PSO and ASO VariantsHybridsExample Applications - PowerPoint PPT Presentation

Title: PSO and ASO VariantsHybridsExample Applications


1
PSO and ASO Variants/Hybrids/Example
Applications Results
Lecture 12 of Biologically Inspired Computing
Purpose Not just to show variants/etc for
these specific algorithms, but to indicate
these as examples of typical ways in which
these and similar methods (especially EAs) are
engineered, combined, etc in attempt to get
the best performance possible on a given
problem.
2
Hybridisation

• A very common algorithm engineering method.
• It simply means creating an algorithm that
  combines aspects of two or more different
  algorithms
• Very many hybridisations have been researched.
• E.g.
• ACO Local Search (e.g. hillclimbing)
• 1. Run 1 generation of ACO with m ants
• 2. Run LS on each of the m ants
• 3. Until a termination condition is
• reached, return to 1.
• EA Local Search
• The same story, but these are called Memetic
  Algorithms

3
Hybridisation II

• Hybridisation with appropriate constructive
  heuristics is
• common, as you know. E.g.
• Generate Initial Population with several runs of
  a stochastic constructive heuristic.
• Carry on from there using ACO, PSO, or whatever.
• Another very common hybrid approach
• Run your standard, single method (e.g. an EA).
• Take the best solution from 1, and run Local
  Search (e.g. hillclimbing) on it for a while to
  try to find improvements.

4
Adaptive Parameters
All the algorithms we have looked at have
parameters. E.g. Mutation rate, crossover rate,
population size, number of ants, C1 and C2 in
PSO, and so on. Instead of (say) keeping the
mutation strength at 1 gene per chromosome, why
not vary it during the algorithm run? Why? ALL
search-based optimisation algorithms balance two
things Exploration to boldly go where no
chromosome/particle/ant/ has gone before.
Reaching out to new areas of the search
space. Exploitation focussing narrowly on
investigating the region close to the best so far
point, in search of better points close by. Too
much exploration? Too much exploitation?
Too often stuck in suboptimal areas
Much too slow progress high risk/low reward
5
Questions re Adaptive Operators

• In PSO, let d be the average distance that a
  particle moves, at the beginning of the run.
• How does d change with time?
• What is d like after running the algorithm for a
  very long time? Is this a good thing?
• How important is C2 (influence of global best) at
  the beginning of the run, and at the end of the
  run?
• In an EA with both crossover and mutation? How
  important is mutation at the end and at the
  beginning of the run.

6
Various ways to control adaptation
In EAs, it may seem sensible for mutation
strength to start low, say at mS and gradually
increase linearly, say to mF. (e.g. perhaps 1/L
and 5/L). Given a limit of 1,000 generations,
say, the rate will increase by a simply
pre-calculated amount per generation. But this
is not really adapting to the current situation
in the search process. It may be fine for some
problems, but on others the population may
converge at 100 generations, or it may still be
very diverse at 1,000 generations, or (of
course), the rates themselves may be very
unsuitable for the problem. So it is common to
use truly adaptive techniques that react to the
current state of the population. The mutation
rate may be based directly on measures of
diversity in the current population, measures of
success in the last few mutation events, and so
on.
7
Useful metrics
Distance between two individuals Hamming
distance no. of genes that are different
Euclidean distance only suitable for .
? Edge distance Permutations
1. ABCDEF and 2. EDFABC
are how different?
Edge-sets 1. AB, BC, CD, DE, EF, FA
2. AB, BC, CE, ED, DF, FA
There are various ways to base a
distance metric on edge sets Distance
metric for grouping problems? Population
diversity Mean values and variances for
each gene. Mean distance between pairs of
individuals Others? Ants
Population diversity measures applied to set of
ants solution Diversity measures for the
amount of pheromome per linkures
8
Measure-based Adaptation
Mutation strength (where D varies from 0
(all the same) to 1 (maximally different) Or
a form of genewise mutation Prob of mutating
gene rises as the variance of that gene in the
population falls. Or Run EA as normal, but
pop diversity gt Dthresh only use
crossover pop diversity lt Dthresh only
use mutation. Or Run PSO as normal, but
pop diversity lt Dthresh do one iteration where
the particle velocities are randomly chosen, then
move on.
9
The Vehicle Routing Problem
Depot
Customer
A number of vehicles are at the depot. Each
customer has to be visited precisely once. Each
vehicle needs a route that takes it from the
depot and back to the depot. What is the least
cost (distance/fuel/vehicles) solution? Several
vehicles normally needed, since (e.g. visiting 3
or 4 customers may take the whole day, but all
customers need to be serviced today. Also,
vehicles have capacity constraints.
10
2-opt mutation for TSP/VRP etc
Choose two edges at random
11
2-opt mutation for TSP/VRP etc
Choose two edges at random
12
2-opt mutation for TSP/VRP etc
Remove them
13
2-opt mutation for TSP/VRP etc
Reconnect in a different way (there is only one
valid new way)
14
2-Opt heuristic
2-opt turns out to be an excellent mutation
operator for the TSP and similar problems. The
2-opt heuristic is an algorithm based on it.
There are variants, But it comes down to
Hillclimbing for n trials, until no
further improvement its possible, using 2-opt as
the mutation operator.
15
Bullnheimer et al (97) Ant System for the VRP
The main difference
Standard transition rule
Extra pheromone is laid by the ant with best tour
16
Deviation from best-known solution (smaller is
better)
Benchmark problems
Run times
AS (ant) is pretty near state of the art, with
good run times.
17
The rectangular Cutting Stock problem
You have a number of shapes to cut out from a
large sheet. How to do it, so as to minimise
waste?
18
The rectangular Cutting Stock problem
You have a number of shapes to cut out from a
large sheet. How to do it, so as to minimise
waste?