4/21/2005 Hybrid SC and EA - Outline Hybrid Soft Computing: • Soft Computing Overview Where Are We Going? -SC Components: PR, FL, NN, EA • Modeling with FL and EA • Hybrid SC Systems -FLC Parameter Tuning by EA Piero P. Bonissone -EA Parameter Setting GE • Conclusions Soft Computing Hybrid SC and EA - Outline • Soft Computing (SC): the symbiotic use of • Soft Computing Overview many emerging problem-solving disciplines. -SC Components: PR, FL, NN, EA • According to Prof. Zadeh: "...in contrast to traditional hard computing, soft computing • Modeling with FL and EA exploits the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, low solution-cost, and better rapport with reality” • Hybrid SC Systems • Soft Computing Main Components: -FLC Parameter Tuning by EA - Approximate Reasoning: -EA Parameter Setting » Probabilistic Reasoning, Fuzzy Logic - Search & Optimization: • Conclusions » Neural Networks, Evolutionary Algorithms Soft Computing: Hybrid Probabilistic Systems Problem Solving Techniques Approximate Functional Approximation/ Reasoning Randomized Search HARD COMPUTING SOFT COMPUTING Probabilistic Multivalued & Neural Evolutionary Fuzzy Logics Algorithms Models Networks Precise Models Approximate Models Bayesian Belief Nets Dempster- Traditional Functional Shafer Symbolic Numerical Approximate Approximation Logic Reasoning Modeling and and Randomized Reasoning Search Search Page 1 1
4/21/2005 Soft Computing: Hybrid Probabilistic Systems Soft Computing: Hybrid Probabilistic Systems Approximate Approximate Functional Approximation/ Functional Approximation/ Reasoning Randomized Search Reasoning Randomized Search Multivalued & Evolutionary Multivalued & Evolutionary Probabilistic Neural Probabilistic Neural Models Fuzzy Logics Networks Algorithms Models Fuzzy Logics Networks Algorithms Bayesian Bayesian Belief Nets Belief Nets Dempster- Dempster- Shafer Shafer HYBRID PROBABILISTIC SYSTEMS HYBRID PROBABILISTIC SYSTEMS Probability of Belief of Probability of Belief of Fuzzy Influence Fuzzy Influence Fuzzy Events Fuzzy Events Fuzzy Events Diagrams Fuzzy Events Diagrams Soft Computing: Hybrid Probabilistic Systems Soft Computing: Hybrid FL Systems Approximate Functional Approximation/ Approximate Functional Approximation/ Reasoning Randomized Search Reasoning Randomized Search Probabilistic Multivalued & Neural Evolutionary Probabilistic Multivalued & Neural Evolutionary Fuzzy Logics Networks Algorithms Models Fuzzy Logics Algorithms Models Networks Bayesian Multivalued Fuzzy Belief Nets Systems Algebras Dempster- Fuzzy Logic Shafer Controllers HYBRID PROBABILISTIC SYSTEMS Probability of Belief of Fuzzy Influence Fuzzy Events Fuzzy Events Diagrams Soft Computing: Hybrid FL Systems Soft Computing: Hybrid FL Systems Approximate Approximate Functional Approximation/ Functional Approximation/ Reasoning Reasoning Randomized Search Randomized Search Multivalued & Neural Evolutionary Multivalued & Neural Evolutionary Probabilistic Probabilistic Models Fuzzy Logics Networks Algorithms Models Fuzzy Logics Networks Algorithms Multivalued Multivalued Fuzzy Fuzzy Systems Algebras Systems Algebras Fuzzy Logic Fuzzy Logic Controllers Controllers HYBRID FL SYSTEMS HYBRID FL SYSTEMS NN modified by FS FLC Tuned by NN NN modified by FS FLC Tuned by NN FLC Generated FLC Generated (Fuzzy Neural (Neural Fuzzy (Fuzzy Neural (Neural Fuzzy and Tuned by EA and Tuned by EA Systems) Systems) Systems) Systems) Page 2 2
4/21/2005 Soft Computing: Hybrid NN Systems Soft Computing: Hybrid FL Systems Approximate Functional Approximation/ Approximate Functional Approximation/ Reasoning Randomized Search Reasoning Randomized Search Multivalued & Neural Evolutionary Probabilistic Probabilistic Multivalued & Neural Evolutionary Fuzzy Logics Algorithms Models Networks Fuzzy Logics Networks Algorithms Models Recurrent Fuzzy Multivalued Feedforward Algebras NN Systems NN Fuzzy Logic Single/Multiple Hopfield SOM ART RBF Controllers Layer Perceptron HYBRID FL SYSTEMS NN modified by FS FLC Tuned by NN FLC Generated (Fuzzy Neural (Neural Fuzzy and Tuned by EA Systems) Systems) Soft Computing: Hybrid NN Systems Soft Computing: Hybrid NN Systems Approximate Approximate Functional Approximation/ Functional Approximation/ Reasoning Reasoning Randomized Search Randomized Search Multivalued & Evolutionary Multivalued & Evolutionary Probabilistic Neural Probabilistic Neural Models Fuzzy Logics Networks Algorithms Models Fuzzy Logics Networks Algorithms Recurrent Recurrent Feedforward Feedforward NN NN NN NN Single/Multiple Single/Multiple SOM SOM RBF Hopfield ART RBF Hopfield ART Layer Perceptron Layer Perceptron HYBRID NN SYSTEMS HYBRID NN SYSTEMS NN parameters NN parameters NN topology &/or NN topology &/or (learning rate η (learning rate η weights weights momentum α ) momentum α ) generated by EAs generated by EAs controlled by FLC controlled by FLC Soft Computing: Hybrid EA Systems Soft Computing: Hybrid EA Systems Approximate Approximate Functional Approximation/ Functional Approximation/ Reasoning Reasoning Randomized Search Randomized Search Probabilistic Multivalued & Neural Evolutionary Probabilistic Multivalued & Neural Evolutionary Fuzzy Logics Networks Algorithms Fuzzy Logics Networks Algorithms Models Models Evolution Evolution Genetic Genetic Strategies Strategies Algorithms Algorithms Evolutionary Genetic Evolutionary Genetic Programs Progr. Programs Progr. HYBRID EA SYSTEMS EA parameters EA-based search EA parameters (N, P cr , P mu ) (Pop size, select.) inter-twined with controlled by FLC hill-climbing controlledby EA Page 3 3
4/21/2005 Soft Computing: Hybrid EA Systems Soft Computing: Hybrid EA Systems Approximate Functional Approximation/ Approximate Functional Approximation/ Reasoning Reasoning Randomized Search Randomized Search Multivalued & Neural Evolutionary Multivalued & Neural Evolutionary Probabilistic Probabilistic Fuzzy Logics Algorithms Fuzzy Logics Algorithms Models Networks Models Networks Evolution Evolution Genetic Genetic Strategies Strategies Algorithms Algorithms Evolutionary Genetic Evolutionary Genetic Programs Progr. Programs Progr. HYBRID EA SYSTEMS HYBRID EA SYSTEMS EA parameters EA parameters EA parameters EA parameters EA-based search EA-based search (N, P cr , P mu ) inter-twined with (Pop size, select.) (N, P cr , P mu ) inter-twined with (Pop size, select.) controlled by FLC controlledby EA controlled by FLC controlledby EA hill-climbing hill-climbing Fuzzy Logic Genealogy Hybrid SC and EA – Outline (2) • Origins: MVL for treatment of imprecision • Soft Computing Overview and vagueness -SC Components: PR, FL, NN, EA - 1930s: Post, Kleene, and Lukasiewicz attempted to represent undetermined , • Modeling with FL and EA unknown, and other possible intermediate truth-values. • Hybrid SC Systems - 1937: Max Black suggested the use of a consistency profile to represent vague -FLC Parameter Tuning by EA (ambiguous) concepts -EA Parameter Setting - 1965: Zadeh proposed a complete theory of fuzzy sets (and its isomorphic fuzzy logic), to • Conclusions represent and manipulate ill-defined concepts Fuzzy Logic : Linguistic Variables Fuzzy Logic : Reasoning Methods • Fuzzy logic give us a language (with syntax and • The meaning of a linguistic variable may be interpreted as a elastic constraint on its value. local semantics), in which we can translate our qualitative domain knowledge. • These constraints are propagated by fuzzy inference operations, based on the generalized • Linguistic variables to model dynamic systems modus-ponens . • These variables take linguistic values that are • A FL Controller (FLC) applies this reasoning characterized by: system to a Knowledge Base (KB) containing the - a label - a sentence generated from the syntax problem domain heuristics. - a meaning - a membership function • The inference is the result of interpolating determined by a local semantic procedure among the outputs of all relevant rules. • The outcome is a membership distribution on the output space, which is defuzzified to produce a crisp output. Page 4 4
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