最优化算法-斐波那契数列搜索

斐波那契数列搜索，参考Edwin《最优化导论》第四版7.3章节，算法采用go语言实现。

/****************************************** FileName : fibonacci_search.go* Author : fredric* Date: .09.01* Note: 斐波那契数列搜索算法* History :*****************************************/package search import("fmt")func _get_fibonacci(i int) int{if i == 1 {return 1}else if i == 2{return 2}else{return _get_fibonacci(i - 1) + _get_fibonacci(i - 2)}}func _test_func(x float64) float64 {return x*x*x*x - 14*x*x*x + 60*x*x - 70*x}func _test_func_01(x float64) float64 {return (x - 1) * (x - 1)}/** 基于黄金分割的思路对分割的比例系数p进行优化* p采用斐波那契数列，即* p1 = 1 - FN/FN+1* p2 = 1 - FN-1/FN* ...* PN = 1 - F1/F2* 总的压缩比：p1*p2*..pN = 1/FN+1* 因此 F N+1 需要能够满足压缩比*/func DoFibonnaciSearch(){fmt.Println("DoFibonnaciSearch")//最小区间为0.2//此时需要斐波那契的压缩比 1 + 2e/F N + 1 <= 最小区间长度／初始长度//取e是一个很小的整数，如0.05//则N等于第五次迭代可以满足要求a0 := 0.0b0 := 2.0p := 0.0delta := 0.05 //最后一次增加一个小整数做偏移for i := 5; i >=1; i-- {if i != 1 {fmt.Printf("a0 = %f, b0 = %f \n", a0, b0)//获取斐波那契数列p1 := _get_fibonacci(i)p0 := _get_fibonacci(i - 1)p = 1 - float64(p0)/float64(p1)a1 := a0 + p * (b0 - a0)b1 := a0 + (1 - p) * (b0 - a0)f_a1 := _test_func_01(a1)f_b1 := _test_func_01(b1)if f_b1 > f_a1 {b0 = b1}else{a0 = a1}fmt.Printf("a1 = %f, b1 = %f f_a1 = %f, f_b1 = %f p = %f\n", a1, b1, f_a1, f_b1, p)}else{a1 := a0 + (1/2 - delta) * (b0 - a0)b1 := a0 + (1/2 - delta) * (b0 - a0)f_a1 := (a1 - 1) * (a1 - 1)f_b1 := (b1 - 1) * (b1 - 1)if f_b1 > f_a1 {b0 = b1}else{a0 = a1}}}//for i := 5; i >=1; i-- {fmt.Printf("a0 = %f, b0 = %f", a0, b0)}