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will be considered here. (The more complicated case, involving "predictive correction" during play of the game, is discussed in the latter half of section 8.4.) Because the detectors di are given and fixed, the strategies in  are completely determined by the weights wi, i = 1, . . . , l, so the search is actually a search through the space of l-tuples of weights, Wl. |
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A typical plan for optimization in Wladjusts the weights independently of each other (ignoring the interactions). However, in complex situations (such as playing checkers) this plan is almost certain to lead to entrapment on a false peak, or to oscillations between points distant from the optimum. Clearly such a plan is not robust. To make the reasons for this loss of robustness explicit, consider the plan  with an initial population  drawn from Wl,but with steps 3 and 4 of  extended as follows: |
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Clearly makes no use of the genetic operators. Over successive generations this plan has the same (stochastic) effect as repetition of the following sequence: |
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1. Form  from  by making (Ai(t)) copies of each element Ai (t), i = 1, . . . M in . (Payoff ½ yields a copy with probability ½, so that the expected number of elements in is  |
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2. All the copies of weights associated with position j of the l-tuples in are collected in a single set Wj(t), j = 1, . . ., . Wj(t) thus, typically, contains many duplicates of each weight in W. |
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3. Element Ai(t + 1) = (a1(i(t + 1), t + 1), . . ., al(i(t + 1), t + 1)), i = 1, . . ., M, is formed from by drawing weight a1(i(t + 1), t + 1) at random from set W1(t), weight a2(i(t + 1), t + 1) from W2(t), etc.  thus consists of M l-tuples formed by M successive drawings from the l sets Wj(t). |
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4. Return to step 1 to generate the next generation. |
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