Genetic Programming Theory and Practice X (Genetic and Evolutionary Computation)
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These contributions, written by the foremost international researchers and practitioners of Genetic Programming (GP), explore the synergy between theoretical and empirical results on real-world problems, producing a comprehensive view of the state of the art in GP.
Topics in this volume include: evolutionary constraints, relaxation of selection mechanisms, diversity preservation strategies, flexing fitness evaluation, evolution in dynamic environments, multi-objective and multi-modal selection, foundations of evolvability, evolvable and adaptive evolutionary operators, foundation of injecting expert knowledge in evolutionary search, analysis of problem difficulty and required GP algorithm complexity, foundations in running GP on the cloud – communication, cooperation, flexible implementation, and ensemble methods. Additional focal points for GP symbolic regression are: (1) The need to guarantee convergence to solutions in the function discovery mode; (2) Issues on model validation; (3) The need for model analysis workflows for insight generation based on generated GP solutions – model exploration, visualization, variable selection, dimensionality analysis; (4) Issues in combining different types of data.
Readers will discover large-scale, real-world applications of GP to a variety of problem domains via in-depth presentations of the latest and most significant results.
(Hindorff et al., 2009b). However, much of the estimated heritability in disease state attributable to genetics has not yet been identified. There has been much speculation about where this “missing heritability” may be lurking (Maher, 2008) including gene-gene and gene-environmentinteractions, pathway and underground networks, or ingene expression variation. While there are a variety of possibilities, little has been done thus far to identify these alternative complex models of disease risk. As
While this process adds some annotation overhead to (E10), it does expose all of the real number constants in a vector which is swarm intelligence friendly. At this point let us take a brief pause. Examine the original s-expression (E10) also (E11.1) and compare it to the new annotated abstract version (E11). Walk through the evaluation process for each version. Satisfy yourself that the concrete s-expression (E11.1) and the abstract annotated (E11) both evaluate to exactly the same interim and
122 sort me.pool ascending by fitness score 123 truncate me.pool to the maxPoolSize most fit constant vectors 124 set me.c = me.pool.first 125 set me.sexp = convertToSExp(me) 126 // Enforce iterative search of constant pool 127 set Ic = Ic + 1 128 if (Ic>=maxPoolSize) then set Ic = 0 end if 129 return me 130 end fun optimizeConstants The results with the enhancements for constant optimization and operator weighted population pruning are shown in Table 9.3. Table 9.3Results with weighted
and x 2. The ranges of the input variables are shown in Table 10.1. Table 10.1Range of input variables – first data set x 1 x 2 x 3 x 4 x 5 x 6 Min 2.4 4.2 112.8 9.9 3,356 109.6 Max 3.3 83.2 125.6 13.8 4,948 115.7 The observed pairwise correlation among the inputs is shown in Table 10.2. Table 10.2Pairwise correlation among the inputs – first data set x 1 x 2 x 3 x 4 x 5 x 6 x 1 1.00 0.50 0.48 0.72 0.58 0.61 x 2 0.50 1.00 0.23 0.67 0.66 0.64
of cards is well placed if all its cards are in descending order and alternating colors. NumCardsNotAtFoundations: Count the number of cards that are not at the foundation piles. FreeCells: Count the number of free FreeCells and cascades. DifferenceFromTop: The average value of the top cards in cascades, minus the average value of the top cards in foundation piles. LowestFoundationCard: The highest possible card value (typically the king) minus the lowest card value in foundation piles.