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Simulated Binary Crossover for Continuous Search Space.

Kalyanmoy Deb, +1 more
- 01 Jan 1995 - 
- Vol. 9
TLDR
A real-coded crossover operator is developed whose search power is similar to that of the single-point crossover used in binary-coded GAs, and SBX is found to be particularly useful in problems having mult ip le optimal solutions with a narrow global basin where the lower and upper bo unds of the global optimum are not known a priori.
Abstract
Abst ract . T he success of binary-coded gene t ic algorithms (GA s) in problems having discrete sear ch space largely depends on the coding used to represent the prob lem var iables and on the crossover ope ra tor that propagates buildin g blocks from parent strings to children st rings . In solving optimization problems having continuous search space, binary-coded GAs discr et ize the search space by using a coding of the problem var iables in binary strings. However , t he coding of realvalued vari ables in finit e-length st rings causes a number of difficulties: inability to achieve arbit rary pr ecision in the obtained solution , fixed mapping of problem var iab les, inh eren t Hamming cliff problem associated wit h binary coding, and processing of Holland 's schemata in cont inuous search space. Although a number of real-coded GAs are developed to solve optimization problems having a cont inuous search space, the search powers of these crossover operators are not adequate . In t his paper , t he search power of a crossover operator is defined in terms of the probability of creating an arbitrary child solut ion from a given pair of parent solutions . Motivated by the success of binarycoded GAs in discrete search space problems , we develop a real-coded crossover (which we call the simulated binar y crossover , or SBX) operator whose search power is similar to that of the single-point crossover used in binary-coded GAs . Simulation results on a nu mber of realvalued test problems of varying difficulty and dimensionality suggest t hat the real-cod ed GAs with the SBX operator ar e ab le to perfor m as good or bet ter than binary-cod ed GAs wit h the single-po int crossover. SBX is found to be particularly useful in problems having mult ip le optimal solutions with a narrow global basin an d in prob lems where the lower and upper bo unds of the global optimum are not known a priori. Further , a simulation on a two-var iable blocked function shows that the real-coded GA with SBX work s as suggested by Goldberg

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Citations
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References
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A Survey of Evolution Strategies.

TL;DR: Evolution Strategies are algorithms which imitate the principles of natural evolution as a method to solve parameter optimization problems and adaptation of the strategy parameters for the mutation variances as well as their covariances are described.
Journal Article

Genetic algorithms, noise, and the sizing of populations

TL;DR: Results suggest how the sizing equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior, and how these results may one day lead to rigorous proofs of convergence for recombinative G As operating on problems of bounded description.

Forma Analysis and Random Respectful Recombination.

TL;DR: Intrinsic parallelism is shown to have application beyond schemata and o-schemata and more general objects called formae are introduced and general operators which manipulate these are introduced.
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