Topology of search strategies

Solution generation

constructive search: solution is identified step by step
perturbative search: a possible solution is modified in order to obtain another possible solution

Search space navigation

systematic search: the entire search space is visited
local search: moving from a point of the search space into a neighbour point (incomplete algorithm) - a state can be visited more times

Deterministic search: identify exactly the solution

Stochastic search: approximate the solution

Search space exploration:

sequential search
parallel search

Local search strategies (LSS)

Simple local search - a single neighbour state is retained
- Hill Climbing → chooses the next neighbour
- Simulated Annealing → probabilistically chooses the best neighbour
- Tabu Search → retains the recent visited solution
Beam local search - more states are retained
- Evolutionary Algorithms
- Particle Swarm Optimisation
- Ant Colony Optimisation

Hill Climbing

continuous moving to better values
Search advances to improved states until an optimal one is identified
How to accept a possible solution: best neighbour of the current solution is better than the current solution
Improvement by:
- maximisation of states quality: steepest ascent hill climbing
- minimisation of states quality: gradient descent hill climbing

Algorithm

function HC(S)
	x = s1
	x* = x
	k = 0
	
	while (not termination criteria) o
		k = k+1
		N = all neighbours of X
		s = best solution from N
	
		if (f(s) is better than f(x)) then
			x = s
		else
			state
		end if
	end while
	x* = x
	return x*
end function

Advantages	Disadvantages
simple implementation → solution approximation	evaluation function is difficult to be approximated
does not require memory as it does not come back into the previous state	if a large number of moves are executed, the algorithm is inefficient and it can block in a local optimum, on a plateau (evaluation is constant), on a peak

Simulated Annealing

inspired by physical process modelling