1 / 11

Random/Exhaustive Search

Random/Exhaustive Search. Generate and Test Generate a candidate solution and test to see if it solves the problem Repeat Information used by this algorithm You know when you have found the solution. Hill Climbing. Generate a candidate solution by modifying the last solution, S

mamaral
Download Presentation

Random/Exhaustive Search

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Random/Exhaustive Search • Generate and Test • Generate a candidate solution and test to see if it solves the problem • Repeat • Information used by this algorithm • You know when you have found the solution

  2. Hill Climbing • Generate a candidate solution by modifying the last solution, S • If the new solution, N, is “better” than S then S := N • Repeat • Local Search • Information used by this algorithm • Compare two candidate solutions and tell which is better

  3. Population of Hill Climbers • Randomly generate initial population of hill climbers (Randomly generate initial candidate solutions) • Do hill climbing in parallel • After time t, choose best solution in population • Information used by this algorithm • Same as hill climbing

  4. Genetic Algorithms • Population of information exchanging hill climbers • Concentrates resources in promising areas of the search space • Information used: • Same as hillclimbing

  5. Hard problems • Computational complexity, problem size = n • Binary Search O(log(n)) • Linear Search O(n) • Bubble Sort O(n^2) • Scheduling NP-complete (at least exponential == O(a^n)

  6. Hard problems • Poorly defined

  7. Search as a solution to hard problems • Strategy: generate a potential solution and see if it solves the problem • Make use of information available to guide the generation of potential solutions • How much information is available? • Very little: We know the solution when we find it • Lots: linear, continuous, … • Modicum: Compare two solutions and tell which is “better”

  8. Search tradeoff • Very little information for search implies we have no algorithm other than RES. We have to explore the space thoroughly since there is no other information to exploit • Lots of information (linear, continuous, …) means that we can exploit this information to arrive directly at a solution, without any exploration • Modicum of information (compare two solutions) implies that we need to use this information to tradeoff exploration of the search space versus exploiting the information to concentrate search in promising areas

  9. Exploration vs Exploitation • More exploration means • Better chance of finding solution (more robust) • Takes longer • More exploitation means • Less chance of finding solution, better chance of getting stuck in a local optimum • Takes less time

  10. Choosing a search algorithm • The amount of information available about a problem influences our choice of search algorithm and how we tune this algorithm • How does a search algorithm balance exploration of a search space against exploitation of (possibly misleading) information about the search space? • What assumptions is the algorithm making?

  11. Genetic Algorithm • Generate pop(0) • Evaluate pop(0) • T=0 • While (not converged) do • Select pop(T+1) from pop(T) • Recombine pop(T+1) • Evaluate pop(T+1) • T = T + 1 • Done

More Related