Lecture 2 - Heuristic Components of Hill Climbing

Question 1

What are the main components of meta/hyper heuristic search/optimisation methods?

Answer 1

Representation (also can be known as encoding) of candidate solutions e.g. binary, integer array
Neighbourhood relation (move operators)
Evaluation function (Objective value)
Initialisation e.g. random
Search process (guideline)
Mechanism for escaping from local optima

Question 2

What are the properties/parts of representation?

Answer 2

Completeness - all solutions must be represented
Connexity - a search path must exist between any two solutions of the search space i.e. any solution can be obtained
Efficiency - the representation must be easy/fast to manipulate by the search operators

Question 3

What are the 4 types of encoding?

Answer 3

Binary - 1s and 0s
Permutation - Each part is a different permutation e.g. different arrangement for the cities in TSP
Integer encoding - Each entry corresponds to an item e.g. 1 is layer 1, 2 is layer 2, etc…
Value encoding - Each entry has an associated value to it

Question 4

What is the Boolean Satisfiability Problem?

Answer 4

Given a certain amount of combinations of variables, is there an assignment of both true and false values that can make the overall equation true?

Question 5

What is a neighbourhood?

Answer 5

A solution x is a set of solutions that can be reached from x by a simple operator (move operator/heuristic)

Question 6

What is the Hamming Distance?

Answer 6

A measure of the amount of different moves that must be made in order to get from one solution to another e.g. if a solution took three bit flips to get to the other solution, then the Hamming distance would be 3.

Question 7

What is the neighbourhood size a measure of?

Answer 7

The neighbourhood size dictates how ‘long’ the solution is e.g. if the solution is 0110, then the neighbourhood size would be 4

Question 8

What are the neighbourhood sizes when using integer/value encoding?

Answer 8

Neighbourhood size is (k-1)n, where k is the size of the alphabet, and n is the size of the solution.

Question 9

What is the neighbourhood size when using permutation encoding?

Answer 9

n(n-1), where n is the size of the solution.

Question 10

What is an evaluation function?

Answer 10

Can also be referred to as objective, cost, fitness, penalty.
Indicates the quality of a given solution.

Question 11

What is delta evaluation?

Answer 11

Calculate the effects of differences between current search position s and a neighbour s’ on the evaluation function value.

Question 12

What is a mutational heuristic/operator?

Answer 12

Processes a given candidate solution and generates a solution which is not guaranteed to be better than the input

Question 13

What is a hill climbing heuristic/operator?

Answer 13

Processes a given candidate solution and generates a better or equal quality solution

Question 14

What is a hill climbing algorithm for a minimisation problem?

Answer 14

Constantly moves in the direction of decreasing level/objective value to find the lowest point of the landscape or best/near optimal solution to the problem

Question 15

What is a hill climbing algorithm for a maximisation problem?

Answer 15

Constantly moves in the direction of increasing level/objective value to find the highest point of the landscape or best/near optimal solution to the problem.

Question 16

What are the different types of simple hill climbing heuristics?

Answer 16

Best improvement (Steepest descent/ascent)
First improvement (next descent/ascent)
Stochastic hill climbing - random selection/random mutation hill climbing
Random-restart (shotgun) hill climbing

Question 17

How does best improvement work?

Answer 17

Only accepts solutions that are strictly better. Ignores equal or worse solutions. After finding a better solution, will remember the bit flipped to obtain it, sets the best eval to the current eval, then reverts back to the original solution. Once this is done, it will then finish the loop, and finally flip the bit for the current solution that was marked as the best.

Question 18

How does first improvement work?

Answer 18

Like best improvement, except it doesn’t revert to the original solution after finding an improvement. It instead keeps exploring the new solution found, to see if there is any better solution further down ‘the chain’.

Question 19

How does Davis’ bit hill climbing work?

Answer 19

Generates a random permutation of numbers from 0 to the length of the solution. Then, using this permutation, it will flip the bit of the current solution at the location pointed to by the permutation’s value found at the loop counter. If the move is better, it accepts the bit flip, otherwise it reverts it.

Question 20

How does random mutation work?

Answer 20

Flips a random bit selected by a random generator between 0 to the length of the solution. If the bit flip produces a better solution, then accept it, otherwise revert the flip.

Question 21

How does a hill climbing algorithm know when to stop?

Answer 21

If target objective is known, then the search can be stopped when that target objective value is achieved.
Hill climbing could be repeatedly applied until a termination criteria is satisfied.

Question 22

What are the differences between hill climbing and random walk?

Answer 22

Hill Climbing:
Exploits promising regions
Neglects exploring a large area of the search space.
Random Walk:
Does an incredibly large amount of exploring of the general search space.
Neglects exploiting promising regions.

Question 23

What are the strengths and weaknesses of hill climbing?

Answer 23

Strengths:
Very easy to implement
Weaknesses:
Local optimum - could get stuck if all neighbouring solutions are worse or the same, as the algorithm will halt.
Plateau - If all neighbouring states are same, then the search will basically just devolve to random walk.
Ridge/valley - The search may ‘bounce’ from one side to another, making very little progress.
As a result, HC might not find the optimal solution and may get stuck at local optimum.
Usually no upper bound on computation time.
Success and failure depends on the starting point at each iteration