Abstract—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. I. INTRODUCTION Target search and rescue path planning is a top priority life-saving task facing human teams when struggling with man-made and natural disasters. It is a pervasive problem increasingly occurring over a variety of civilian and military domains such as homeland security and emergency management. The basic discrete SAR or optimal searcher path problem involving a stationary target is known to be NP-Hard [1]. SAR may be generally characterized through multiple dimensions and attributes including: one-sided search in which targets are non-responsive toward searcher‟s actions, two-sided, describing target behaviour diversity (cooperative, non-cooperative or anti-cooperative), stationary Vs. moving target search, discrete Vs. continuous time and space search (efforts indivisibility/divisibility), observation model, static/dynamic as well as open and closed-loop decision models, pursued objectives, target and searcher multiplicity and diversity. Early work on related search problems emerges from search theory, [2], [3]. Search-theoretic approaches mostly relate to the effort (time Manuscript received October 9, 2012; revised January 18, 2013. J. Berger is with the Defence Research and Development Canada – Valcartier, Quebec City, Canada (e-mail: jean.berger@drdc-rddc.gc.ca). N. Lo is with the T-OptLogic Ltd., Quebec City Canada (e-mail: nassirou.lo@t-optlogic.com). M. Noel is with the Téluq, Université du Québec, Quebec City Canada (e-mail: noel.martin@teluq.uqam.ca). spent per visit) allocation decision problem rather than path construction. Based upon a mathematical framework, efforts have increasingly been devoted to algorithmic contributions to handle more complex dynamic problem settings and variants [4]–[7]. In counterpart, many contributions on search path planning may be found in the robotics literature in the area of robot motion planning [8] and, namely, terrain acquisition [9], [10] and coverage path planning [11]–[13]. Robot motion planning explored search path planning, primarily providing constrained shortest path type solutions for coverage problem instances [14], [15]. These studies typically examine uncertain search environment problems with limited prior domain knowledge, involving unknown sparsely distributed static targets and obstacles. Recent taxonomies and comprehensive surveys on target search problems from search theory and artificial intelligence distributed robotic control perspectives may be found in [5], [17]–[19] respectively. Exact problem-solving methods for sequential decision search problem formulations show computational complexity to scale exponentially. For instance, dynamic programming [5], [7], [19], [20] or tree-based search techniques [21] may satisfactorily work under specific constraints and conditions but ultimately face the curse of dimensionality, showing poor scalability even for moderate size problem. This paved the way to the development of efficient heuristic and approximate methods. But published procedures still deliver approximate solution and mostly fail to provably estimate real performance optimality gap for practical size problems, questioning their real expected relative efficiency. In this paper, we propose a new exact mixed-integer linear programming formulation to optimally solve the single agent discrete search path planning problem for a stationary object. In the problem model, „open-loop with anticipated feedback‟ refers to offline planning, while capturing information resulting from predicted agent observations (projected cell visit action outcome) as opposed to real feedback. Anticipated feedback augments pure open-loop formulations which simply ignore information feedback, while significantly improving solution quality, and mitigating computational complexity limitations traditionally associated with closed-loop problem formulations (e.g. dynamic programming, and partially observable Markov decision processes). In that setting, the open-loop with anticipated feedback information (observations) decision model involves an agent (the searcher) with imperfect sensing capability (but false alarm -free) searching an area (grid) to maximize cumulative probability of success in detecting a target, given a time horizon and prior cell occupancy probability distribution. The model takes advantage of anticipated feedback information resulting from observations outcomes along the path to update target occupancy beliefs and make better decisions. A network flow representation significantly Exact Solution for Search-and-Rescue Path Planning Jean Berger, Nassirou Lo, and Martin Noel International Journal of Computer and Communication Engineering, Vol. 2, No. 3, May 2013 266 DOI: 10.7763/IJCCE.2013.V2.185