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# s02lec23 - 15.053 Two types of Complexity Thursday May 9...

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1 15.053 Thursday, May 9 Heuristic Search: methods for solving difficult optimization problems Handouts: Lecture Notes See the introduction to the paper on Very Large Scale Neighborhood Search. (It’s on the web site.) 2 Two types of Complexity. 1. Problems with complex and conflicting objectives subject to numerous restrictions. z most problems in practice 2. Problems that may be easily understood but for which there are so many possible solutions, one cannot locate the best one. z games (chess, go) z IPs such as the traveling salesman problem. 3 Example: Fire company location. Consider locating fire companies in different districts. Objective: use as few fire companies as possible so that each district either has a fire company in it, or one that is adjacent. 4 Example for the Fire Station Problem 1 2 3 4 5 6 7 8 9 11 10 12 14 15 13 16 5 Reason for heuristics. Heuristics are usually much faster than optimization, such as branch and bound Heuristics, if well developed, can obtain excellent solutions for many problems in practice Some special cases of heuristics z Construction methods z Improvement methods 6 A construction heuristic for the TSP begin choose an initial city for the tour; while there are any unvisited cities, then the next city on the tour is the nearest unvisited city; end Construction heuristics: carries out a structured sequence of iterations that terminates with a feasible solution. It may be thought of as building a tour, but the intermediate steps are not always paths.

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7 Illustration for TSP 8 Illustration for TSP 9 A more effective but slower construction heuristic The previous heuristic always added the next city at the end of the current path. Idea: add the next heuristic anywhere in the current path Better idea: keep a cycle at each iteration and insert the next city optimally into the cycle This is an insertion heuristic 10 Start with a tour for 3 cities 11 Insert the 4 th city 12 Insert the 5 th city
13 Insert the 6 th city 14 Insert the 7 th city 15 Insert the 8 th city 16 Insert the 9 th city 17 Insert the 10 th city 18 Insert the 11 th city

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19 Insert the 12 th city 20 Insert the 13 th city 21 Insert the 14 th city 22 Insert the 15 th city 23 Insert the 16 th city 24 Insert the 17 th city
25 Insert the 18 th city 26 Insert the 19 th city 27 Insert the final city

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s02lec23 - 15.053 Two types of Complexity Thursday May 9...

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