An Unorthodox View on Memetic Algorithms

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Memetic Algorithms have become one of the key methodologies behind solvers that are capable of tackling very large, real-world, optimisation problems. They are being actively investigated in research institutions as well as broadly applied in industry. In this talk we provide a pragmatic guide on the key design issues underpinning Memetic Algorithms (MA) engineering. We begin with a brief contextual introduction to Memetic Algorithms and then move on to define a Pattern Language for MAs. For each pattern, an associated design issue is tackled and illustrated with examples from the literature. We then fast forward to the future and mention what, in our mind, are the key challenges that scientistis and practitioner will need to face if Memetic Algorithms are to remain a relevant technology in the next 20 years.

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An Unorthodox View on Memetic Algorithms

  1. 1. 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, FranceFriday, 15 April 2011
  2. 2. Outline of the Talk • An Unorthodox View of Memetic Algorithms • Futurology • Conclusions, Q&A IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  3. 3. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  4. 4. So… What Are Memetic Algorithms? MAs, one of the key methodologies behind successful discrete/continuous optimisation, are: IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  5. 5. So… What Are Memetic Algorithms? 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  6. 6. Lets Discuss: Are MAs a Nature Inspired Methodology? IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  7. 7. Lets Discuss: Are MAs a Nature Inspired Methodology? Does it mater? IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  8. 8. 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. IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  9. 9. The “Canonical” MA From Eiben’s & Smith “Introduction To Evolutionary Computation” IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  10. 10. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  11. 11. 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 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). IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  12. 12. 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 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). IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  13. 13. 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.” IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  14. 14. 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. IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  15. 15. Invariants and Decorations A Compact “Memetic” Algorithm by Merz (2003) IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  16. 16. Invariants and Decorations A “Memetic” Particles Swarm Optimisation by Petalas et al (2007) IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  17. 17. Invariants and Decorations A “Memetic” Artificial Immune System by Yanga et al (2008) IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  18. 18. Invariants and Decorations A “Memetic” Learning Classifier System by Bacardit & Krasnogor (2009) IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  19. 19. Invariants and Decorations • 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  20. 20. So… What Are Memetic Algorithms? IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  21. 21. So… What Are Memetic Algorithms? A carefully orchestrated interplay between (stochastic) global search and (stochastic) local search algorithms IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  22. 22. So… What Are Memetic 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  23. 23. 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! IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  24. 24. Template Patterns The high-level MA pattern can be refined through multiple “Template Patterns” Defines Algorithmic Backbones & “Pipelines” IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  25. 25. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  26. 26. 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! IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  27. 27. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  28. 28. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  29. 29. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  30. 30. Population Diversity Handling Strategy Pattern (PDHSP) IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  31. 31. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  32. 32. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  33. 33. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  34. 34. Multiple Local Searchers IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  35. 35. 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). IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  36. 36. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  37. 37. Outline of the Talk • An Unorthodox View of Memetic Algorithms • Futurology • Conclusions, Q&A IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  38. 38. 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, $$$, etc) Programming (self) adaptive Self-generating solving 1 problem – several classes instances ReuseSelf-Engineering Effort (e.g. Time, Reuse Feedback $$$, etc) Programming (self) adaptive Self-generating Solving multiple problem – several classes instances IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  39. 39. 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? IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  40. 40. Specialised Function Organs Potential To Develop into Ultimate Solver multiple different Commitment types of cells Individual Cells Tissue DNA/RNA IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  41. 41. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  42. 42. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  43. 43. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  44. 44. As Biologists have done through an ubiquitous, worldwide spanning bioinformatics infrastructure, we must build an online worldwide computational problem solving infrastructure IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  45. 45. Outline of the Talk • An Unorthodox View of Memetic Algorithms • Futurology • Conclusions, Q&A IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  46. 46. 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. IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  47. 47. 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 IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  48. 48. 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! IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  49. 49. IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011
  50. 50. Questions?!? THANKS TO: Dr. Zexuan Zhu Dr. Maoguo Gong Dr. Zhen Ji Dr. Yew-Soon Ong IEEE Symposium Series on Computational Intelligence 2011 - Paris, FranceFriday, 15 April 2011

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