<p>In this article we have derived two versions, ξk and ρk were derived from an algorithm based on the first suggested modified Fletcher-Reeves method in the article for the two-term CG method and another term to get a downward search towards the function minimum point with the search for an inaccurate line and we have proved rapprochement. These two algorithms combined with the Cuckoo algorithm to achieve a remarkable performance in reducing the number of repetitions in order to reach the

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... ization of 10 functions is unconstrained in the numerical results.</p><p> </p>