APPROXIMATE DYNAMIC PROGRAMMING FOR OPTIMAL SEARCH WITH AN OBSTACLE

Yasin GÖÇGÜN

Öz


In this paper, we study a class of optimal search problems where the search region includes a target and an obstacle, each of which has some shape. The search region is divided into small grid cells and the searcher examines one of those cells at each time period with the objective of finding the target with minimum expected cost. The searcher may either take an action that is quick but risky, or another one that is slow but safe, and incurs different cost for these actions. We formulate these problems as Markov Decision Processes (MDPs), but because of the intractability of the state space, we approximately solve the MDPs using an Approximate Dynamic Programming (ADP) technique and compare its performance against heuristic decision rules. Our numerical experiments reveal that the ADP technique outperforms heuristics on majority of problem instances.

Anahtar Kelimeler


Optimal search, Markov decision processes, Approximate dynamic programming

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Referanslar


Derr K, Manic, M. “Multi-robot, multi-target particle swarm optimization search in noisy wireless environments”. Proceedings of the 2nd conference on human system interactions, Catania, Italy, 2009.

Najemnik J, Geisler WS. “Eye movement statistics in humans are consistent with an optimal search strategy”, J. Vis. 8, 1-14, 2008.

Wettergren TA. “Performance of search via track-before-detect for distributed sensor networks”, IEEE Transactions on Aerospace and Electronic Systems, 44, 2008.

Benkoski S J. Monticino, M. G., Weisinger, J. R.. “A survey of the search theory literature”. Naval Research Logistics. 38, 469-494, 1991.

Dobbie JM. “A survey of search theory”. Operations Research. 16(3), 527–537, 1968.

Haley WB, Stone LD. “Search Theory and Applications”, Plenum Press, New York, 1980.

Stone LD. “Theory of Optimal Search”, Academic Press, 1975.

Washburn A.” Search and Detection”, Fourth Edition, Institute for Operations Research and the Management Sciences, 2002.

Dell RF, Eagle JN. Martins, G. H. A., Santos, A. G. “Using multiple searchers in constrained-path, moving-target search problems”. Naval Research Logistics. 43, 463-480, 1996.

Eagle JN, Yee JR. “An optimal branch-and-bound procedure for the constrained path, moving target search problem”, Operations Research. 38, 110-114, 1990.

Singh S. Krishnamurthy, V. “The optimal search for a markovian target when the search path is constrained: the infinite-horizon case”. IEEE Transactions on Automatic Control, 2003.

Botea A, Baier J, Harabor D, Hernandez C. “Moving target search with compressed path databases”. In Proceedings of ICAPS-13, 2013.

Chung TH, Burdick JW. “A decision-making framework for control strategies in probabilistic search”. Proceedings of IEEE International Conference on Robotics and Automation, 2007.

Chung TH. “On probabilistic search decisions under searcher motion constraints”. Algorithmic Foundations of Robotics, 2010.

Lossner U, Wegener I. “Discrete sequential search with positive switch cost”. Mathematics of Operations Research. 7(3), 426–440, 1982.

Ross SM. “A problem in optimal search and stop”. Operations Research. 17, 984–992, 1969.

Snider J. “Optimal random search for a single hidden target”. Physical Review. 83, 011105, 2011.

Kulich M, Preucil L, Jose J, Bront M. “Single robot search for a stationary object in an unknown environment”, IEEE International Conference on Robotics Automation, 2014.

Wegener I. “The discrete sequential search problem with nonrandom cost and overlook probabilities”. Mathematics of Operations Research. 5, 373–380, 1980.

Shechter SM, Ghassemi F, Gocgun Y, Puterman ML. “Trading off quick versus slow actions in optimal search”. Operations Research. 63, 353-362, 2015.

Zhao Y, Patek SD, Beling PA. “Decentralized Bayesian Search Using Approximate Dynamic Programming Methods”. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 38, 2008.

Bertsekas D, Tsitsiklis J. “Neuro-Dynamic Programming”, Athena Scientific, 1996.

Powell WB. “Approximate Dynamic Programming: Solving the Curses of Dimensionality”, Wiley, 2007.

Adelman D. “Price-directed replenishment of subsets: methodology and its application to inventory routing”. Manufacturing and Service Operations Management. 5, 4, 348-371, 2003.

Adelman D. “A price-directed approach to stochastic inventory routing”. Operations Research. 52, 4, 499-514, 2004.

De Farias DP, Roy BV. “The linear programming approach to Approximate Dynamic Programming”. Operations Research. 51, 850-865, 2003.

Chang HS, Fu MC, Hu J, Marcus SI. “Simulation-based algorithms for Markov Decision Processes”, Springer, 2007.

Sutton RS, Barto AG. “Reinforcement Learning : an introduction”, MIT Press, 1998.

Maxwell MS, Henderson SG, and Topaloglu H. “Tuning Approximate Dynamic Programming Policies for Ambulance Redeployment via Direct Search”. Stochastic Systems. 3, 1-40, 2013.

Suman B, Kumar B. “A survey of simulated annealing as a tool for single and multiobjective optimization”. Journal of the Operational Research Society. 57, 1143–1160, 2006.


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Telif Hakkı (c) 2019 Selçuk Üniversitesi Mühendislik, Bilim ve Teknoloji Dergisi

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