An Unorthodox View on Memetic Algorithms

An Unorthodox View on
Memetic Algorithms
Prof. N. Krasnogor

Interdisciplinary Optimisation Laboratory
Automated Scheduling, Optimisation and Planning Research Group
School of Computer Science & Information Technology
University of Nottingham

www.cs.nott.ac.uk/~nxk

IEEE Symposium Series on Computational Intelligence 2011 - Paris, France

Friday, 15 April 2011

Outline of the Talk

• An Unorthodox View of Memetic
Algorithms
• Futurology
• Conclusions, Q&A



Based on papers at www.cs.nott.ac.uk/~nxk/
o N. Krasnogor. Handbook of Natural Computation, chapter Memetic Algorithms. Natural Computing. Springer
Berlin / Heidelberg, 2009.
o J. Bacardit and N. Krasnogor. Performance and efficiency of memetic pittsburgh learning classifier systems.
Evolutionary Computation, 17(3), 2009.
o Q.H. Quang, Y.S. Ong, M.H. Lim, and N. Krasnogor. Adaptive cellular memetic algorithm. Evolutionary
Computation, 17(3), 2009.
o N. Krasnogor and J.E. Smith. Memetic algorithms: The polynomial local search complexity theory perspective.
Journal of Mathematical Modelling and Algorithms, 7:3-24, 2008.
o M. Tabacman, J. Bacardit, I. Loiseau, and N. Krasnogor. Learning classifier systems in optimisation problems: a case
study on fractal travelling salesman problems. In Proceedings of the International Workshop on Learning Classifier
Systems, volume (to appear) of Lecture Notes in Computer Science. Springer, 2008.
o N. Krasnogor and J.E. Smith. A tutorial for competent memetic algorithms: model, taxonomy and design issues.
IEEE Transactions on Evolutionary Computation, 9(5):474- 488, 2005.
o W.E. Hart, N. Krasnogor, and J.E. Smith, editors. Recent advances in memetic algorithms, volume 166 of Studies in
Fuzzyness and Soft Computing. Springer Berlin Heidelberg New York, 2004. ISBN 3-540-22904-3.
o N. Krasnogor. Self-generating metaheuristics in bioinformatics: the protein structure comparison case. Genetic
Programming and Evolvable Machines, 5(2):181-201, 2004.
o N.Krasnogor and S. Gustafson. A study on the use of “self-generation” in memetic algorithms. Natural Computing, 3
(1):53 - 76, 2004.
o M. Lozano, F. Herrera, N. Krasnogor, and D. Molina. Real-coded memetic algorithms with crossover hill-climbing.
Evolutionary Computation, 12(3):273-302, 2004.

Survey Combinatorial Optimisation Continuous Optimisation



So… What Are Memetic Algorithms?
MAs, one of the key methodologies behind
successful discrete/continuous optimisation, are:



MAs, one of the key methodologies behind
successful discrete/continuous optimisation, are:

a carefully orchestrated interplay between
(stochastic) global search and (stochastic)
local search algorithms
N. Krasnogor. Handbook of Natural Computation, chapter Memetic Algorithms.
Natural Computing. Springer Berlin / Heidelberg, 2009



Lets Discuss:
Are MAs a Nature Inspired Methodology?



Lets Discuss:
Are MAs a Nature Inspired Methodology?

Does it mater?



A Research Paradigm

{
• Key Design Issues
underpinning MAs

N. Krasnogor and J.E.
Smith. A tutorial for
competent memetic
algorithms: model,
taxonomy and design
issues. IEEE Transactions
on Evolutionary
Computation, 9(5):474-
488, 2005.



The “Canonical” MA
From Eiben’s & Smith “Introduction To Evolutionary Computation”



What Memetic Algorithms are NOT?
They are NOT Algorithms!
➡They do not stop, we stop them.
➡They are not short pieces of code, but large
systems



systems
Factoring: Let n be the number to be factored.

1.

Let Δ be a negative integer with Δ = -dn where d is a multiplier and Δ is the negative
discriminant of some quadratic form.

2.

Take the t ﬁrst primes , for some .

3.

Let fq be a random prime form of GΔ with .

4.

Find a generating set X of GΔ

5.

Collect a sequence of relations between set X and {fq : q ∈ PΔ} satisfying:

6.

Construct an ambiguous form (a, b, c) which is an element f ∈ GΔ of order dividing 2 to
obtain a coprime factorization of the largest odd divisor of Δ in which Δ = -4a.c or a(a - 4c)
or (b - 2a).(b + 2a)

7.

If the ambiguous form provides a factorization of n then stop, otherwise ﬁnd another
ambiguous form until the factorization of n is found. In order to prevent that useless
ambiguous forms are generated, build up the 2-Sylow group S2(Δ) of G(Δ).



systems Calculating Pi
Factoring: Let n be the number to be factored.

1.

Let Δ be a negative integer with Δ = -dn where d is a multiplier and Δ is the negative
discriminant of some quadratic form.

2.

Take the t ﬁrst primes , for some .

3.

Let fq be a random prime form of GΔ with .

4.

Find a generating set X of GΔ

5.

Collect a sequence of relations between set X and {fq : q ∈ PΔ} satisfying:

6.

Construct an ambiguous form (a, b, c) which is an element f ∈ GΔ of order dividing 2 to
obtain a coprime factorization of the largest odd divisor of Δ in which Δ = -4a.c or a(a - 4c)
or (b - 2a).(b + 2a)

7.

If the ambiguous form provides a factorization of n then stop, otherwise ﬁnd another
ambiguous form until the factorization of n is found. In order to prevent that useless
ambiguous forms are generated, build up the 2-Sylow group S2(Δ) of G(Δ).



Computational Research Paradigms as Design
Patterns and Pattern Languages
In Alexander, C., Ishikawa, S., Silverstein, M., Jacobson, M., Fiksdahl-King, I.,
Angel, S.: A Pattern Language - Towns, Buildings, Construction. Oxford
University Press (1977):

“In this book, we present one possible pattern language,...
The elements of this language are entities called patterns.
Each pattern describes a problem which occurs over and
over again in our environment, and then describes the
core of the solution to that problem, in such a way that you
can use this solution a million times over, without ever
doing it the same way twice.”



How are Patterns Described?
A collection of well
High Level deﬁned patterns, i.e. a
• Pattern name rich pattern language,
substantially enhances
• Problem statement our ability to
• The solution communicate solutions
• The Consequences to recurring problems
without the need to
• Examples discuss specific
implementation details.



Invariants and Decorations

A Compact
“Memetic”
Algorithm by
Merz (2003)




A “Memetic”
Particles Swarm
Optimisation by
Petalas et al
(2007)




A “Memetic”
Artificial
Immune
System by
Yanga et al
(2008)




A “Memetic”
Learning
Classifier
System by
Bacardit &
Krasnogor
(2009)



• Many others based on Ant Colony Optimisation,
NN, Tabu Search, SA, DE, etc.
• Key Invariants:
– Global search mode
– Local search mode
• Many Decorations, e.g.:
– Crossover/Mutations (EAs based MAs)
– Pheromones updates (ACO based MAs)
– Clonal selection/Hypermutations (AIS based MAs)
– etc



A carefully orchestrated interplay between (stochastic) global
search and (stochastic) local search algorithms



A carefully orchestrated interplay between (stochastic) global
search and (stochastic) local search algorithms

A Pattern Language for
computational problem solving
N. Krasnogor. Handbook of Natural Computation, chapter Memetic Algorithms.
Natural Computing. Springer Berlin / Heidelberg, 2009



Memetic Algorithm Pattern (MAP)
• Problem: how to successfully orchestrate multi-
scale search (e.g. local VS global search)

• Solution: for a given domain find exploration and
exploitation mechanisms that work in synergy.

• Consequence: increase CPU? Resampling?
Diversity lost?

• Examples: too many!


Template Patterns
The high-level MA pattern can be refined through multiple “Template
Patterns”

Defines Algorithmic Backbones & “Pipelines”



Evolutionary Memetic Algorithm
Template Pattern (EMATP)
• Problem: Achieving synergy between an EA (global
search) and a problem specific heuristic

• Solution: standard cycle of I  Eval  Mate 
Mut  Select is hooked with H, A or E methods at
one or more of the stages.

• Consequence: if naively implemented results in
diversity crisis and wastefull increased CPU time
• Examples: literature is rich in examples


Strategy Patterns
The MAs template pattern can be refined through strategy
patterns
• Strategy Patterns represent a family of interchangeable
algorithms

There are
multiple
strategy
patterns
in the MAs’
pattern
language!



Refinement Strategy Pattern (RSP)
• Problem: what local search heuristic should be used? i.e.,
what’s the fitness landscape to employ?
• Solution: will consider the graph structure, the assignment
of fitness labels and of navigation strategies. Must allow
for obtaining/avoiding deep local optima, navigate large
neutral plateaus, strategically using hubs, etc.
• Consequence: must understand multiple fitness
landscapes, mean and worst case path to optima (PLS
results, complexity results), etc.
• Examples: SA-LS, Multimeme Algorithms, Variable
Depth Search by Smith, Krasnogor, Sudhold, etc



Exact and Approximate Hybridisation
Strategy Pattern (EAHSP)
• Problem: Hybridisation strategy different than for
heuristic methods. Usually E&A methods are cpu hungry
• Solution: loose integration/tandem or tighter integration.
• Consequences: effort balance must be carefully
calibrated. Sometimes the exact method is relaxed into
beam search. Tradeoff between effort in building good
enough models and guaranteed solutions must be
analysed.
• Examples: Gallardo et al (2007), Mezmaz et al (2007),
Raidl et al (2008), Pirkwieser (2008), etc



Population Diversity Handling Strategy
Pattern (PDHSP)
• Problem: handling diversity is a critical issue as both RSP and
EAHSP tend to focus search and hence promote diversity loss
• Solution: smart initialisations, tabu-like and archive-like
mechanisms to avoid re-sampling, adaptive operators, multiple
operators, age monitoring, diversity tracking at G,P & F levels,
etc.
• Consequences: care must be put on what one wants high/low
diversity to imply in terms of search behaviour.
• Examples: Neri et al (2007), Burke & Landa Silva (2004),
Gustafson et al (2006), Krasnogor (2002), etc



Population Diversity Handling Strategy Pattern
(PDHSP)



Surrogate Objective Function Strategy
Pattern (SOFSP)
• Problem: how to replace an expensive, noisy or unknown fitness
functions?
• Solution: weighted histories, neural networks, SVM, LCS, fitness
inheritance, reduction of variance techniques (e.g. latin hypercubes
sampling), DOE, regression models, etc.
• Consequences: must consider the level at which surrogacy will be
implemented, e.g., objective function or problem itself? Are local or
global approximation to be used?, etc
• Examples: (also called metamodels, local models and partial
objective functions) Battacharya (2007), Bull (1999), Paenke and Jin
(2006), Zhou et al (2007), Lim ( 2011), etc



Continuous Problems Refinement
Strategy Pattern (CPRSP)
• Problem: Local optimum detection and, more generally, search
scale is a critical issue
• Solution: methods include derivative-based and derivative-free,
truncated searches and selective application of LS, LS intensity
and frequency,
• Consequences: very difficult to a priori know the above
parameters, hence, best course of action is (self)adaptation.
Multimeme algorithms most successful, CMA-ES great
• Examples: Smith (1998-), Ong & Keane (2004), Lozano et al.
(2004), Hart (2005), etc



Multimeme Strategy Pattern (MSP)
• Problem: impossible to decide a priori best refinement, a method
(and its parameters) to use.
• Solution: Use adaptation and self-adaptation on the methods
themselves (rather than simply on the parameters). The MAP is
provided with multiple LSs and a learning mechanism to adapt to
problem, instance and stage of search.
• Consequences: Bookkeeping mechanism is needed.
Reinforcement learning, neural network, LCS, etc. must be
tightly integrated to EMATP. Simple schemes, however, very
effective and cheap.
• Examples: Krasnogor & Smith (2001,2005,2008), Jakob (2006),
Neri et al (2007), etc



Multiple Local Searchers



Self-Generating Strategy Pattern
(SGSP)
• Problem: How to implement a search mechanism that
learns how to search in a reusable manner?
• Solution: To use (GB)ML to, given problem instances,
capture problem-solving algorithmic building blocks. GP
is a perfect candidate for this
• Consequences: only applicable in sufficiently hard
problems and for instances that share common “patterns”
• Examples: Krasnogor & Gustafson (2002,2004), Smith
(2002, 2003), Krasnogor (2004), Burke et al (2007),
Kendal et al (2008/9), Fukunaga (2008) Tabacman et al
(2008).


A Pattern Language for Memetic Algorithms
Memetic Algorithms by N. Krasnogor. Handbook of Natural Computation (chapter) in Natural Computing. Springer Berlin / Heidelberg, 2009.
www.cs.nott.ac.uk/~nxk/publications.html



A General Trend: moving away from close-loop
optimisation towards open-ended and embodied
optimisation
Effort (e.g. Time,
Programming solving 1 problem – single instances
$$$, etc)

Programming (self) adaptive solving 1 problem – several instances Effort (e.g. Time,
$$$, etc)

Reuse Feedback Effort (e.g. Time,
$$$, etc)
Programming (self) adaptive Self-generating solving 1 problem – several classes instances

Reuse

Self-Engineering Effort (e.g. Time,
Reuse Feedback
$$$, etc)

Programming (self) adaptive Self-generating Solving multiple problem – several classes instances



The Future of MAs
Software Nurseries
• Fundamental Change of Scales Rethink
• Software will be “seeded” and grown, very much like
a plant or animal (including humans)
• Software will start in an “embryonic” state and
develop when situated on a production environment
• What would a software “incubation” machine look
like?
• What would a software “nursery” look like?



Specialised
Function

Organs

Potential To
Develop into
Ultimate Solver
multiple different Commitment
types of cells

Individual

Cells Tissue

DNA/RNA



Production Environment
Input

TSP Organ

SC TSP
Software Cell SC

SC
SC

SC SC
Euclidean TSP Organ Solver
Software
Organism
Pluripotential Solver
“DNA”
GraphicalTSP Organ



An Ecosystem of solvers

Vehicle Routing
Solver
Protein Structure Prediction Graph Coloring
Software
Solver Solver
Organism
Software Software
Organism Organism

Network Interdiction
Solver
Software
Organism
Bin Packing
Solver
Software
Organism
Quadratic Assignment
Solver
Software
Organism

SAT
Solver
Graph Isomorphism TSP Software
Solver Solver Organism
Software Software
Organism Organism



Learn From Physics, Chemistry &
Biology The Invariants & Patterns Not
The Decorations
• Evolution Missing
• Self-Assembly & Self-Organisation Components
• Developmental systems
– Depend on a core genome coding for essential functionality
– Epigenomics canalises development
• Hierarchical control systems that modify programs including
susceptibility to horizontal gene (program libraries) transfer
• Infrastructure



As Biologists have done through an ubiquitous, worldwide
spanning bioinformatics infrastructure, we must build an online
worldwide computational problem solving infrastructure



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 by hand and we don’t know yet why a given
architecture performs well/bad in a specific

•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)
• The emerging trend is one of moving away from close-loop
optimisation towards open-ended and embodied optimisation

• Requires strong links with data mining, ALIFE and, of course, AI
(beyond existing trends in constraint satisfaction), search based
software engineering (beyond current trends on testing/debugging)

• Requires on-line electronic, computer friendly ontologies of code
(e.g the pattern language presented here), self-describing source
code,etc



Ideas To Tackle/Explore at Home
• Memetic Algorithms are NOT
algorithms:
– they dont always stop, we stop them
– they are big systems not short
algorithms
• On Biology & Software
– What is more complex, Bio or Soft?
– What can Synt Bio teach us?
• Thinking LOONNNGGG term!


Questions?!?

THANKS TO:
Dr. Zexuan Zhu
Dr. Maoguo Gong
Dr. Zhen Ji
Dr. Yew-Soon Ong



An Unorthodox View on Memetic Algorithms

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