Recent Advances in Memetic Algorithms

Transcription

Recent Advances in Memetic
Algorithms
Dr. N. Krasnogor
Automated Scheduling, Optimisation and Planning Research Group
University of Nottingham
www.cs.nott.ac.uk/~nxk
Plenary Talk at the “EU/ME Workshop: Design and Evaluation of Advanced Hybrid Metaheuristics”
This talk is based on our new book
“Recent Advances in Memetic
Algorithms” edited by Hart,
Krasnogor & Smith
As such my talk today contains only
a small snapshot of the book
First book that deals
exclusively on MAs!
So before continuing let me thank the chapter’s
authors:
• K. Katayama, H. Narihisa, D.A. Pelta, C. Prins, S. Bouchenoua, K.
Knodler, J.Poland, P.Merz, N. Krasnogor, J,E. Smith, W.E. Hart, A.
Zell, X. Yao, F. Wang, K, Padmanabhan, S. Salcedo-Sanz, S. Areibi,
S. Gustafson, A. Sinha, Y. Chen, D. E. Goldberg, E.K. Burke, J.D.
Landa-Silva, J. Knowles, D. Corne, D. Wyatt, L. Bull, F. Comellas, R.
Gallegos
• and of course my co-eds Jim Smith and Bill Hart.
• The pictures, graphs and stats in this talk are taken from the book and
belong to their authors.
• I want also to thank the organizers of this workshop for inviting me to
give one of the two plenary talks
Outline of the Talk
PART 1 (25 min)
• Memetic Algorithms: the issues involved
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Motivation
Lamarckianism vs Baldwinism
Diversity
Operators Choice
Use of Knowledge
Specific Considerations for Continuous Domains
Initialisation
Other Hybridisations
PART 2: (15 min)
•Showcase Applications:
–Maximum Diversity Problem
–Protein Structure Prediction
–Optimal Engine Calibration
–Circuit Partitioning
PART 3: (15 min)
•Methodologies:
–Teams of Heuristics
–Cooperative Local Search
–On-the-fly Operators Discovery
PART 4: (5 min)
•Questions
PART 1
Memetic Algorithms: the issues involved
Motivation
There are several reasons why it is worthwhile hybridizing:
•Complex problems can be decomposable, different subproblems be better solved by different
methods:
•EA could be used as pre/post processors
•Subproblem specific information can be placed into variation operators or into local searchers
•In some cases there are exact/approximate methods for subproblems
•Well established: generally good black-box optimisers do not exist. This is why successful EAs
are usually found in “hybridized form”
•EA are good at exploring the search space but find it difficult to zoom-in good solutions
•Problems have constraints associated to solutions and heuristics/local search are used to repair
solutions found by the EA
•If heuristic/local search strategies in MAs are “first class citizens” then a much richer definition
of adaptive hybrid metaheuristics is possible: the strategies are generated au pair with the
solutions they intend to improve (I.e. self-generating or co-evolving memes)
A conservation of competence principle applies: the better one
algorithm is solving one specific instance (class) the worst it is
solving a different instance (class) [Wolpert et.al.]
It cannot be expected that a black-box metaheuristic will suit all
problem classes and instances all the time, that is, it is
theoretically impossible to have both ready made of-the-shelf
general & good solvers.
MAs are good algorithmic templates that aid in the balancing act of
successfully using a general, of-the-shelf, reusable solvers (EAs)
with adds-on instance (class) specific features.
The Canonical MA
From Eiben’s & Smith “Introduction To Evolutionary Computation”
At design
time lots of
issues arise
Baldwinism VS Lamarckianism
• Lamarkian
• traits acquired by an individual during its lifetime can
be transmitted to its offspring
• e.g. replace individual with fitter neighbour
• Baldwinian
• traits acquired by individual cannot be transmitted to
its offspring
• e.g. individual receives fitness (but not genotype) of
fitter neighbour
Baldwin’s “filter”
Raw fitness
Diversity
The loss of diversity is specially problematic in MAs as the LS tends
to focus excesively in a few good solutions.
If the MA uses LS up to local optimae then it becomes important
to constantly identify new local optimae
If the MA uses partial LS you could still be navigating around the
basins of attractions of a few solutions
Diversity
There are various ways to improve diversity (assuming that’s what
one wants!):
•if the population is seeded only do so partially.
•instead of applying LS to every individual choose whom to apply it to.
•use variation operators that ensure diversity (assorted)
•in the local search strategy include a diversity weigth
•modify the selection operator to prevent duplicates
•archives
•modify the acceptance criteria in the local search:
Diversity
The following modified MC exploits solutions (zooms-in) when the
population is diverse. If the population is converged it explores
(zooms-out)
The temperature T of the MC is defined for each generation as:
A new solution is accepted when:
when population is diverse
T? 0?
only accepts improvements
when population is converged
T ???
accepts both better and worst
solutions (explores)
Operators Choice
The choice of LS/Heuristic is one of the most important steps in
the design of an MA
1.
2.
3.
Local searchers induce search landscapes and there has been various attempts to
characterize these. Kallel et.al. and Merz et.al. have shown that the choice of LS can
have dramatic impact on the efficiency and effectiveness of the MA
Krasnogor formally proved that to reduce the worst case run time of MAs LS move
operators must induce search graphs complementary (or disjoint) than those of the
crossover and mutation.
Krasnogor and Smith have also shown that the optimal choice of LS operator is not
only problem and instance dependent but also dependent on the state of the overall
search carried by the underlying EA
The obvious way to implement 2&3 is to use multiple local searchers within an MA
(multimeme algorithms)
and we will see that the obvious way of including feedback like that suggested by 1 is to
use self-generated multiple local searchers (self-generating MAs aka co-evolving MAs)
Search landscapes
Thanks to P. Merz!
Multiple Local Searchers
Use of Knowledge
The use of knowledge is essential for the success of a search methods
There are essentially two stages when knowledge is used:
•At design time: eg, in the form of local searchers/heuristics, specific variation
operators, initialization biases, etc.
•At run time:
•using tabu-like mechanisms to avoid revisiting points (explicit)
•using adaptive operators that bias search towards unseen/promising regions of
search space (implicit)
•creating new operators on-the-fly, eg., self-generating or co-evolving MAs
(implicit)
With appropriate data-mining techniques we can turn implicit
knowledge into explicit and feed it back into the design process!
There are several factors which makes CD optimisation difficult:
•Different scales might be required for local/global searches
•It is not always possible to determine when a solution is locally
optimal
•Long local searchers might be needed to ensure convergence to
good optima
•Several local searchers exists but they are general methods so they
violate the conservation of competence principle.
The design of CD MAs can be different than the one needed for
DD.
As there is a need to both do long local searchers and balance it
with global search then:
•LS is truncated after a number of fitness evaluations
•LS is applied sporadically
•But these strategies makes it difficult to guarantee
convergence
To the best of my knowledge the only MAs for CD that have
guaranteed convergence to LO are Hart’s Memetic Evolutionary
Pattern Search.
Initialisation
Intelligent initialisation of the MA is one of the obvious ways of
reusing knowledge:
•One does not reinvent the wheel ‘cos existing solutions are reused.
•Bias the search mechanism towards more suitable regions of the
search space.
•Given a CPU budget allocation it might pay to spend some part of
the budget in smart initialisations rather than in a pure EA.
F
Fitness
F: fitness after a smart initialization
T: time needed by an EA with random initialization to
reach F
T? T T?
Time
T? ,T? Time needed by the Intelligent
Initialization
but remember
diversity!
If T? < T then it is worth initializing.
If T < T? then it is not worth doing it
Other Hybridisations
EA + LS have been used in various other hybridisation schemes:
•during the genotype to phenotype mapping prior to evaluation, e.g.
in timetabling, scheduling and VRP.
•during the mutation or crossover stages, e.g., DPX is a good
example of intelligent crossover, and Unger & Moult used a try-best
approach for protein folding. Note however that these differ from
Xover hill-climbing in that the later does not use problem/instance
specific knowledge
PART 2
Showcase Applications
The Maximum Diversity Problem
Katayama & Narihisa solve the MDP by means of a sophisticated
MA. The MDP:
The problem consists in selecting out of a set of N elements, M
which maximize certain diversity measure Dij
This problem is at the core of various important real-world
applications:
•Immigration and admission policies
•Committee formation
•Curriculum design
•Portfolio selection
•Combinatorial chemical libraries
•etc
Various features: distinct repair & LS, GRASP
for init, diversification phase, accelerated LS.
Protein Structure Prediction
Estructura primaria
Estructura Secundaria
Estructura terciaria
Krasnogor, Krasnogor & Smith, Krasnogor & Pelta, Smith have used
MAs to study fundamentals of the algorithmics behind PSP in
simplified models.
Standard MA template except that Multiple Memes which promote
diversity by means of fuzzy rules are used
Membership function for “acceptable” solutions
Two distinct “acceptability” concepts
Promotes
improvements
Promotes
Diversity
New optimal solutions
Optimal Engine Calibration
The OEC problem is paradigmatic of many industrial problems.
In this problem many combinatorial optimisation problems occur:
1. Optimal Design of Experiments
2. Optimal Test Bed Schedule
3. Look-up Table Calculation
By P.Merz:
Standard MA template
Circuit Partitioning
CP is the task of dividing a circuit into smaller parts. Its an
important component of the VLSI Layout problem:
is a minimization
objective
1. this
the division
permits the
fabrication of circuits
physically
this is a in
constraint
distinct components
2. By dividing we conquer: resulting circuits can fit fabrication
norms, complexity is reduced
3. Can reduce heat dissipation, energy consumption, etc.
Circuit Partitioning
From S.Areibi’s chapter:
A graphical example
Intelligent initialisation= GRASP+LS
Sophisticated problem specific LS (Fiduccia-Mattheyses)
Final LS pass
PART 3
Methodologies
Teams of Heuristics
In Burke and Landa Silva’s chapter it is suggested that:
The canonical MA template could benefit from including features that
Multimeme algorithms
other metaheuristics already exploit:
included these concepts in
recommendations
Variable Neighbourhood Search: under this approach a number of different
neighbourhood structures are systematically explored, tries to improve the current
solution while avoiding poor local optima.
A-teams of Heuristics: in A-Teams a set of constructive, improvement and
destructive heuristics are asynchronously used to improve solutions.
Hyperheuristics: the main concept behind the hyperheuristic is that of managing the
application of other heuristics adaptively with the purpose of improving solutions.
Methodologies
Cooperative Local Search
Burke and Landa Silva’s chapter observes:
In a cooperative local search scheme, each individual carries out
its own LS. When an individual gets stuck it ask for the
cooperation of the population in order to find something to do to
get unstuck and continue the search from another position in the
solution space. The results achieved by each individual may be
different at different times and this encourages diversity within
the population
Methodologies
Cooperative Local Search
Cycle of each individual in pop
The search cycle of each
individual begins
Cooperation mechanism
Gets stuck
sharing moves,
parts, centralized
control, etc
Finds something to do. Gets unstuck
Note that this differs from teams of heuristics in that here the
cooperation is made explicit
Methodologies
On-the-fly operators discovery
All the previous methodologies clearly benefits the end user as
they have been shown to provide improvements in robustness,
quality, etc.
But what do we do if we do not have, or don’t know, good heuristics
which could be used by,eg., A-teams, VNS or CLS?
Also, why don’t we use the information the algorithm produces
to better understand and make explicit new knowledge of the search
landscape capturing this knowledge in new operators?
Methodologies
Two alternatives:
1. Off-line: Whitley and Watson did it successfully for TS, and
Kallel et al for other methods.
2. In-line: Krasnogor, Krasnogor & Gustafson, Smith for MAs
The problem with 1 is that it takes ages to data mine the data and make
it reusable, although it is STILL worth doing it.
And what about 2?
Methodologies
Canonical MA cycle
Methodologies
Self-Generating/Co-evolving MAs
Methodologies
•Inheritance: an agent inherits the
meme of the most successful of its
parents
There are various processes that
guide the Agent’s cultural
evolution of local search
strategies:
•Imitation: an agent imitates a
successful non-genetically-related
individual
•Innovation: an agent blindly
(i.e.randomly) change its meme
•Mental Simulation: an agent
purposely (e.g. hill-climbs to ) improve
its meme
From Krasnogor & Gustafson chapter
From Smith chapter
Conclusions (I)
•There is much more in MA that meets the eye. Its not a simple
matter of ad-hoc putting LS somewhere in the EA cycle.
•Just a small space of the architectural space of MAs has been
explored and we don’t know yet why a given architecture
performs well/bad in a specific problem (see my thesis)
•People usually use one “silver bullet” LS. That’s fine if that
SB exists. However when it does not exist use multimeme
algorithms, or other heuristics teams/cooperative algorithms as
lots of simple heuristics can synergistically do the trick.
Conclusions (II)
•ADAPT: the search process is dynamic and your method should
detect and adapt to changing circumstances. Adaptation is not too
expensive or complex to code!
•Carefully consider how your variation operators interact with LS
•Ideam for Baldwinian VS Lamarckianism
•Understand that the fitness landscape explored by your MA is not
a one-operator landscape but the results of the superposicion with
interference of varios landscapes.
Conclusions (III)
•Use more expresive acceptance criteria in your local search, eg.,
fuzzy criteria
•If you don’t know what operators to apply let the the MA find it
for you by some Self-Generating mechanism, e.g., co-evolution.
•Self-Generating mechanisms are a great niche for GPers!
FINALLY:
check out the literature, almost surely you will find MAs.
among the best success stories in applications to real world probs!
Thank you!
Questions?

Recent Advances in Memetic Algorithms

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