evolutionary computational inteliigence
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Evolutionary Computational Inteliigence. Lecture 6a: Multimodality. Multimodality. Most interesting problems have more than one locally optimal solution and our goal is to detect all of them. Multi-Objective Problems (MOPs). - PowerPoint PPT PresentationTRANSCRIPT
Evolutionary Computational Inteliigence
Lecture 6a: Multimodality
Multimodality
Most interesting problems have more than one locally optimal solution and our goal is to detect all of them
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
MOP Car example
I want to buy a car I would like it’s 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
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.
n
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MOPs 2: Dominance
we say x dominates y if it is at least as good on all criteria and better on at least one
Dominated by x
f2
f1
Pareto frontx
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
Periodic migration of individual solutions between populations
Implicit 1: “Island” Model Parallel EAs
EAEA
EA EA
EA
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
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
Implicit 2: Diffusion Model Parallel EAs
Impose spatial structure (usually grid) in 1 pop
Currentindividual
Neighbours
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
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
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
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
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Meaning of the distance is representation dependent
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
Fitness Sharing vs. Crowding
Fitness Sharing
Crowding
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
Fast Evolutionary Deterministic Algorithm (2006)
FEDA is composed by:– Quasi Genetic Algorithm (QGA, 2004)– Fitness Sharing Selection Scheme (FSS) – Multistart Hooke Jeeves Algorithm (HJA)
Quasi Genetic Algorithm
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
Grounding Grid Problem 1
Grounding Grid Problem 2
Grounding System Problem
Evolutionary Computational Inteliigence
Lecture 6b: Towards Parameter Control
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 ?
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?
Parameter tuning
Parameter tuning: the traditional way of testing andcomparing different values before the “real” runProblems: 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)
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)
Parameter control
Parameter control: setting values on-line, during theactual 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)
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