# mean-square deviation

## mean-square deviation

[′mēn ′skwer dē·vē′ā·shən]
(statistics)
A measure of the extent to which a collection v1, v2, …, vn of numbers is unequal; it is given by the expression (1/ n)[(v1- v̄)2+ ⋯ + (vn - v̄)2], where v̄ is the mean of the numbers.
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1 714 51 0.70 1 7.3101 7.4634 2 1200 100 0.60 1 6.5444 6.5416 3 1500 150 0.50 1 5.0583 4.8784 4 714 100 0.50 1.5 6.3165 6.1068 5 1200 150 0.70 1.5 5.7280 5.4203 6 1500 51 0.60 1.5 6.9680 7.3099 7 714 150 0.60 2 5.4955 5.0436 8 1200 51 0.50 2 3.8404 4.1524 9 1500 100 0.70 2 5.6861 5.6987 Average value, [x.sub.cp] 5.883 5.846 Maximum value, [x.sub.max] 7.310 7.463 Minimum value, [x.sub.min] 3.840 4.152 Variation range, R=[x.sub.max] 3.469 3.311 - [x.sub.min] Mean linear deviation, a = [1/n] 0.8015 0.8972 [[summation].sup.n.sub.i=1] [absolute value of [x.sub.i] - [bar.x]] Mean-square deviation, [sigma] = 0.9436 0.9981 [square root of [1/n][[summation].sup .n.sub.i=1][([x.sub.i] - [bar.x]).sup.2]] Coefficient of correlation 0.9697 Experiment Relative No.
Through a mass of experiments and the experience of GA, we assume that the probability of performing crossover is 0.7, the probability of mutation is 0.005, the convergent function is the mean-square deviation between the estimated coordinate (formula 1) and the reality coordinate of the unknown nodes, and the termination criteria is that the mean-square deviation declines.
In formula 1, ([x.sub.i], [y.sub.i]) is the estimated coordinate of unknown node, i = 1 ~ n; ([x'.sub.i], [y'.sub.i]) is the reality coordinate of the unknown node, i = 1~n;, n is the amount of the unknown nodes; f is the mean-square deviation mentioned above.
Calculate the mean-square deviation of the distances between unknown nodes and their neighbor beacon nodes of the best individual in the first generation, set the mean-square deviation as the convergence function, and set the probability of performing crossover, probability of mutation and termination criteria.

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