An Unorthodox View on Memetic Algorithms

IEEE Symposium Series on Computational Intelligence 2011 - Paris, France

An Unorthodox View on Memetic Algorithms

Prof. N. Krasnogor

Interdisciplinary Optimisation LaboratoryAutomated Scheduling, Optimisation and Planning Research Group

School of Computer Science & Information TechnologyUniversity of Nottingham

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

Friday, 15 April 2011

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

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


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


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

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


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

So… What Are Memetic Algorithms?



a carefully orchestrated interplay between (stochastic) global search and (stochastic)

local search algorithmsN. Krasnogor. Handbook of Natural Computation, chapter Memetic Algorithms. Natural Computing. Springer Berlin / Heidelberg, 2009

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




Are MAs a Nature Inspired Methodology?

Lets Discuss:



Are MAs a Nature Inspired Methodology?

Lets Discuss:

Does it mater?



• Key Design Issues underpinning MAs

A Research Paradigm

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” MAFrom Eiben’s & Smith “Introduction To Evolutionary Computation”



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

systems

What Memetic Algorithms are NOT?




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).


http://en.wikipedia.org/wiki/Sylow_theorems

http://en.wikipedia.org/wiki/Sylow_theorems



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).

Calculating Pi



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?

High Level• Pattern name• Problem statement• The solution• The Consequences• Examples

A collection of well defined patterns, i.e. a rich pattern language, substantially enhances our ability to communicate solutions to recurring problems without the need to 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




So… What Are Memetic Algorithms?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

A Pattern Language for computational problem solving

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



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 PatternsThe 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 PatternsThe MAs template pattern can be refined through strategy patterns

• Strategy Patterns represent a family of interchangeable algorithms

There are multiple strategy patternsin 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 AlgorithmsMemetic Algorithms by N. Krasnogor. Handbook of Natural Computation (chapter) in Natural Computing. Springer Berlin / Heidelberg, 2009.

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


http://www.cs.nott.ac.uk/~nxk/publications.html

http://www.cs.nott.ac.uk/~nxk/publications.html


Outline of the Talk





A General Trend: moving away from close-loop optimisation towards open-ended and embodied

optimisationEffort (e.g. Time, $$$, etc)Programming solving 1 problem – single instances

Programming solving 1 problem – several instances(self) adaptive

Programming solving 1 problem – several classes instances(self) adaptive Self-generating

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

Self-Engineering

Reuse

Reuse

Effort (e.g. Time, $$$, etc)



Feedback

Reuse Feedback



• 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?

The Future of MAsSoftware Nurseries



Cells

Organs

Tissue

Individual

DNA/RNA

Potential To Develop into

multiple different types of cells

Commitment

Specialised Function

Ultimate Solver


http://faculty.washington.edu/kepeter/119/images/sheep_heart4.jpg






























Software Cell SC

SC

SC

SC

SCSC

Pluripotential Solver“DNA”

TSP Organ

Euclidean TSP Organ

GraphicalTSP Organ

TSPSolver

SoftwareOrganism

Production EnvironmentInput


Protein Structure PredictionSolver

SoftwareOrganism

Vehicle RoutingSolver

SoftwareOrganism

Graph IsomorphismSolver

SoftwareOrganism

SATSolver

SoftwareOrganism

Bin PackingSolver

SoftwareOrganism

Graph ColoringSolver

SoftwareOrganism

Network InterdictionSolver

SoftwareOrganism


Quadratic AssignmentSolver

SoftwareOrganism

TSPSolver

SoftwareOrganism

An Ecosystem of solvers



Learn From Physics, Chemistry & Biology The Invariants & Patterns Not

The Decorations

• Evolution • Self-Assembly & Self-Organisation• 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

Missing Components



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



Outline of the Talk





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.


• 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


Conclusions (II)



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

Education

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