Shifted Ackley function的matlab代码

以下是Shifted Ackley函数的Matlab代码：

function [y] = ShiftedAckley(x,shift)
% Shifted Ackley Function
% x: matrix of input vectors
% shift: shift vector
% y: column vector of function values
dim = size(x,2);
a = 20;
b = 0.2;
c = 2*pi;
% shift the input vectors
x = x - repmat(shift,size(x,1),1);
% calculate the function values
term1 = -a * exp(-b * sqrt(sum(x.^2,2)/dim));
term2 = -exp(sum(cos(c*x),2)/dim);
y = term1 + term2 + a + exp(1);
end

相关问题

matlab函数Shifted Ackley function是什么

以下是一个基本的红黑树实现，包括插入和删除操作：

#include <stdio.h>
#include <stdlib.h>

enum Color {RED, BLACK};

typedef struct Node {
    int key;
    enum Color color;
    struct Node *left;
    struct Node *right;
    struct Node *parent;
} Node;

Node *root = NULL;

void rotate_left(Node *x) {
    Node *y = x->right;
    x->right = y->left;
    if (y->left != NULL) {
        y->left->parent = x;
    }
    y->parent = x->parent;
    if (x->parent == NULL) {
        root = y;
    } else if (x == x->parent->left) {
        x->parent->left = y;
    } else {
        x->parent->right = y;
    }
    y->left = x;
    x->parent = y;
}

void rotate_right(Node *x) {
    Node *y = x->left;
    x->left = y->right;
    if (y->right != NULL) {
        y->right->parent = x;
    }
    y->parent = x->parent;
    if (x->parent == NULL) {
        root = y;
    } else if (x == x->parent->right) {
        x->parent->right = y;
    } else {
        x->parent->left = y;
    }
    y->right = x;
    x->parent = y;
}

void insert_fixup(Node *z) {
    while (z->parent != NULL && z->parent->color == RED) {
        if (z->parent == z->parent->parent->left) {
            Node *y = z->parent->parent->right;
            if (y != NULL && y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->right) {
                    z = z->parent;
                    rotate_left(z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                rotate_right(z->parent->parent);
            }
        } else {
            Node *y = z->parent->parent->left;
            if (y != NULL && y->color == RED) {
                z->parent->color = BLACK;
                y->color = BLACK;
                z->parent->parent->color = RED;
                z = z->parent->parent;
            } else {
                if (z == z->parent->left) {
                    z = z->parent;
                    rotate_right(z);
                }
                z->parent->color = BLACK;
                z->parent->parent->color = RED;
                rotate_left(z->parent->parent);
            }
        }
    }
    root->color = BLACK;
}

void insert(int key) {
    Node *z = (Node *)malloc(sizeof(Node));
    z->key = key;
    z->color = RED;
    z->left = NULL;
    z->right = NULL;
    z->parent = NULL;
    Node *y = NULL;
    Node *x = root;
    while (x != NULL) {
        y = x;
        if (z->key < x->key) {
            x = x->left;
        } else {
            x = x->right;
        }
    }
    z->parent = y;
    if (y == NULL) {
        root = z;
    } else if (z->key < y->key) {
        y->left = z;
    } else {
        y->right = z;
    }
    insert_fixup(z);
}

Node *minimum(Node *x) {
    while (x->left != NULL) {
        x = x->left;
    }
    return x;
}

void delete_fixup(Node *x) {
    while (x != root && x->color == BLACK) {
        if (x == x->parent->left) {
            Node *w = x->parent->right;
            if (w->color == RED) {
                w->color = BLACK;
                x->parent->color = RED;
                rotate_left(x->parent);
                w = x->parent->right;
            }
            if (w->left->color == BLACK && w->right->color == BLACK) {
                w->color = RED;
                x = x->parent;
            } else {
                if (w->right->color == BLACK) {
                    w->left->color = BLACK;
                    w->color = RED;
                    rotate_right(w);
                    w = x->parent->right;
                }
                w->color = x->parent->color;
                x->parent->color = BLACK;
                w->right->color = BLACK;
                rotate_left(x->parent);
                x = root;
            }
        } else {
            Node *w = x->parent->left;
            if (w->color == RED) {
                w->color = BLACK;
                x->parent->color = RED;
                rotate_right(x->parent);
                w = x->parent->left;
            }
            if (w->left->color == BLACK && w->right->color == BLACK) {
                w->color = RED;
                x = x->parent;
            } else {
                if (w->left->color == BLACK) {
                    w->right->color = BLACK;
                    w->color = RED;
                    rotate_left(w);
                    w = x->parent->left;
                }
                w->color = x->parent->color;
                x->parent->color = BLACK;
                w->left->color = BLACK;
                rotate_right(x->parent);
                x = root;
            }
        }
    }
    x->color = BLACK;
}

void delete(int key) {
    Node *z = root;
    Node *x, *y;
    while (z != NULL) {
        if (key == z->key) {
            break;
        } else if (key < z->key) {
            z = z->left;
        } else {
            z = z->right;
        }
    }
    if (z == NULL) {
        return;
    }
    if (z->left == NULL || z->right == NULL) {
        y = z;
    } else {
        y = minimum(z->right);
    }
    if (y->left != NULL) {
        x = y->left;
    } else {
        x = y->right;
    }
    if (x != NULL) {
        x->parent = y->parent;
    }
    if (y->parent == NULL) {
        root = x;
    } else if (y == y->parent->left) {
        y->parent->left = x;
    } else {
        y->parent->right = x;
    }
    if (y != z) {
        z->key = y->key;
    }
    if (y->color == BLACK) {
        delete_fixup(x);
    }
}

void inorder(Node *x) {
    if (x != NULL) {
        inorder(x->left);
        printf("%d ", x->key);
        inorder(x->right);
    }
}

int main() {
    insert(7);
    insert(3);
    insert(18);
    insert(10);
    insert(22);
    insert(8);
    insert(11);
    insert(26);
    insert(2);
    insert(6);
    insert(13);
    printf("Inorder traversal: ");
    inorder(root);
    printf("\n");
    delete(18);
    delete(11);
    delete(3);
    delete(10);
    printf("Inorder traversal: ");
    inorder(root);
    printf("\n");
    return 0;
}

以上代码实现了红黑树的基本操作，包括左旋、右旋、插入、删除等。可以通过调用 `insert` 和 `delete` 函数来插入和删除元素，通过 `inorder` 函数遍历整个树。

优化算法中的shifted function

Shifted function是经典的优化问题之一，其目标是在给定的函数中找到最小值。该问题通常被用作测试优化算法的基准，因为它具有以下特点：

1. Shifted function是一个多峰函数，即在函数中存在多个局部最小值和一个全局最小值。

2. Shifted function是一个高维函数，即每个变量都可以取多个值。

3. Shifted function是一个非线性函数，即函数的值与变量之间的关系是非线性的。

为了解决Shifted function问题，可以使用各种优化算法，如遗传算法、粒子群算法、模拟退火算法等。这些算法的共同点是它们都是启发式算法，即它们通过尝试不同的解来寻找最佳解。

另外，为了使Shifted function问题更具挑战性，可以将函数进行平移，即将函数沿着各个维度移动一个随机向量。这样做可以使函数的最小值位置发生变化，从而使算法更难以找到最佳解。