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N 0 (0,1)

x 0. Mutation 0. σ ’ 0. +. x’ n-1. x’ 1. x’ 0. N 0 (0,1). x 1. Mutation 1. σ ’ 1. +. N 1 (0,1). x n-. Mutation n-1. σ ’ n-1. +. N n-1 (0,1). Hidden Layer Neurons. Figure 1.1: Implementation of Regular ES using an ANN. x 0. Mutation 0. σ ’ 0. +. x’ n-1. x’ 1. x’ 0.

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N 0 (0,1)

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  1. x0 Mutation 0 σ’0 + x’n-1 x’1 x’0 N0(0,1) x1 Mutation 1 σ’1 + N1(0,1) xn- Mutation n-1 σ’n-1 + Nn-1(0,1) Hidden Layer Neurons Figure 1.1: Implementation of Regular ES using an ANN

  2. x0 Mutation 0 σ’0 + x’n-1 x’1 x’0 N0(0,1) x1 Mutation 1 σ’1 + N1(0,1) Xn- Mutation n-1 σ’n-1 + Nn-1(0,1) Hidden Layer Neurons Figure 1.2: Using a Linear ANN as a Mutation calculator for ES

  3. x0 Mutation 0 σ’0 + x’n-1 x’0 x’1 N0(0,1) x1 Mutation 1 σ’1 + N1(0,1) Xn- Mutation n-1 σ’n-1 + Nn-1(0,1) Bias Input = +1 Hidden Layer Neurons Figure 1.6: Using a NonLinear ANN as a Mutation calculator for ES

  4. x0 + Mutation 0 σ’0 x’n-1 x’1 x’0 x1 N0(0,1) + Mutation 1 σ’1 N1(0,1) Xn- x0 Hidden Layer Neurons Mutation n-1 σ’n-1 x1 + Nn-1(0,1) Xn-1 Figure 1.9: Using a Linear NN with PDVs fed back to calculate mutations for ES

  5. x0 + Mutation 0 σ’0 x’n-1 x’1 x’0 x2 N0(0,1) + Mutation 1 σ’1 N1(0,1) Xn- x0 Hidden Layer Neurons Mutation n-1 σ’n-1 x1 + Nn-1(0,1) Xn-1 Figure 1.10: Using a NonLinear NN with PDVs fed back to calculate mutations for ES Bias Input = +1

  6. Mutation 0 N0(0,1) Mutation 1 N1(0,1) Mutation 2 + x’0 + x’1 + x’n-1 Summer Nodes X0 X1 Xn-1 Nn-1(0,1) Weights = Mutation Vectors Hidden Layer Neurons Bias Input = +1 Gaussian Random Numbers Current Problem Domain Variables Tie Points Mutation Calculator Figure 2.3: Implementation of Regular ES using an ANN

  7. Fig. 4.1Contour Plots for Ratio Change in Variable Importance = 10 and Rotation Angles = 0, 30, 45 ,60

  8. Fig. 4.2Contour Plots for Ratio Change in Variable Importance = 100 and Rotation Angles = 0, 30, 45 ,60

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