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Table 1 summarizes the test functions used in the following experiments together with the initial m(0) and σ(0). The initial covariance matrix C(0) and the diagonal decoding matrix D(0) are always set to the identity matrix. The random vectors and the random matrix appearing in Table 1 are initialized randomly for each problem instance, but the same values are used for different algorithms for fair comparison. A trial is considered as success if the target function value of 10-8 is reached before the algorithm spends 5×104n function evaluations, otherwise regarded as failure. For n40 we conducted 20 independent trials for each setting, 10 for 80n320, and 3 for n640. When the computational effort of evaluating the test function scales worse than linear with the dimension (i.e., on rotated functions) we may omit dimensions larger than 320.

Table 1:
Test function definitions and initial conditions. The unit vector u is either e1=(1,0,,0) for separable scenarios, or random vectors drawn uniformly on the unit sphere for nonseparable scenarios or for Ell-Cig and Ell-Dis. A vector z represents an orthogonal transformation Rx of the input vector x, where the orthogonal matrix R is the identity matrix for separable scenarios, or is constructed by generating normal random elements and applying the Gram-Schmidt procedure. The diagonal matrix Dell=diag(1,,10i-1n-1,,10) represents a coordinate-wise scaling and the vector y is a coordinate-wisely transformed input vector y=Dell2x.
f(xm(0)σ(0)
Sphere x2 3·1 
Cigar u,x2+106(x2-u,x2) 3·1 
Discus 106u,x2+(x2-u,x2) 3·1 
Ellipsoid Dell3z2 3·1 
TwoAxes 106i=1n/2[z]i2+i=n/2+1n[z]i2 3·1 
Ell-Cig 10-4mu,y2+(y2-u,y2) 3·1 
Ell-Dis 104u,y2+(y2-u,y2) 3·1 
Rosenbrock i=1n-1100([z]i2-[z]i+1)2+([z]i-1)2 0 0.1 
Bohachevsky i=1n-1([z]i2+2[z]i+12-0.3cos(3π[z]i) N(0,82I) 
 -0.4cos(4π[z]i+1)+0.7)   
Rastrigin i=1n[z]i2+10(1-cos(2π[z]i)) N(0,32I) 
f(xm(0)σ(0)
Sphere x2 3·1 
Cigar u,x2+106(x2-u,x2) 3·1 
Discus 106u,x2+(x2-u,x2) 3·1 
Ellipsoid Dell3z2 3·1 
TwoAxes 106i=1n/2[z]i2+i=n/2+1n[z]i2 3·1 
Ell-Cig 10-4mu,y2+(y2-u,y2) 3·1 
Ell-Dis 104u,y2+(y2-u,y2) 3·1 
Rosenbrock i=1n-1100([z]i2-[z]i+1)2+([z]i-1)2 0 0.1 
Bohachevsky i=1n-1([z]i2+2[z]i+12-0.3cos(3π[z]i) N(0,82I) 
 -0.4cos(4π[z]i+1)+0.7)   
Rastrigin i=1n[z]i2+10(1-cos(2π[z]i)) N(0,32I) 

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