Selection of Encoding Cardinality for a Class of Fitness Functions to Obtain Order-1 Building Blocks

AbstractEncoding plays a key role in determining the optimization efficiency of a genetic algorithm. In the optimization of a continuous function, binary encodings are normally used due to their low coding-alphabet cardinalities. Nevertheless, from the viewpoint of building-block supply, it is remarked that a binary encoding is not necessarily the best choice to express a fitness function which is linearly combined of sinusoidal functions with frequencies exponential to a positive integer m when m is not equal to 2. It is proved that, if the frequencies are exponential to m, an encoding of cardinality m can provide a better supply of order-1 building blocks than the encodings of other cardinalities. Taking the advantage of building-block supplies, a genetic algorithm with an encoding of cardinality m has higher chance to find fitter solutions. This assumption is verified via a number of randomly generated fitness functions, and encodings with different cardinalities are compared according to the optimizat...

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