1. Introduction to Soft Computing Docent Xiao-Zhi Gao Department of Automation and Systems Technology xiao-zhi.gao@aalto.fi

2. What is Soft Computing? • Unlike conventional (hard) computing, soft computing applies a combination of different methods: Fuzzy Logic (FL), Neural Networks (NN), and Genetic Algorithms (GA) • Soft computing mimics human thinking • For example, reasoning/inference in decision making and imprecise information processing Over 100 000 publications today

3. Zadeh’s Definition on Soft Computing • Soft computing is an emerging approach to computing, which parallels the remarkable ability of the human mind to reason and learn in an environment of uncertainty and imprecision • Lotfi A. Zadeh, Father of Soft Computing, University of California-Berkeley

4. Lotfi A. Zadeh (1921-) Director, Berkeley Initiative in Soft Computing (BISC)Professor EmeritusUniversity of California, BerkeleyBerkeley, California USA

5. FL, NN, and GA • Fuzzy Logic • Fuzzy IF-THEN reasoning rules • Neural Networks • Capable of approximation and adaptation • Genetic Algorithms • All-purposederivative-free optimization method

6. Fuzzy Systems (FS) • Fuzzy systems can approximate decision making processes of human under uncertain environments • Fuzzy systems are based on fuzzy sets and fuzzy reasoning • fuzzy sets are generalization of crisp sets • fuzzy reasoning infers conclusions from known facts using given fuzzy rules

7. Fuzzy Systems (FS) • Modeling of human thinking • Numerical values are not efficient • Linguistic variables exist in real world • An example: • Chatting with a stranger on the phone • Estimation of your partner’s age: (40? probability of 40? or aboutmiddle-aged?) • about middle aged (linguistic term)

8. Fuzzy Systems (FS) • Fuzzy logic derives conclusions based on given fuzzy IF-THEN rules and known facts • An example: • Given a fuzzy rule: IF bath is very hot, THEN add a lot of cold water • Known fact: bath is a little hot • Conclusion: how much cold water should be added? • Fuzzy conclusion: a small amount of cold water

9. Structure of Fuzzy Systems (FS)

10. Structure of Human Brain

11. Human Neurons

12. Neural Networks (NN) • Neural networks are highly simplified models of human brain to deal with specific tasks • massively connected neurons • Several kinds of neural networks are proposed • feedforward neural networks • recurrent neural networks • supervised neural networks • unsupervised neural networks • Applications of neural networks are intensive

13. Neural Networks (Feedforward) Back-Propagation Neural Networks (Multiple Layer Perceptron)

14. Neural Networks (Recurrent) Hopfield Neural Networks (Hopfield [1982] [1986])

15. Charles Darwin (1809-1882)

16. ’The Origin of Species’ by Darwin [1859]

17. Species Evolution and Natural Selection

18. Flow Chart of Genetic Algorithms

19. Fusion of Soft Computing Methods • Soft computing methods are considered complementary rather than competitive • There are various kinds of combinations of soft computing methods • Fusion of soft computing methods not only stays on algorithm level, but also system level

20. Framework of Soft Computing

21. Example I:Genetic Algorithms + Fuzzy Logic

22. Example II:Neural Networks + Fuzzy Logic ANFIS by R. Jang [Jang 97]

23. Model Construction:Comparison between SC and HC • Mathematical models are linear and non-linear functions

24. Model Construction (Traditional Rules) • Rules with sharp boundaries IF 0 ≤ x ≤ 1, THEN y=1 IF 1 ≤ x ≤ 2, THEN y=0.99 … IF 9 ≤ x ≤ 10, THEN y=0 IF 0≤x ≤ 1, THEN y=f(x) IF 1 ≤ x ≤ 2, THEN y=g(x) … IF 9 ≤ x ≤ 10, THEN y=h(x)

25. Model Construction (Fuzzy Logic) • Multiple fuzzy rules are fired with each input simultaneously IF x0, THEN y  1 IF x  5, THEN y  0.5 IF x  10, THEN y  0

26. Model Construction (Neural Networks) • Model-free approximation based on training data x=0, y=1.0 x=0.5, y=0.99 … x=10, y=0

27. An Application Example (HC vs SC) Inverted Pendulum Difficult to solve with Hard Computing

28. Neural Networks-based Solution to Inverted Pendulum Control

29. Neural Networks-based Solution to Inverted Pendulum Control

30. Fuzzy Logic-based Solution to Inverted Pendulum Control

31. Fuzzy Logic-based Solution to Inverted Pendulum Control

32. Power Control in Mobile Communications Systems: A Case Study of HC and SC

33. Mobile Power Control with Hard Computing

34. Mobile Power Control with Soft Computing

35. Features of Soft Computing • Advantages of soft computing methods • Take advantage of human intuition • Cope with imprecision and uncertainty • Disadvantages of soft computing methods • Complex structures and algorithms • Heavy computation burden • Still not as widely used as Hard Computing in engineering areas yet

36. Soft Computing and Hard Computing • Soft computing and hard computing are also complementary rather than competitive [Ovaska 99, 02, 04]

37. Fusion of SC and HC

38. SC and HC (Independent)

39. SC and HC (Parallel)

40. Fusion of SC & HC in Missile Autopilot McDowell [1997]

41. SC and HC (Serial) PreProcessing PostProcessing

42. Fusion of SC and HC in Electric Load Forecasting Kamiya [2003]

43. Fusion of SC and HC in Power Control of Mobile Communications Gao [2001]

44. Fusion of SC and HC in Boiler-Turbines Systems Fault Diagnosis Ben-Abdennour [1996]

45. HC-Designed SC & SC-Designed HC

46. Fusion of SC and HC in Time Series Prediction Akhmetov [2001] General Parameter Method

47. Fusion of SC and HC in NuclearSteam Generator Control Systems Zhao[1997]

48. HC-Assisted SC & SC-Assisted HC

49. Fusion of SC and HC in Large-Scale Power Plant Control Kamiya [2003]

50. Problems of HC Solved by SC