Population-Based Search 2-3-16 Reading Quiz Question 1: Which of - - PowerPoint PPT Presentation
Population-Based Search 2-3-16 Reading Quiz Question 1: Which of the following attributes do stochastic beam search and genetic algorithms NOT share. a) a temperature parameter b) a population of states c) probabilistic survival of
Question 1: Which of the following attributes do stochastic beam search and genetic algorithms NOT share. a) a temperature parameter b) a population of states c) probabilistic survival of individuals d) exhaustive generation of neighbors
state = get_candidate() best_state = state temp = INIT_TEMP for round = 1:MAX_ITERS: neighbor = random_step(state) if cost(neighbor) < cost(best_state) best_state = neighbor if accept(state, neighbor, temp) state = neighbor temp *= DECAY return best_state function accept(state, neighbor, temp): delta = cost(state) - cost(neighbor) r ~ U[0,1] return r < e^(delta / temp)
INIT_TEMP = 20; DECAY = .95; round = 4
Given the following state:
If the following neighbor is generated, what is the probability that it is accepted?
If the following neighbor is generated, what is the probability that it is accepted?
function accept(state, neighbor, temp): delta = cost(state) - cost(neighbor) r ~ U[0,1] return r < e^(delta / temp)
population = [POP_SIZE random states] temp = INIT_TEMP for i = 1:MAX_ITERS: candidates = [] for individual in population: add all neighbors of individual to candidates population = [POP_SIZE lowest-cost candidates] temp *= DECAY return best state encountered
population = [POP_SIZE random states] temp = INIT_TEMP for i = 1:MAX_ITERS: candidates = [] for individual in population: add all neighbors of individual to candidates population = gibbs_samples(candidates, temp, POP_SIZE) temp *= DECAY return best state encountered
function gibbs_samples(candidates, temp, POP_SIZE): weights = [e^(-cost(n)/temp) for each candidate n] distribution = [weights[n] / sum(weights) for each candidate n] population = [POP_SIZE random draws from distribution] return population
Note that the samples are drawn independently, which means that some states may be repeated in the new population.
INIT_TEMP = 20; DECAY = .95; round = 4
Suppose we have the following candidates: cost(Boston, DC, Philly, NY) = 13.8 cost(Philly, Boston, DC, NY) = 16.6 cost(NY, Boston, Philly, DC) = 13.8 cost(DC, Philly, Boston, NY) = 13.8 cost(DC, NY, Philly, Boston) = 16.6 cost(DC, Boston, NY, Philly) = 13.8 What is the probability distribution from which the next population will be drawn?
w = [e^(-cost(n)/temp) for each candidate n] distr = [w[n] / sum(w) for each candidate n]
population = [POP_SIZE random states] for i = 1:MAX_ITERS: new_population = [] for j = 1:POP_SIZE: parent1, parent2 = select(population) add offspring(parent1, parent2) to new_population temp *= DECAY return best state encountered
There are many ways this could be done, but a good one is Gibbs sampling. Call the function from before with POP_SIZE = 2. This means we need to add a temperature parameter.
function gibbs_samples(candidates, temp, POP_SIZE): weights = [e^(-cost(n)/temp) for each candidate n] distribution = [weights[n] / sum(weights) for each candidate n] population = [POP_SIZE random draws from distribution] return population
function offspring(parent1, parent2) cross_point = random location in state representation child = parent1[start:cross_point] + parent2[cross_point:end] for each variable in child: if (small mutation probability): give it a random new value return child
parent1 = (1,2,4,2,2,5), parent2 = (2,6,4,6,5,0) cross_point = random integer in [0,5] # suppose it’s 4
each element mutated with probability .02 # suppose 1 is mutated mutated elements get random new values # suppose it’s 0
Q Q Q Q Q Q
What effect does crossover have on the state representation for these problems? Is there an alternative state representation that would work better?