Download presentation

Presentation is loading. Please wait.

Published byHaley Sudweeks Modified over 4 years ago

1
CPSC 433 Artificial Intelligence Or-Tree Modeling Example CPSC 433 T01 & T02 Andrew Kuipers

2
CPSC 433 Artificial Intelligence Problem Description Let T be a set of tasks, and W a set of workers Let e:T W [0,1] be a function mapping tasks and workers onto efficiency ratings For a given sequence of tasks S = t 1, …, t n , assign tasks to workers such that : –the overall time to complete the sequence is minimized, and –no worker is assigned to a task for which he has an efficiency rating of 0

3
CPSC 433 Artificial Intelligence Or-Tree Model Defining a Problem Instance pr = S = t 1, …, t n , A = (w i, t’ 1i, …, t’ mi ) | w i W, t’ ij T S : the sequence of tasks to complete (not yet assigned) A : an assignment of workers to sequences of tasks W: the set of workers T : the set of tasks

4
CPSC 433 Artificial Intelligence Or-Tree Model Evaluating Solutions f(pr) = max( { i=1..mj ( e(t ij, w j ) -1 ) | (w j, t 1j, …, t mj A } ) For each worker, calculate the time to complete its assigned tasks Time taken by worker is 1 / efficiency for a particular task Workers work in parallel The total time is the max of the times taken by each worker

5
CPSC 433 Artificial Intelligence Or-Tree Model When is a branch Solvable / Unsolvable? Erw ,wt ((pr, ?), (pr, no)) (w i, t 1i, …, t mi ) A, j {1…m i } | e(t ji, w i ) = 0 ie: if a worker is assigned a task for which it has 0 efficiency Erw ,wt ((pr, ?), (pr, yes)) Erw ,wt ((pr, ?), (pr, no)) and |S| = 0 * where pr = S, A ie: is not unsolvable, and no tasks left to assign

6
CPSC 433 Artificial Intelligence Or-Tree Model Branching Definition Altern(pr 0, pr 1, …, pr n ) pr 0 = s 0 : S, A pr i = S, Assign(A, w i, s 0 ) w i W Assign the first task in S to each worker on a different branch Assign(A, w, s) = A’ s.t : if (w, t 1, …, t n ) A then (w, t 1, …, t n, s ) A’ else (w, s ) A’

7
CPSC 433 Artificial Intelligence Or-Tree Model pr = S = t 1, …, t n , A = (w i, t’ 1i, …, t’ mi ) | w i W, t’ ij T f(pr) = max( { i=1..mj ( e(t ij, w j ) -1 ) | (w j, t 1j, …, t mj A } ) Erw ,wt ((pr, ?), (pr, no)) (w i, t 1i, …, t mi ) A, j {1…m i } | e(t ji, w i ) = 0 Erw ,wt ((pr, ?), (pr, yes)) Erw ,wt ((pr, ?), (pr, no)) and |S| = 0 * where pr = S, A Altern(pr 0, pr 1, …, pr n ) pr 0 = s 0 : S, A pr i = S, Assign(A, w i, s 0 ) w i W Assign(A, w, s) = A’ s.t : if (w, t 1, …, t n ) A then (w, t 1, …, t n, s ) A’ else (w, s ) A’

8
CPSC 433 Artificial Intelligence Example Problems W = { A, B, C } T = { p, q, r } e : S = p, p, q, r, p, q W = { A, B, C } T = { p, q, r } e: S = q, r, q, p, r, q, p ABC p10.20 q0.510.2 r00.51 ABC p0.200 q0.500.2 r0.10.20.5

Similar presentations

OK

Priority Queues Two kinds of priority queues: Min priority queue. Max priority queue.

Priority Queues Two kinds of priority queues: Min priority queue. Max priority queue.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google