PDF-article Sw arm Optimization for Minimax Problems E

C Lask ari KE arsop oulos and MN rahatis Departmen of Mathematics Univ ersit of P atras Arti cial In telligence Researc Cen ter UP AIR C GR26110 P atras Greece elena k ostasp vrahatis mathupatrasgr Abstract This pap er in estigates the abilit of the. Lauren Feinstein . lpf24@cornell.edu. Vladimir . Kovalevsky vk285@cornell.edu. Nicolas . Begasse. . nb442@cornell.edu. Presentation Overview. Optimization Overview. Disc Brake Analysis. Response Surface Optimization. Two Player Game Playing. Use backtracking to implement computer version of 2-player games: tic-tac-toe, chess, checkers, connect four. Minimax algorithm: . Backtracking algorithm for choosing next move in an 2-player game. Jonathan Hollingshead. Terms used in this presentation. Web page or page – a single document . on the Internet, typically with a single topic. Web site or site – a collection of individual web pages interconnected by hyperlinks. Optimization methods help us find solutions to problems where we seek to find the best of something.. This lecture is about how we formulate the problem mathematically.. In this lecture we make the assumption that we have choices and that we can attach numerical values to the ‘goodness’ of each alternative.. (Chapter 5). World Champion chess player Garry Kasparov . is . defeated by IBM’s Deep Blue chess-playing computer in a . six-game . match in May, . 1997. (. link. ). © Telegraph Group . Unlimited 1997. Presented by. : . Samia. . Abid. Student: MS(CS). Supervised by: Dr. . Nadeem. . Javaid. Associate Professor, Department of Computer Science, . COMSATS Institute of Information . Technology, 44000, Islamabad, Pakistan.. Borrowed & modified from. https://web.stanford.edu/group/sisl/k12/optimization/. So… what is mathematical optimization, anyway?. “Optimization” comes from the same root as “optimal”, which means . 14 Deltoid. 11 . Infraspinatus. 12 . Teres. minor. 13. 22b Long head of triceps brachii. 22 Triceps brachii. 25 Profunda brachii artery. 24 radial nerve. 42 Extensor carpi radialis longus. 43 Extensor carpi . earch. Why study games?. Games can be a good model of many competitive activities. Military confrontations, negotiation, auctions, …. Games are a traditional hallmark of intelligence. Contrarian viewpoint (textbook): . J. McCalley. 1. Real-time. Electricity markets and tools. Day-ahead. SCUC and SCED. SCED. Minimize f(. x. ). s. ubject to. h. (. x. )=. c. g. (. x. ). <. . b. BOTH LOOK LIKE THIS. SCUC: . x. contains discrete & continuous variables.. Games and adversarial s earch Why study games? Games can be a good model of many competitive activities Military confrontations, negotiation, auctions, … Games are a traditional hallmark of intelligence Or how to be 1-competitive with any set of strategies. Slides courtesy of . Avrim. Blum . Plan. Online Algorithms. Game Theory. Using “expert” advice. We solicit . N. “experts” for their advice. (Will the market go up or down?). Uncertainty. Irreducible uncertainty . is inherent to a system. Epistemic uncertainty . is caused by the subjective lack of knowledge by the algorithm designer. In optimization problems, uncertainty can be represented by a vector of random variables . Date Monday June 17 2013 till Thursday June 20 2013TimeVenue Included 2 Co31ee Breaks and a Lunch EE Short CourseTopics to be CoveredDue to the limited space RSVP is required byemailing the local coo