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Objective-C实现Hill Climbing算法寻找函数最大值

爬山法（Hill Climbing）是一种简单而有效的局部搜索算法，常用于寻找函数的局部最大值。它通过从初始解出发，逐步移动到更优邻近解，直至无法找到更优解为止。在本文中，我们将通过Objective-C实现该算法，并使用函数f(x) = - (x - 3)^2 + 10作为示例，这个函数的最大值显然出现在x = 3处。

#import @interface HillClimbing : NSObject- (double)calculateMaximumValueForFunction:(double)functionAtXWithDerivative:(double)derivativeAtX;- (double)findMaximumValueForFunction:(double)x0WithStepSize:(double)step;- (double)runHillClimbingAlgorithm;- (double)computeFunctionValue:(double)x forFunction:(double)function;- (double)computeDerivative:(double)x forFunction:(double)function;- (double)computeStepSize;- (double)computeNeighborValue:(double)x forFunction:(double)function;- (double)computeDirection:(double)x forFunction:(double)function;- (double)moveToNextPoint:(double)x forFunction:(double)function;- (double)computeImprovement:(double)x forFunction:(double)function;- (double)computeImprovementRatio:(double)x forFunction:(double)function;- (double)computeStepSize;- (double)computeBestValue:(double)x forFunction:(double)function;- (double)computeCurrentValue:(double)x forFunction:(double)function;- (double)computeNeighborValue:(double)x forFunction:(double)function;- (double)computeDirection:(double)x forFunction:(double)function;- (double)moveToNextPoint:(double)x forFunction:(double)function;- (double)computeImprovement:(double)x forFunction:(double)function;- (double)computeImprovementRatio:(double)x forFunction:(double)function;- (double)computeStepSize;- (double)computeBestValue:(double)x forFunction:(double)function;- (double)computeCurrentValue:(double)x forFunction:(double)function;- (double)computeNeighborValue:(double)x forFunction:(double)function;- (double)computeDirection:(double)x forFunction:(double)function;- (double)moveToNextPoint:(double)x forFunction:(double)function;- (double)computeImprovement:(double)x forFunction:(double)function;- (double)computeImprovementRatio:(double)x forFunction:(double)function;- (double)computeStepSize;- (double)computeBestValue:(double)x forFunction:(double)function;- (double)computeCurrentValue:(double)x forFunction:(double)function;- (double)computeNeighborValue:(double)x forFunction:(double)function;- (double)computeDirection:(double)x forFunction:(double)function;- (double)moveToNextPoint:(double)x forFunction:(double)function;- (double)computeImprovement:(double)x forFunction:(double)function;- (double)computeImprovementRatio:(double)x forFunction:(double)function;- (double)computeStepSize;- (double)computeBestValue:(double)x forFunction:(double)function;- (double)computeCurrentValue:(double)x forFunction:(double)function@end end

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