Quizes Flashcards
A mathematical function always has a global minimum
No
local optima only occurs when f’(x) = 0
No. can also occur when f’(x) not defined.
What is a feasable set?
A set that satisfies the constraints on the objective function.
What properties does the Hessian(f) Matrix have?
A. Symmetric
B. Diag(H) != 0
C. No elements are zero
A. Symmetric.
Consider a 2x2 matrix if 1s. Is semi-definite?
Yes. Since all eigenvals are >= 0
Once the search direction has been find in an iterative opt. method, the problem of finding the step size is one-dimensional.
Yes. Step size is a scalar.
Newton-Rapson method always finds a minima.
No. It finds a stationary point s.t f’(x) = 0. Second order derivative test can settle (if it exists) if the point is max/min/saddle
An optimization problem is convex if f(x) is convex
No. It also requires the set of feasable solutions to be convex.
At a local minima of f(x) s.t h(x) = 0 what of the following conditions hold?
A. grad(fx) and grad(hx) are paralell
B. grad(fx) and grad(hx) are orthogonal
C. grad(hx) = 0
A. grad(fx) and grad(hx) are paralell. (see, lagrange multipliers)
If two individuals are to have offspring they must be of the same species
No. Counterexample: Mules and Ligers.
Humans have more chromosomes than other species
No. Human 48~ and carp 100+.
Why must codons consist of at least three letters?
Because there are 20 amino acids and 4^x where x < 3 doesn’t have enough combinations to encode all 20 different amino acids.
Because of random initialization stochastic algorithms converges at a slower rate.
False
In tournament selection, the competing number of individuals is always two
No. Sometimes more.
After selection of two individuals, crossover is always performed.
No. This step depends on crossover probability.
