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Spears, W. M. and K. A. De Jong,, "Analyzing GAs using Markov Models with Semantically Ordered and Lumped States," forthcoming Foundations of Genetic Algorithms 4, 1996.

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An Investigation of GA Performance Results for Different.. - Rees, Koehler (1997)   (Correct)

....extended the Vose model to cover 2 this case. Their method of analysis follows the binary case fairly closely, as might be expected. Recently, an exact model for the general cardinality case has been developed by Koehler, Bhattacharyya and Vose [10] De Jong et al. 6] and Spears and De Jong [14] presented how the exact model for the binary genetic algorithm can give important insights to transient GA behavior. This paper will use a similar approach to study the impact of different cardinalities using the Koehler Bhattacharyya Vose general cardinality model. In Section 2 we provide ....

....by different penalty structures or the different ways that the 1,631 invalid strings can be chosen and their impact on reproduction. Another strategy is to stretch the original fitness function to cover the whole range of the representation. For example, using a binary representation with = 14 given the original ranges of x i 01 80 , we might have x s 2 80 127 128 = and x s s 1 80 127 128 128 = 13 However, this method has drawbacks. Some ( x x 1 2 , points will be mapped into more frequently than others. For example, s = 13 and ....

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Spears, W. M. and K. A. De Jong,, "Analyzing GAs using Markov Models with Semantically Ordered and Lumped States," forthcoming Foundations of Genetic Algorithms 4, 1996.


An Overview of Multidimensional Visualization Techniques - Spears (1999)   (1 citation)  Self-citation (Spears)   (Correct)

....space. An extension of this technique for time varying data is to animate a parallel coordinate plot, redrawing the multidimensional points as they change over time. This has been especially useful in our investigations of how the column mass of a Markov chain of an EA changes over time (Spears and De Jong, 1996). ....

W. Spears and K. De Jong (1996). Analyzing GAs using Markov models with semantically ordered and lumped states. Foundations of Genetic Algorithms 4, 85--100.


A Compression Algorithm For Probability Transition Matrices - William Spears (1996)   (3 citations)  Self-citation (Spears)   (Correct)

....Further investigation into the nature of these search spaces may help characterize when arbitrary Markov chains are hard easy to compress with this algorithm. 6.2. Timing Experiments. It is now necessary to examine the computational cost of the compression algorithm. Our prior work, 2] and [9], focused heavily on the insights gained by actually examining Q n u , which involved computations on the order of N 3 (to multiply Q u repeatedly) Thus, the primary motivation for producing the compression algorithm was to gain the same insights more efficiently by dramatically reducing N . ....

W. Spears and K. De Jong, Analyzing GAs using Markov models with semantically ordered and lumped states. Foundations of GAs Workshop. Morgan Kaufmann, (1996), pp. 85 -- 100.

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