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Evolutionary Computation
EEL 4818H
Ivan Garibay
12201 Research Parkway, Suite 501
http://ivan.research.ucf.edu
Fall 2008
1 Stochastic Search
āFurther research into intelligence of machinery will probably be very greatly concerned with searches... There is the genetical or evolutionary search by which a combination of genes is looked for, the criterion being the survival value. The remarkable success of this search confirms to some extent the idea that intellectual activity consist mainly of various kinds of searchā
āALAN TURING, āIntelligent Machineryā, 1948
As early as the very beginnings of the science of computation, in the times of Charles Babbage and his āanalytical engineā, search has been recognized as an important conceptual tool for problem solving. Later, in the initial stages of modern computational theory and artificial intelligence, Alan Turing proposed various kinds of search as a means to achieve machine intelligence. Since then, search, in particular heuristic search, has played an important and historical role in artificial intelligence. In heuristic search, a computer seeks the answer to a problem by searching through the space of all possible candidate solutions using heuristics to guide the search toward promising areas. These heuristics are simply guiding principles obtained by using knowledge about the nature of the problem being solved. Since the very beginning, there has been an intuitive understanding that, because heuristics are based on specific knowledge of the target problem, a universally best search algorithm, which is good for all problems, does not exist. It is only recently, however, that Wolpert and Macready (1997) have provided a formal proof. In their No Free Lunch theorems, they show, in essence, that an algorithm that performs well in one problem class is guaranteed to perform poorly on another. More importantly, they show that all search algorithms
perform the same when averaged over all possible problems. As a result, there is a fundamental tradeoff between algorithm robustness across problems and algorithm performance. Given that there is no universal search algorithm we are left with the task of designing algorithms that are specialized for a particular problem or a problem class. When there is an abundance of domain knowledge about the problem that we are trying to solve, a good deterministic algorithm can be designed and often its convergence to the optimal can be guaranteed. If the domain knowledge is incomplete, we still have the possibility of using some appropriate heuristic to guide the search. Unfortunately, for many interesting theoretical and practi- cal problems, the space to be searched is too complex or too vast or both for us to devise an obvious heuristic or to collect a meaningful amount of domain knowledge. These problems are difficult. For the worst of these cases, the best we can do is random or brute-force exhaustive search. Fortunately, many of these difficult problems share a key property that can be leveraged to guide the search: there is a positive correlation between the form and quality of candidate solutions. In other words, small changes in the form of a solution cause small changes in the resulting quality of the solution. Stochastic search algorithms are the class of search algorithms based on this key property. Stochastic search algorithms are more robust than other types of search algorithms in the sense that the key property they are based upon is quite general across problems and that they require less domain knowledge. They are weaker than other search algorithms in the sense that convergence to an optimum is usually not guar- anteed. However, stochastic search algorithms often outperform random search and they have been shown to have wide applicability on this class of difficult problems where no strong heuristics are available, especially on computationally hard combinatorial problems such planning, scheduling, constraint satisfaction, and satisfiability. The class of stochastic search algorithms includes, among others, the follow- ing algorithms, simulated annealing, stochastic hill-climbing, tabu search, ant colony optimization, and evolutionary computation.
2 Evolutionary Computation
This preservation of favorable individual differences and variations and the destruction of those which are injurious, I have called Natural Selection, or the Survival of the Fittest.
āCHARLES DARWIN, āThe Origin of Speciesā, 1859.
Evolutionary Computation (EC) is a relatively young field. Acording to the Handbook of Evolutionay Computation (BĀØack, Fogel & Michalewicz 1997), the term itself was coined in 1991 as an attempt to bring together three related research communities: Evolutionary Programming (Fogel 1962, Fogel 1964), Evolution Strategies (Rechenberg 1965) and Genetic Algorithms (Holland 1962,
procedure GA { initialize population; while termination condition not satisfied do { evaluate current population; select parents; apply genetic operators to parents to create offspring; set current population equal to be the new offspring population; } }
Figure 1: Basic steps of a typical genetic algorithm.
the main source of variation is mutation. The idea of a genotype to phenotype separation, as found in nature, has been a central part of the GA since its inception. Individuals are represented by structures called genotypes. GA operators manipulate the genotypes of each individual. After a decoding process, these genotypes are translated into phe- notypic structures upon which fitness is evaluated. The GA genotypes are typi- cally, but not always, restricted to bit strings. A segment or various segments of the genotype that represent a component of a solution are usually called genes. Figure 1 shows the basic steps of a GA. The initial population may be initialized randomly or with user-defined individuals. The GA then iterates thru an evaluate-select-reproduce cycle until either a stopping condition is satisfied or the computational resources are exhausted.
References
BĀØack, T., Fogel, D. B. & Michalewicz, Z., eds (1997), Handbook of Evolutionary Computation, IOP Publishing Ltd and Oxford University Press.
Darwin, C. (1859), The Origin of Species, J. M. Dent and Sons Ltd, 1975.
Fogel, L. J. (1962), āAutonomous automataā, Industrial Research 4 , 14ā19.
Fogel, L. J. (1964), On the Organization of Intellect, PhD thesis, University of California at Los Angeles.
Fraser, A. (1957), āSimulation of genetic systems by automatic digital comput- ersā, Australian Journal of Biological Sciences 10 , 484ā499.
Friedberg, R. M. (1958), āA learning machine: Part iā, IBM Journal 2 , 2ā13.
Friedberg, R. M., Dunham, B. & North, J. H. (1959), āA learning machine: Part iiā, IBM Journal 3 , 282ā287.
Goldberg, D. E. (1989), Genetic algorithms in search, optimization, and ma- chine learning, Addison Wesley.
Holland, J. H. (1962), āOutline for a logical theory of adaptive systemsā, ACM 9 , 297ā314.
Holland, J. H. (1975), Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, MI.
Rechenberg, I. (1965), Cybernetic solution path of an experimental problem, Translation 1122, Royal Aircraft Establishment Library.
