Evolutionary Computational Inteliigence

1
Evolutionary Computational Inteliigence

• Lecture 6a Multimodality

2
Multimodality

• Most interesting problems have more than one
  locally optimal solution and our goal is to
  detect all of them

3
Multi-Objective Problems (MOPs)

• Wide range of problems can be categorised by the
  presence of a number of n possibly conflicting
  objectives
• buying a car speed vs. price vs. reliability
• Two part problem
• finding set of good solutions
• choice of best for particular application

4
MOP Car example

• I want to buy a car
• I would like its the cheapest the possible
  (minimize f1) and the most comfortable the
  possible (maximize f2)
• If I consider the two functions separately I
  obtain
• min f1
• max f2

5
MOPs 1 Conventional approaches

• rely on using a weighting of objective function
  values to give a single scalar objective function
  which can then be optimised
• to find other solutions have to re-optimise with
  different wi.

6
MOPs 2 Dominance

• we say x dominates y if it is at least as good on
  all criteria and better on at least one

7
Implications for Evolutionary Optimisation

• Two main approaches to diversity maintenance
• Implicit approaches (decision space)
• Impose an equivalent of geographical separation
• Impose an equivalent of speciation
• Explicit approaches (fitness)
• Make similar individuals compete for resources
  (fitness)
• Make similar individuals compete with each other
  for survival

8
Implicit 1 Island Model Parallel EAs
Periodic migration of individual solutions
between populations
9
Island Model EAs

• Run multiple populations in parallel, in some
  kind of communication structure (usually a ring
  or a torus).
• After a (usually fixed) number of generations (an
  Epoch), exchange individuals with neighbours
• Repeat until ending criteria met
• Partially inspired by parallel/clustered systems

10
Island Model Parameter Setting

• The idea is simple but its success is subject to
  a proper parameter setting
• It must be somehow known the number of
  islands,i.e. basins of attraction we are
  considering
• It must be set the population size for each
  separate island
• If some a priori information regarding the
  fitness landscape is given, island model can be
  efficient, otherwise it can likely fail

11
Implicit 2 Diffusion Model Parallel EAs

• Impose spatial structure (usually grid) in 1 pop

Current individual
Neighbours
12
Diffusion Model EAs

• Consider each individual to exist on a point on a
  grid
• Selection (hence recombination) and replacement
  happen using concept of a neighbourhood a.k.a.
  deme
• Leads to different parts of grid searching
  different parts of space, good solutions diffuse
  across grid over a number of gens

13
Diffusion Model Example

• Assume rectangular grid so each individual has 8
  immediate neighbours
• For each point we can consider a population mad
  up of 9 individuals
• One of the other 8 remaining point is selected
  (e.g. by means of roulette wheel)
• Recombination between starting and selected point
  occurs
• In a steady state logic replacement of the
  fittest occurs

14
Implicit 3 Automatic Speciation

• It restricts the recombination on the basis
  genotypic structure of the solutions in order to
  have recombination only amongst individual of the
  same specie
• comparing the maximum genotypic distance between
  solutions
• Adding a tag (genotypic enlargement) in order
  to characterize the belonging of each individual
  to a certain specie
• In both cases, problem requires a lot of
  comparisons and the computational overhead can be
  very high

15
Explicit 1 Fitness Sharing

• Restricts the number of individuals within a
  given niche by sharing their fitness, so as to
  allocate individuals to niches in proportion to
  the niche fitness
• need to set the size of the niche ?share in
  either genotype or phenotype space
• run EA as normal but after each gen set

Meaning of the distance is representation
dependent
16
Explicit 2 Crowding

• Attempts to distribute individuals evenly amongst
  niches
• relies on the assumption that offspring will tend
  to be close to parents
• randomly selects a couple of parents, produce 2
  offspring
• each offspring compete in a pair-tournament for
  surviving with the most similar parent (steady
  state) i.e. the parent which has minimal distance
  

17
Fitness Sharing vs. Crowding
Fitness Sharing Crowding
18
Multimodality and Constraints

• In some cases we are not satisfied by finding all
  the local optima but only a subset of them having
  certain properties (e.g. fitness values)
• In such cases the combination of algorithmic
  components can be beneficial
• A rather efficient and simple option is to
  properly combine a cascade

19
Fast Evolutionary Deterministic Algorithm (2006)

• FEDA is composed by
• Quasi Genetic Algorithm (QGA, 2004)
• Fitness Sharing Selection Scheme (FSS)
• Multistart Hooke Jeeves Algorithm (HJA)

20
Quasi Genetic Algorithm
21
FEDA

• The set of solutions coming from QGA (usually a
  lot) are processed by FSS
• We thus obtain a smaller set of points which have
  good fitness values and are spread out in the
  decision space
• The HJA is then applied to each of those solutions

22
Grounding Grid Problem 1
23
Grounding Grid Problem 2
24
Grounding System Problem
25
Evolutionary Computational Inteliigence

• Lecture 6b Towards Parameter Control

26
Motivation 1

• An EA has many strategy parameters, e.g.
• mutation operator and mutation rate
• crossover operator and crossover rate
• selection mechanism and selective pressure (e.g.
  tournament size)
• population size
• Good parameter values facilitate good performance
• Q1 How to find good parameter values ?

27
Motivation 2

• EA parameters are rigid (constant during a run)
• BUT
• an EA is a dynamic, adaptive process
• THUS
• optimal parameter values may vary during a run
• Q2 How to vary parameter values?

28
Parameter tuning

• Parameter tuning the traditional way of testing
  and
• comparing different values before the real run
• Problems
• users mistakes in settings can be sources of
  errors or sub-optimal performance
• costs much time
• parameters interact exhaustive search is not
  practicable
• good values may become bad during the run (e.g.
  Population size)

29
Parameter Setting Problems

• A wrong parameter setting can lead to an
  undesirable algorithmic behavious since it can
  lead to stagnation or premature convergence
• Too large population size, stagnation
• Too small population size, premature convergence
• In some moments of the evolution I would like
  to have a large pop size (when I need to explore
  and prevent premature convergence) in other
  moments I would like to have a small one (when
  I need to exploit available genotypes)

30
Parameter control

• Parameter control setting values on-line, during
  the
• actual run, I would like that the algorithm
  decides by itself how to properly vary
  parameter setting over the run
• Some popular options for pursuing this aim are
• predetermined time-varying schedule p p(t)
• using feedback from the search process
• encoding parameters in chromosomes and rely on
  natural selection (similar to ES self-adaptation)

31
Related Problems

• Problems
• finding optimal p is hard, finding optimal p(t)
  is harder
• still user-defined feedback mechanism, how to
  optimize?
• when would natural selection work for strategy
  parameters?
• Provisional answer
• In agreement with the No Free Lunch Theorem,
  optimal control strategy does not exist.
  Nevertheless, there are a plenty of interesting
  proposals that can be very performing in some
  problems. Some of these strategies are very
  problem oriented while some others are much more
  robust and thus applicable in a fairly wide
  spectrum of optimization problems