems have been unsuccessful to estimate an optimality gap. A mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-agent discrete search and rescue (SAR) path planning problem, maximizing cumulative probability of success in detecting a target. It extends a single agent decision model to a multi-agent setting capturing anticipated feedback information resulting from possible observation outcomes during projected path execution while expanding possible agent actions to all possible neighboring move directions, considerably augmenting computational complexity. A network representation is further exploited to alleviate problem modeling, constraint specification, and speed-up computation. The proposed MIP approach uses CPLEX problem-solving technology in promptly providing nearoptimal solutions for realistic problems, while offering a robust upper bound derived from Lagrangean integrality constraint relaxation. Modeling extension to a closed-loop environment to incorporate real-time action outcomes over a receding time horizon can even be envisioned given acceptable run-time performance. A generalized parameter-driven objective function is then proposed and discussed to suitably define a variety of user-defined objectives. Computational results reporting the performance of the approach clearly show its value.

Optimization Letters, 2015

Discrete search path planning is known to be a NP-Hard problem, and problem-solving methods proposed so far rely on heuristics with no way to reasonably estimate solution quality for practical size problems. Departing from traditional nonlinear model formulations, a novel information-theoretic -based approach using integer linear programming (ILP) is proposed to optimally solve the discrete open-loop centralized search path planning problem with anticipated feedback, involving a team of homogeneous agents. The approach takes advantage of objective function separability and conditional probability independence of observations to efficiently minimize expected system entropy. A network representation is exploited to simplify modeling, reduce constraint specification and speed-up problem-solving. near-optimal solutions for realistic problems while providing for the first time, a robust lower bound through Lagrangian relaxation. Long planning problem horizon may be dynamically adapted by periodically solving new problem instances incorporating actual observation outcomes from previous episodes over receding horizons. Computational results clearly show the value of the approach in comparison to a myopic heuristic over various problem instances.

Annals of Operations Research, 2016

As discrete multi-agent static open-loop target search path planning known to be computationally hard recently proved to be solvable in practice in the homogeneous case, its heterogeneous problem counterpart still remains very difficult. The heterogeneous problem introduces broken symmetry reflected by dissimilar sensing ability/capacity, agent capability and relative velocity and, is further exacerbated when operating under near real-time problemsolving constraints, as key decision variables grow exponentially in the number of agents. Departing from the homogeneous agent model already published, new integer linear and quadratic programming formulations are proposed to reduce computational complexity and near-optimally solve the discrete static search path planning problem involving heterogeneous agents. The novelty consists in taking advantage of typical optimal path solution property to derive new tractable problem models. At the expense of a slightly accrued computational complexity, the proposed quadratic integer program formulation conveys considerable benefit by keeping key decision variables linear in the number of agents. The convexity property of its defined objective function further allows ensuring global optimality when a local optimum is computed. Special agent network representations capturing individual agent decision moves are also devised to simplify problem modeling and expedite constraint modeling specification. As a result, cost-effective quadratic program implementation for realistic problems may be achieved to rapidly compute near-optimal solutions, while providing a robust bound on solution quality through Lagrangian relaxation.

In this paper, we propose a nonlinear integer program to model a path planning for a single airborne search asset in a continuous space and time for a fixed time period, through a connected space. The intent is to maximize the detection of a cooperative target (e.g., search and rescue). The proposed model is based on the assumption of existing a priori information (e.g., result of information fusion) to establish a spatial distribution of possible locations. Solution of the nonlinear program provides a path as well as effort allocation to each location. We illustrate the results of the paper on an empirical example.

Naval Research Logistics, 2010

We 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 specialized 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 network 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.

2010

We describe the first phase development of a path finding simulation in a military environment. This concept demonstrator can be used for mission planning by constructing what-if scenarios to investigate trade-offs such as location of deployment and mode of transport.

2010 13th International Conference on Information Fusion, 2010

In 1974 the U.S. Coast Guard put into operation its first computerized search and rescue planning system CASP (Computer-Assisted Search Planning) which used a Bayesian approach implemented by a particle filter to produce probability distributions for the location of the search object. These distributions were used for planning search effort. In 2003, the Coast Guard started development of a new decision support system for managing search efforts called Search and Rescue Optimal Planning System (SAROPS). SAROPS has been operational since January, 2007 and is currently the only search planning tool that the Coast Guard uses for maritime searches. SAROPS represents a major advance in search planning technology. This paper reviews the technology behind the tool.

IEEE Robotics and Automation Letters, 2020

In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to be NP-hard, and present the first set of Mixed-Integer Linear Programming (MILP) models to tackle the MESPP problem. Our models are the first to encompass multiple searchers, arbitrary capture ranges, and false negatives simultaneously. While state-of-the-art algorithms for MESPP are based on simple path enumeration, the adoption of MILP as a planning paradigm allows to leverage the powerful techniques of modern solvers, yielding better computational performance and, as a consequence, longer planning horizons. The models are designed for computing optimal solutions offline, but can be easily adapted for a distributed online approach. Our simulations show that it is possible to achieve 98% decrease in computational time relative to the previous stat...