Evolutionary Computational Intelligence
This lecture provides an in-depth overview of Evolutionary Programming (EP) and Differential Evolution (DE), focusing on their historical context and foundational concepts. Developed in the USA during the 1960s, EP emphasizes adaptive behavior for intelligence prediction, leveraging finite state machines for machine learning tasks. Key characteristics include a flexible framework with no recombination, self-adaptive parameters, and parent selection based on deterministic mutation. Additionally, DE is introduced, detailing its approach to optimization through real-number vectors and success-driven offspring selection.
Evolutionary Computational Intelligence
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Presentation Transcript
Evolutionary Computational Intelligence Lecture 5a: Overview about Evolutionary Programming Ferrante Neri University of Jyväskylä Lecture 5: EP and DE
EP quick overview • Developed: USA in the 1960’s • Early names: D. Fogel • Typically applied to: • traditional EP: machine learning tasks by finite state machines • contemporary EP: (numerical) optimization • Attributed features: • very open framework: any representation and mutation op’s OK • crossbred with ES (contemporary EP) • consequently: hard to say what “standard” EP is • Special: • no recombination • self-adaptation of parameters standard (contemporary EP) Lecture 5: EP and DE
EP technical summary tableau Lecture 5: EP and DE
Historical EP perspective • EP aimed at achieving intelligence • Intelligence was viewed as adaptive behaviour • Prediction of the environment was considered a prerequisite to adaptive behaviour • Thus: capability to predict is key to intelligence Lecture 5: EP and DE
Finite State Machine as predictor • Consider the following FSM • Task: predict next input • Quality: % of in(i+1) = outi • Given initial state C • Input sequence 011101 • Leads to output 110111 • Quality: 3 out of 5 Lecture 5: EP and DE
Representation • For continuous parameter optimization • Chromosomes consist of two parts: • Object variables: x1,…,xn • Mutation step sizes: 1,…,n • Full size: x1,…,xn,1,…,n Lecture 5: EP and DE
Mutation • Chromosomes: x1,…,xn,1,…,n • i’ = i•(1 + • N(0,1)) • x’i = xi + i’• Ni(0,1) • 0.2 • boundary rule: ’ < 0 ’ = 0 • Other variants proposed & tried: • Lognormal scheme as in ES • Using variance instead of standard deviation • Mutate -last • Other distributions, e.g, Cauchy instead of Gaussian Lecture 5: EP and DE
Recombination • None • Rationale: one point in the search space stands for a species, not for an individual and there can be no crossover between species • Much historical debate “mutation vs. crossover” • Pragmatic approach seems to prevail today Lecture 5: EP and DE
Parent selection • Each individual creates one child by mutation • Thus: • Deterministic • Not biased by fitness Lecture 5: EP and DE
Survivor selection • P(t): parents, P’(t): offspring • Pairwise competitions in round-robin format: • Each solution x from P(t) P’(t) is evaluated against q other randomly chosen solutions • For each comparison, a "win" is assigned if x is better than its opponent • The solutions with the greatest number of wins are retained to be parents of the next generation • Parameter q allows tuning selection pressure • Typically q = 10 Lecture 5: EP and DE
Example application: evolving checkers players (Fogel’02) • Neural nets for evaluating future values of moves are evolved • NNs have fixed structure with 5046 weights, these are evolved + one weight for “kings” • Representation: • vector of 5046 real numbers for object variables (weights) • vector of 5046 real numbers for ‘s • Mutation: • Gaussian, lognormal scheme with -first • Plus special mechanism for the kings’ weight • Population size 15 Lecture 5: EP and DE
Example application: evolving checkers players (Fogel’02) • Tournament size q = 5 • Programs (with NN inside) play against other programs, no human trainer or hard-wired intelligence • After 840 generation (6 months!) best strategy was tested against humans via Internet • Program earned “expert class” ranking outperforming 99.61% of all rated players Lecture 5: EP and DE
Evolutionary Computational Intelligence Lecture 5b:Differential Evolution Lecture 5: EP and DE
Brief historical overview • The Term Differntial Evolution has been coined in 1994 by Storn and Proce (Germany-USA) • Some important invesigations have been recently done by Lampinen • The so far only existing book has been published in 2005 Lecture 5: EP and DE
Representation • Differential Evolution in its original implementation is intended for vectors of real numbers • Nevertheless it can be employed also in the case of integer problems, probably loosing in terms of efficiency Lecture 5: EP and DE
Population models • GA and “comma” ES employ a generational logic: offspring population replaces entirely the previous population • “plus” ES considers both parents and offspring and after having sorted them selects a predetermined number of best performing individuals • Differential Evolution (DE) emplys a steady-state logic (also used in some GAs): the successfull offspring immediately “kills” the weakest parent Lecture 5: EP and DE
Initial Sampling • A set of vectors in sampled, usually at random with the boundaries of the decision space • And these vector represent the design variables that we are willing to optimize • Our population size must be at least four Lecture 5: EP and DE
Parent selection • Four individuals x1, x2, x3, x4 are selected at random from the population by means of a uniformly distributed function • Like in ES there is no selection pressure for the choice of the parents undergoing variation operators (recombination and mutation) Lecture 5: EP and DE
Recombination • A provisional offspring xoffp is generated by: xoffp=x1+K(x2-x3) where K is s constant value usually set equal to 0.7 Lecture 5: EP and DE
Mutation • With a certain probability some genes of the provisional offspring are replaced with some genes of x4. • The probability of happening such mutation is usually set to 0.3 Lecture 5: EP and DE
Survivor seelection • The offspring xoff is thus generated. • The fitness value of xoff is calculated and,according to a steady-state strategy, • if xoff outperforms x4, it replaces x4, • if on the contrary f(xoff)>f(x4), no replacement occurs. Lecture 5: EP and DE
Observations • The steady state logic makes the DE structure without generation loops since the replacements occurs as soon as a better solution is generated • Exploratory logic of DE has a slight analogy with Nelder Mead since it lets the search directions been led by means of existing solutions. Analogy for 2 dimension case is rather strong • The DE is very promising but the biggest limit it has is the risk of stagnation Lecture 5: EP and DE
Premature Convergence/ Stagnation • There are the main defects in EAs • Premature Convergence: It occurs when all the population does not have any difference (one genotype) and the corrensponding fitness value is suboptimal (+ strategy) • Stagnation:It occurs when, notwithstanding a high diversity, there are no improvements (superfit individual) Lecture 5: EP and DE
Evolutionary Computational Intelligence Lecture 5c:Handling Multimodality Lecture 5: EP and DE
Motivation 1: Multimodality Most interesting problems have more than one locally optimal solution. Lecture 5: EP and DE
Motivation 2: Genetic Drift • Finite population with global (panmictic) mixing and selection eventually convergence around one optimum • Often might want to identify several possible peaks • This can aid global optimisation when sub-optima has the largest basin of attraction Lecture 5: EP and DE
Biological Motivation 1: Speciation • In nature different species adapt to occupy different environmental niches, which contain finite resources, so the individuals are in competition with each other • Species only reproduce with other members of the same species (Mating Restriction) • These forces tend to lead to phenotypic homogeneity within species, but differences between species Lecture 5: EP and DE
Biological Motivation 2: Punctuated Equilbria • Theory that periods of stasis are interrupted by rapid growth when main population is “invaded” by individuals from previously spatially isolated group of individuals from the same species • The separated sub-populations (demes) often show local adaptations in response to slight changes in their local environments Lecture 5: EP and DE
Implications for Evolutionary Optimization • Two main approaches to diversity maintenance: • Implicit approaches: • Impose an equivalent of geographical separation • Impose an equivalent of speciation • Explicit approaches • Make similar individuals compete for resources (fitness) • Make similar individuals compete with each other for survival Lecture 5: EP and DE
