2. 程式人生 > >使用模擬退火與禁忌搜尋解決Capacitated Facility Location Problem

使用模擬退火與禁忌搜尋解決Capacitated Facility Location Problem

阿新 • • 發佈：2018-12-26

Capacitated Facility Location Problem

問題描述

Suppose there are n facilities and m customers. We wish to choose:
(1) which of the n facilities to open
(2) the assignment of customers to facilities
The objective is to minimize the sum of the opening cost and the assignment cost.
The total demand assigned to a facility must not exceed its capacity.

數學建模

將上述問題轉化為數學模型。

  • 一共可選擇開的工廠數目為factory_num
  • 客戶的數目為customer_num
  • 每個工廠服務不同的客戶的消費不同，使用allocating_cost[i][j]表示工廠i服務客戶j的消費
  • 每個使用者有不同的需求，用demand[i]表示客戶i的需求，
  • 每個工廠有不同的容量，用capacity[i]表示工廠i的容量。
  • 工廠沒有服務客戶時就不開，否則就要開，用open_list[i]表示工廠i是否開。
  • 如果開，就要有開工廠的消費，用fixedcost[i]表示開工廠i的費用。
  • 每個客戶只能由一個工廠服務，即只能由一個工廠處理一個客戶的所有需求，用allocating_list[i]表示客戶i所選擇的工廠。

則這個問題對應的解為
m i n { ∑ i =

0 f a c t o r y _ n u m o p e n _ l i s t [ i ] ∗ f i x e d _ c o s t [ i ] + ∑ i = 0 c u s t o m e r _ n u m a l l o c a t i n g _ c o s t [ a l l o c a t i n g _ l i s t [ i ] ] } min\{\sum_{i = 0}^{factory\_num} open\_list[i] * fixed\_cost[i] + \sum_{i = 0}^{customer\_num} allocating\_cost[allocating\_list[i]] \}

解決方案一：模擬退火法

演算法描述

演算法的基本思想如下：

  1. 初始化：初始溫度T充分大，初始解狀態S，每個T值的迭代次數L
  2. 對k=1…L，做3-6步
  3. 產生新的解S’
  4. 計算增量Δt’ = C(S’) - C(S)，C(S)為評價函式
  5. 若Δt’ < 0則接受S’作為新的當前解，否則以概率exp(-Δt’/T)接受S’為新的當前解
  6. 如果滿足終止條件則輸出當前解為最優解
  7. T逐漸減少，且T->0，然後轉到第2步

產生隨機初始解

作為一個解的首要條件是能服務全部的客戶，因此從客戶進行考慮，為全部的客戶隨機分配一個工廠，如果工廠不能滿足，則換一個分配到一個為止。之後再判斷每個工廠是否開。

void generate_random_solution(){
	for(int i = 0; i < customer_num; i++){
		while(true){
			int allocated = rand() % factory_num;
			if(capacity[allocated] >= demand[i]){
				allocating_list[i] = allocated;
				open_list[allocated] += 1;
				allocating_list[i] = allocated;
				capacity[allocated] -= demand[i];
				break;
			}
		}		
	}
}

鄰域解

同樣也是從客戶進行考慮，隨機選一個客戶，然後隨機為其換一個工廠服務。換了之後可能出現新的工廠不能滿足這個客戶，對於這種情況則重新選一個解。

終止條件

對於一個溫度，使用一個策略來退出這個溫度，這裡的策略是重複迭代一定次數。

評價函式

直接用成本來評價這個解。但對於增量來說，這裡沒有必要全部都要再算一次。只要判斷所涉及的兩個工廠和兩個使用者的變化即可，即判斷這種操作過後有沒有導致工廠新開或者關閉，再算分配的代價的變化。

double calculate_delta_cost(int customer, int factory){
	int result = 0;
	//open new factory
	if(open_list[factory] == 0){
		result += fixed_cost[factory];
	}
	int f = allocating_list[customer];
	if(open_list[f] == 1){
		result -= fixed_cost[f];
	}
	result += allocating_cost[factory][customer] - allocating_cost[f][customer];
	return result;

}

溫度的變化

使用函式 T = 0.99 T T=0.99T 來降溫，當T小於某一特定值時，演算法終止，產生最終解，最小溫度定為0.01。

完整程式碼

#include<iostream>
#include<fstream>
#include<stdlib.h>
#include<cmath>
#include<time.h>

using namespace std;
#define FILE_NUM 71
#define T 500
#define T_min 0.01
#define L 10

int factory_num;
int customer_num;
int* capacity;
int* fixed_cost;
double* demand;
double** allocating_cost;

// how many customer to allocate
int* open_list;
// witch factory to allocate
int* allocating_list;

double get_total_cost(){
	double cost = 0;

	for(int i = 0; i < factory_num; i++){
		if(open_list[i] != 0){
			cost += fixed_cost[i];
		}
	}
	for(int i = 0; i < customer_num; i++){
		cost += allocating_cost[allocating_list[i]][i];
	}
	return cost;
}
void generate_random_solution(){
	for(int i = 0; i < customer_num; i++){
		while(true){
			int allocated = rand() % factory_num;
			if(capacity[allocated] >= demand[i]){
				allocating_list[i] = allocated;
				open_list[allocated] += 1;
				allocating_list[i] = allocated;
				capacity[allocated] -= demand[i];
				break;
			}
		}
		
	}
}
double calculate_delta_cost(int customer, int factory){
	int result = 0;
	//open new factory
	if(open_list[factory] == 0){
		result += fixed_cost[factory];
	}
	int f = allocating_list[customer];
	if(open_list[f] == 1){
		result -= fixed_cost[f];
	}
	result += allocating_cost[factory][customer] - allocating_cost[f][customer];
	return result;
}

void accept(int customer, int factory){
	int f = allocating_list[customer];
	capacity[f] += demand[customer];
	capacity[factory] -= demand[customer];
	allocating_list[customer] = factory;
	open_list[f] -= 1;
	open_list[factory] += 1;
}
int main(){
	int file_num = 0;
	ofstream result("SAresult");
	srand((int)time(0));
	while(file_num != FILE_NUM){
		file_num++;
		string file_name = "Instances/p" + to_string(file_num);	
		ifstream file(file_name);
		if(!file.is_open()){
			cout << "open error" << endl;
		}
		file >> factory_num >> customer_num;
		capacity = new int[factory_num];
		fixed_cost = new int[factory_num];

		for(int i = 0; i < factory_num; i++){
			file >> capacity[i] >> fixed_cost[i];
		}
		demand = new double[customer_num];
		for(int i = 0; i < customer_num; i++){
			file >> demand[i];
		}
		//allocating_cost[i][j] means the cost allocating of 
		//customer j to facity i
		allocating_cost = new double*[factory_num];
		
		for(int i = 0; i < factory_num; i++){
			allocating_cost[i] = new double[customer_num];		
		}
		for(int i = 0; i < factory_num; i++){
			for(int j = 0; j < customer_num; j++){
				file >> allocating_cost[i][j];
			}		
		}

		open_list = new int[factory_num];
		allocating_list = new int[customer_num];
		for(int i = 0; i < factory_num; i++){
			open_list[i] = 0;
		}
		
		//Simulated Annealing
		clock_t start = clock();
		generate_random_solution();
		int repeat = 100;
		int t = T;
		double current_cost = get_total_cost();
		double min_cost = current_cost;
		int time = 0;
		while(t > T_min){
			time++;
			int n = 0;
			while(n != repeat){
				int customer = rand() % customer_num;
				int factory = rand() % factory_num;
				//not valid neibor
				if(capacity[factory] < demand[customer]) continue;
				if(allocating_list[customer] == factory) continue;
				n++;
				int delta = calculate_delta_cost(customer, factory);
				if(delta <= 0){
					accept(customer, factory);
				}else{
					if((rand() % 10000) / 10000.0 < exp(-1.0 * delta / t)){
						accept(customer, factory);
					}
				}
			}			
			//cout << get_total_cost() << endl;
			t = 0.99 * t;		
		}
		clock_t end = clock();		
		//get result
		//string file_name = "result/p" + to_string(file_num);
		result << "p" << file_num << ": ";
		result << get_total_cost() << ' ';
		result << (end - start) * 1.0 / CLOCKS_PER_SEC << "s" << endl;
		
		for(int i = 0; i < factory_num; i++){
			result << open_list[i] << ' ';
		}
		result << endl;
		for(int i = 0; i < customer_num; i++){
			result << allocating_list[i] << ' ';
		}
		result << endl;
		
		//release
		delete capacity;
		delete fixed_cost;
		delete demand;
		delete open_list;
		for(int i = 0; i < factory_num; i++){
			delete allocating_cost[i];
		}
		delete allocating_list;
		delete allocating_cost;

	}

	
}

結果

p1: 8916 0.027765s
7 5 8 7 11 0 7 0 5 0 
2 2 1 6 3 8 2 4 4 1 4 8 3 2 8 3 2 0 6 4 3 8 6 4 2 6 1 6 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 4 0 2 0 4 0 
p2: 7949 0.027256s
8 5 5 8 11 0 5 2 4 2 
8 2 1 6 3 8 2 4 4 1 9 0 3 2 8 3 4 0 9 7 3 4 6 4 2 6 3 1 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 7 0 4 0 4 0 
p3: 9575 0.036489s
8 5 5 7 11 0 7 3 4 0 
8 2 1 6 3 8 2 4 4 1 4 8 3 2 0 3 4 0 6 7 3 7 6 4 2 6 1 6 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 7 0 4 0 4 0 
p4: 11046 0.045844s
7 0 6 8 11 9 0 0 5 4 
2 2 5 5 3 8 2 4 4 5 9 8 3 2 8 3 4 0 9 4 3 8 9 4 2 5 3 5 0 5 2 5 0 3 9 4 4 3 0 4 5 8 3 5 4 0 4 0 4 0 
p5: 9037 0.053169s
6 7 6 6 7 0 5 2 7 4 
8 2 1 6 3 8 2 4 2 1 9 8 3 2 8 3 4 0 9 7 3 8 6 4 2 6 1 1 0 1 2 6 0 3 9 4 4 3 8 4 1 8 1 6 7 0 9 0 4 0 
p6: 7892 0.049795s
7 6 5 5 7 4 3 3 7 3 
8 8 1 6 1 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 8 6 4 2 5 1 5 0 5 2 6 0 3 9 4 7 3 0 4 1 8 1 5 7 0 2 0 4 3 
p7: 9843 0.051843s
6 6 5 5 8 5 3 0 7 5 
8 8 1 6 1 8 2 4 4 1 9 8 3 2 8 3 2 0 9 9 3 2 6 4 5 5 1 5 8 5 2 6 0 3 9 4 4 3 0 4 1 8 1 5 4 0 9 0 4 0 
p8: 11378 0.042351s
6 8 5 6 7 0 5 3 7 3 
8 8 1 6 1 8 2 4 4 1 9 8 3 2 8 3 4 0 9 7 3 8 6 4 2 6 1 1 0 1 2 6 0 3 9 4 4 3 0 4 1 8 1 6 7 0 2 3 7 0 
p9: 8576 0.02834s
7 7 5 6 10 0 5 0 7 3 
8 8 1 6 3 8 2 4 4 1 9 8 3 2 8 3 4 0 9 4 3 8 6 4 2 6 1 1 0 1 2 6 0 3 9 4 4 3 0 4 1 8 1 6 4 0 2 0 4 0 
p10: 7772 0.020728s
7 6 5 5 10 4 3 0 7 3 
8 8 1 6 1 8 2 4 4 1 9 8 3 2 8 3 4 0 9 4 3 8 6 4 2 5 1 5 0 5 2 6 0 3 9 4 4 3 0 2 1 8 1 5 4 0 4 0 4 0 
p11: 9128 0.027357s
10 9 4 0 11 0 6 2 8 0 
8 8 1 6 1 8 2 4 4 1 4 8 0 2 8 0 4 0 6 7 1 8 6 4 2 6 1 1 0 1 2 6 0 0 4 4 4 0 8 4 1 8 1 6 7 0 4 0 4 0 
p12: 10449 0.036066s
7 7 6 6 11 0 6 0 7 0 
8 8 1 6 3 8 2 4 4 1 4 8 3 2 8 3 4 0 6 4 3 8 6 4 2 6 1 1 0 1 2 6 0 3 2 4 4 3 0 4 1 8 1 6 4 0 2 0 4 0 
p13: 8280 0.041783s
5 5 0 0 0 0 0 0 0 5 6 0 0 7 4 6 0 6 0 6 
0 1 10 10 1 13 17 13 14 17 15 19 19 10 13 14 15 10 17 9 14 15 15 19 9 1 0 17 1 17 13 15 13 0 1 10 17 19 19 13 9 0 15 0 9 13 14 10 19 9 
p14: 7169 0.031457s
0 0 0 6 0 0 5 0 0 0 5 0 0 6 3 6 6 6 0 7 
16 3 10 10 19 15 17 13 14 17 15 19 19 6 13 3 15 10 17 6 14 15 15 19 6 17 16 17 3 17 13 15 13 16 3 10 3 19 19 13 6 16 16 16 3 13 14 10 19 6 
p15: 8964 0.032357s
0 0 0 6 0 0 5 0 0 0 5 0 0 7 3 6 5 6 0 7 
16 3 10 10 19 13 17 13 14 17 15 19 19 6 13 3 15 10 17 6 14 15 15 19 6 17 16 17 3 17 13 15 13 16 3 10 3 19 19 13 6 16 15 16 3 13 14 10 19 6 
p16: 11765 0.041187s
5 4 0 6 0 0 0 5 0 0 7 0 0 6 0 6 0 6 0 5 
0 1 10 10 1 15 17 13 7 17 15 19 1 7 13 3 15 10 17 10 15 15 15 19 10 17 7 17 1 17 13 7 13 0 3 10 3 19 19 13 3 0 0 0 3 13 7 10 19 3 
p17: 8455 0.038385s
5 0 0 6 0 0 5 0 0 0 5 0 0 6 3 7 0 6 0 7 
0 3 10 10 19 15 17 13 14 17 15 19 19 6 13 3 15 10 17 6 14 15 15 19 6 17 0 17 3 17 13 15 13 0 3 10 3 19 19 13 6 0 15 0 3 13 14 10 19 6 
p18: 7821 0.033585s
5 4 0 4 0 0 5 0 0 0 6 0 0 6 3 7 0 5 0 5 
0 1 10 10 1 15 17 13 14 17 15 19 1 6 13 3 15 10 17 6 14 15 15 19 6 10 0 17 1 17 13 15 13 0 3 10 3 19 19 13 6 0 15 0 3 13 14 10 19 6 
p19: 9324 0.035205s
5 6 0 0 0 0 6 0 0 0 6 0 0 6 4 6 0 6 0 5 
10 1 10 10 1 15 17 13 14 17 15 19 1 6 13 14 15 10 17 6 14 15 15 19 6 1 0 17 1 17 13 15 13 0 1 10 17 19 19 13 6 0 0 0 6 13 14 10 19 6 
p20: 11997 0.02347s
5 5 0 0 0 6 4 0 3 0 5 0 0 0 5 0 0 6 6 5 
0 1 10 10 1 18 17 18 14 17 5 19 1 6 18 14 5 10 17 6 14 5 5 19 6 17 0 17 1 17 18 14 18 0 1 10 8 19 19 18 6 0 5 0 8 5 14 10 19 8 
p21: 8419 0.038995s
6 7 0 4 0 0 0 0 0 3 7 0 5 7 0 5 0 6 0 0 
0 12 10 10 1 12 17 13 12 17 15 1 1 10 13 3 15 10 17 9 12 15 15 13 9 17 0 17 1 17 13 15 13 0 3 10 3 1 1 13 10 0 0 0 3 13 12 10 1 9 
p22: 7226 0.040295s
0 5 0 0 0 0 0 0 0 4 7 0 0 6 4 7 5 7 0 5 
16 1 10 10 1 15 17 13 14 17 15 19 1 10 13 14 15 10 17 9 14 15 15 19 9 17 16 17 1 17 13 15 13 16 1 10 17 19 19 13 10 16 15 16 9 13 14 10 19 9 
p23: 9105 0.037604s
6 7 0 0 0 0 0 7 0 4 7 0 0 7 0 0 0 7 0 5 
0 1 10 10 1 13 17 13 7 17 7 19 1 10 13 1 7 10 17 9 1 7 7 19 9 17 0 17 1 17 13 7 13 0 1 10 17 19 19 13 10 0 0 0 9 13 7 10 19 9 
p24: 11303 0.041301s
0 5 0 8 0 0 7 8 0 0 0 0 5 6 0 0 6 0 0 5 
16 12 7 7 1 12 3 13 12 3 7 19 1 6 13 3 7 7 1 6 12 7 7 19 6 1 16 3 1 3 13 7 13 16 3 6 3 19 19 13 6 16 16 16 3 13 12 6 19 6 
p25: 13113 0.0407s
12 0 9 0 0 14 2 10 9 0 0 14 0 0 18 0 0 10 0 0 21 0 0 0 22 9 0 0 0 0 
20 25 20 2 20 5 14 24 14 17 24 20 8 20 2 14 14 17 5 11 14 7 24 7 24 20 2 24 5 24 5 25 6 25 20 20 24 24 7 14 0 14 24 14 24 14 7 20 11 8 25 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 24 0 24 5 7 6 11 0 24 8 24 20 14 24 20 7 20 17 7 17 2 7 20 5 2 24 17 11 17 5 2 7 25 8 20 17 17 25 2 25 7 0 14 8 14 14 2 11 11 11 24 24 24 24 5 8 11 20 20 0 5 24 0 0 0 11 24 25 8 14 0 5 20 17 0 8 20 14 8 11 25 5 2 5 
p26: 11506 0.031927s
17 0 9 0 0 14 0 0 15 5 0 12 0 0 17 0 0 11 0 0 19 0 0 0 18 13 0 0 0 0 
20 11 20 2 8 5 2 24 14 17 9 8 8 20 0 14 14 17 5 11 2 0 5 0 5 8 17 24 24 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 20 11 8 25 14 14 5 20 20 14 11 11 14 0 5 20 25 11 11 24 0 9 9 8 20 11 0 24 8 9 20 2 9 20 0 20 17 2 17 17 0 20 5 2 24 17 11 0 5 2 14 25 8 8 17 14 25 2 25 0 11 14 8 14 14 17 11 11 25 24 24 24 24 5 8 25 20 20 0 5 24 0 25 0 25 24 24 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p27: 14115 0.025686s
12 0 10 0 0 17 0 7 12 0 0 13 0 0 16 0 0 10 0 0 20 0 0 0 21 10 0 0 2 0 
20 11 20 2 20 5 14 24 14 17 5 8 8 20 7 14 14 17 5 11 2 0 24 7 5 8 2 24 5 24 5 25 20 25 20 20 24 24 7 14 0 14 24 28 24 14 7 20 25 8 11 14 14 5 20 20 2 11 0 14 0 5 20 11 11 11 24 0 24 5 20 20 11 17 24 8 24 20 14 24 20 7 8 17 2 17 17 0 20 5 2 24 17 11 0 24 2 0 11 20 8 17 17 25 2 25 7 11 14 8 14 14 2 11 25 25 24 24 24 24 5 28 25 20 8 0 5 24 0 5 0 25 24 5 8 14 7 5 20 17 0 8 20 14 8 11 25 5 2 5 
p28: 17339 0.039803s
10 0 9 0 0 18 0 7 9 0 0 13 0 5 18 0 0 10 0 0 20 0 0 0 19 7 0 5 0 0 
20 11 13 14 20 5 2 24 14 17 24 8 20 20 7 14 14 17 5 11 2 0 5 2 5 8 2 24 5 24 5 25 13 25 20 20 24 24 0 14 0 14 24 8 24 14 0 13 27 8 5 8 14 5 13 20 17 11 11 14 0 5 20 11 11 25 24 0 11 24 20 13 11 17 24 8 5 20 14 24 20 7 20 17 17 17 2 7 20 5 2 24 17 11 7 5 2 7 27 20 8 17 14 25 14 11 7 0 14 8 14 14 2 11 11 27 24 24 24 24 5 20 25 20 20 27 5 24 0 25 0 27 24 5 14 14 7 5 20 17 0 20 20 14 8 11 25 5 2 5 
p29: 14945 0.039794s
13 0 12 0 0 15 0 0 8 0 0 14 0 6 14 6 3 14 0 0 14 0 0 0 14 9 0 4 4 0 
20 25 13 14 13 5 2 24 14 17 15 16 8 20 0 14 14 17 25 11 2 0 5 2 5 8 2 24 5 15 5 11 16 25 20 20 24 15 0 14 0 14 15 8 24 14 17 13 11 28 25 28 14 5 20 20 17 11 11 14 0 5 20 27 11 11 24 0 5 24 13 13 11 17 24 8 24 20 2 24 20 0 20 17 2 17 17 0 20 5 2 24 17 11 17 5 2 2 25 13 8 17 17 25 2 25 17 11 14 28 14 14 2 11 11 11 24 15 24 24 5 8 25 20 16 0 5 15 0 27 0 11 24 27 8 14 0 5 20 17 0 8 20 14 28 27 25 5 2 5 
p30: 12291 0.030974s
13 0 10 0 0 14 0 0 13 0 0 17 0 7 14 0 0 15 0 0 13 0 0 0 15 15 0 1 3 0 
20 25 13 14 20 5 2 24 14 17 11 8 8 20 2 14 14 17 25 11 2 0 25 17 24 8 2 24 24 25 25 25 13 25 20 20 24 24 0 14 0 8 24 8 24 14 0 13 11 8 25 14 14 5 13 20 17 11 11 14 0 5 20 27 11 11 5 0 24 25 20 20 11 17 24 8 5 20 14 24 13 0 13 17 17 17 17 0 20 25 2 24 0 11 17 5 2 2 25 20 28 17 17 11 2 11 17 11 28 28 14 14 2 11 25 11 24 24 5 5 5 8 11 13 8 0 5 5 0 11 0 11 24 25 8 14 17 5 8 17 0 8 20 14 8 25 25 5 2 5 
p31: 14070 0.040869s
12 0 12 0 0 15 0 0 14 9 0 15 0 8 14 0 0 15 0 0 13 0 0 0 13 10 0 0 0 0 
20 11 13 2 20 5 14 9 14 17 9 8 8 20 2 14 14 17 5 11 2 0 5 2 25 8 2 24 5 9 5 25 13 25 20 20 24 24 0 14 0 14 24 8 24 14 11 20 11 8 5 2 14 5 13 20 17 11 0 14 0 5 20 11 11 11 9 0 9 5 13 13 11 17 24 8 9 20 14 9 13 0 13 17 17 17 17 0 20 5 2 24 17 11 17 9 2 2 25 8 8 17 17 25 2 25 17 11 8 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 20 0 5 24 0 11 0 11 24 9 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p32: 17270 0.028115s
13 0 9 0 0 14 0 4 14 7 0 13 0 7 14 0 0 16 0 0 13 0 0 0 14 12 0 0 0 0 
20 25 13 14 20 5 2 24 14 17 24 8 8 20 2 14 17 17 25 11 2 0 9 17 5 8 17 24 5 24 5 25 13 25 20 20 24 9 0 14 0 14 24 8 24 14 7 20 11 8 5 2 14 5 13 20 17 0 11 14 0 5 20 11 11 11 24 0 25 9 8 13 11 17 24 8 9 20 14 9 20 7 13 17 17 17 2 7 20 5 0 24 17 11 0 9 2 17 11 13 8 17 17 25 2 25 7 11 14 8 14 14 2 11 11 25 24 24 5 24 5 8 25 13 8 0 5 9 0 25 0 0 24 25 8 14 17 5 20 17 0 8 20 14 8 11 25 5 2 5 
p33: 13280 0.021133s
15 0 11 0 0 17 0 2 13 0 0 12 0 6 15 0 0 14 0 0 15 0 0 0 19 11 0 0 0 0 
20 11 13 14 13 5 2 24 14 17 5 8 8 20 17 14 14 17 25 11 2 0 11 2 5 8 2 24 5 24 5 25 13 25 20 20 24 24 0 14 0 14 24 8 24 14 0 13 25 8 5 14 14 5 20 20 17 11 11 14 0 5 20 11 11 11 5 0 24 24 20 20 11 17 24 8 24 20 2 24 20 0 13 17 17 17 17 0 20 5 2 24 7 0 17 24 2 2 25 13 8 17 17 25 2 25 17 0 14 8 14 14 2 11 25 11 24 24 5 24 5 8 25 20 8 0 5 24 0 0 0 11 24 5 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 
p34: 11959 0.021929s
9 0 8 0 0 18 0 4 13 4 0 15 0 5 16 0 0 16 0 0 17 0 0 0 15 10 0 0 0 0 
20 11 13 2 20 5 2 9 14 17 5 8 8 20 17 14 14 17 25 11 14 17 5 17 5 8 2 24 5 9 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 25 13 11 8 5 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 9 0 5 5 20 20 11 17 24 8 24 20 14 9 20 0 20 17 17 17 17 7 20 25 2 24 17 11 17 5 2 14 25 13 8 17 17 25 2 25 7 11 8 8 14 14 2 11 11 5 24 24 24 24 5 8 25 13 13 7 5 24 0 11 0 11 24 24 8 14 7 5 20 17 0 8 20 14 8 11 25 5 2 5 
p35: 14540 0.028361s
13 0 12 0 0 15 0 0 12 0 0 10 0 5 14 0 0 15 0 0 17 0 4 0 18 10 0 5 0 0 
13 25 20 2 13 5 2 24 2 17 22 8 8 20 17 14 14 17 5 11 2 0 5 2 22 8 2 24 5 24 5 25 20 25 20 20 24 24 11 14 0 14 24 8 24 14 17 13 27 8 5 14 14 5 20 20 17 27 0 14 0 5 20 27 11 11 24 0 22 24 20 20 11 17 24 8 22 20 14 24 20 0 13 17 17 17 17 0 20 5 2 24 17 11 0 5 2 2 25 20 8 17 17 11 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 20 0 5 24 0 27 0 27 24 25 8 14 0 5 20 17 0 8 20 14 8 25 25 5 2 5 
p36: 15852 0.024144s
11 0 12 0 0 18 0 5 14 0 0 10 0 0 15 0 0 15 0 0 19 0 0 0 19 12 0 0 0 0 
20 11 20 2 20 5 2 24 14 17 24 8 8 20 2 14 14 17 5 11 2 7 25 17 5 8 0 24 5 24 25 25 20 25 20 20 24 24 7 14 0 14 24 14 24 14 7 20 11 8 5 14 14 5 20 20 17 25 0 14 0 5 20 11 11 11 24 0 5 5 8 20 5 17 24 8 24 20 14 24 20 17 8 17 2 17 17 0 20 5 2 24 17 11 17 24 2 2 25 8 8 7 17 25 2 25 17 0 14 8 14 2 2 11 11 25 24 24 5 24 5 8 25 20 20 0 5 24 7 0 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p37: 13651 0.027567s
9 0 10 0 0 14 0 0 12 0 0 11 0 4 16 3 0 19 0 0 18 0 0 0 18 10 0 6 0 0 
20 25 13 2 13 5 2 24 14 17 25 20 8 20 2 14 14 17 25 11 2 0 5 17 24 8 2 24 5 24 5 25 20 25 20 20 24 15 11 14 0 14 15 14 24 14 27 20 27 8 11 14 14 5 20 20 17 27 11 14 0 5 20 11 0 11 24 0 5 24 20 20 11 17 24 8 24 20 14 24 20 17 13 17 17 17 17 17 20 5 2 24 17 11 17 24 2 8 25 13 8 17 17 11 2 25 17 0 14 8 14 14 2 11 11 25 24 15 24 24 5 8 25 20 8 17 5 24 0 27 0 27 24 5 8 14 17 5 20 17 0 8 20 14 8 27 25 5 2 5 
p38: 11738 0.026482s
9 0 11 0 0 16 0 0 14 0 0 12 0 6 14 0 0 19 0 0 15 0 0 0 20 10 0 4 0 0 
13 11 13 14 20 5 2 24 14 17 5 8 8 20 17 8 14 17 5 11 2 17 5 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 17 14 0 14 24 8 24 14 17 13 27 8 5 14 14 5 20 20 17 25 0 14 0 5 20 11 11 11 24 0 5 24 20 20 11 17 24 8 24 20 2 24 20 0 13 17 17 17 17 2 20 25 2 24 17 11 17 24 2 14 11 13 8 17 17 11 2 25 17 11 14 8 14 2 2 11 25 25 24 24 24 24 5 8 25 13 8 0 5 24 11 25 0 27 24 27 8 14 0 5 20 17 0 8 20 14 8 27 25 5 2 5 
p39: 14076 0.025329s
12 0 10 0 0 14 0 2 11 4 0 13 0 0 18 0 0 18 0 0 21 0 0 0 19 8 0 0 0 0 
20 11 20 14 20 5 2 9 14 17 24 8 8 20 2 14 14 17 5 11 2 0 24 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 14 24 14 0 20 11 8 5 14 14 5 20 20 17 11 7 14 0 5 20 11 0 11 24 0 24 24 20 20 11 17 24 8 24 20 14 24 20 17 20 17 17 17 17 17 20 5 2 9 17 0 17 9 2 2 25 8 20 17 17 25 2 25 17 11 14 14 14 14 2 11 11 0 24 24 24 24 5 8 25 20 8 17 5 9 0 25 0 11 24 11 8 14 7 5 20 17 0 8 20 14 8 11 25 5 2 5 
p40: 15767 0.021328s
14 0 11 0 0 17 0 0 8 0 0 11 0 5 16 0 0 16 0 0 20 0 0 0 19 13 0 0 0 0 
20 11 20 2 13 5 2 24 14 17 5 20 8 20 2 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 25 13 25 20 20 24 24 0 14 0 14 24 8 24 14 0 20 0 8 25 14 14 5 13 20 17 25 0 14 0 5 20 11 11 11 24 0 5 5 20 20 11 17 24 8 24 20 14 24 20 0 20 17 17 17 17 0 20 5 2 24 17 11 17 24 2 2 25 13 20 17 17 25 2 25 17 11 14 14 14 14 2 11 25 0 24 24 24 24 5 20 25 13 20 11 5 24 0 11 0 25 24 25 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p41: 6995 0.024675s
10 0 11 6 11 8 17 11 7 9 
5 6 4 6 7 9 3 7 8 8 4 9 2 6 2 7 7 3 0 6 6 6 4 4 6 5 5 4 8 5 8 0 0 0 3 9 2 6 6 9 2 7 3 3 3 5 0 5 6 4 4 6 6 6 2 7 2 8 8 8 0 0 6 5 0 6 6 6 4 4 0 4 4 0 7 7 2 2 9 5 7 2 2 7 9 7 9 9 9 2 
p42: 7122 0.027451s
0 0 0 7 0 7 4 0 0 0 9 10 7 0 0 11 0 9 8 8 
12 10 11 5 15 18 12 3 17 17 11 18 6 10 6 15 15 17 10 10 5 11 5 11 12 12 11 12 17 3 17 19 6 18 10 10 10 15 15 15 15 3 3 12 11 5 18 19 15 15 17 17 17 3 17 5 12 5 10 5 11 11 3 11 11 3 15 15 19 6 10 18 19 19 19 18 18 18 19 19 
p43: 6458 0.029136s
8 0 0 0 0 7 6 0 0 9 0 0 3 0 0 0 0 0 4 0 0 8 0 11 0 0 0 9 5 0 
18 21 18 23 23 0 9 21 27 5 5 23 23 9 18 6 21 21 12 0 0 9 0 0 9 23 27 6 27 27 5 23 23 23 0 9 23 12 21 6 27 12 28 23 5 9 9 9 0 6 21 0 9 18 6 6 21 21 23 5 5 27 28 5 27 28 27 27 28 28 
p44: 7393 0.026649s
9 8 8 11 10 10 7 12 6 9 
4 4 4 4 4 4 4 4 0 0 0 0 6 0 0 0 1 1 1 7 1 7 1 2 2 2 2 2 7 2 2 3 3 3 3 3 3 3 3 3 4 0 1 1 2 8 7 5 9 7 7 6 5 5 8 8 7 7 9 5 5 5 3 3 0 6 6 8 1 5 4 9 9 7 7 8 6 6 5 8 7 9 9 9 9 9 6 5 7 5 
p45: 7236 0.02323s
10 0 0 9 0 11 9 0 7 6 0 11 6 0 0 0 0 0 7 4 
0 0 0 0 0 0 0 6 6 6 6 6 6 6 6 3 3 3 3 3 3 11 11 12 11 11 11 12 11 5 5 5 5 5 5 5 5 5 0 0 3 3 11 12 18 5 19 3 18 19 8 8 11 19 18 19 5 6 9 9 12 9 0 8 18 8 11 12 9 9 18 12 18 8 11 11 8 8 9 18 
p46: 6767 0.023007s
0 6 10 0 0 0 6 0 5 0 9 0 4 8 6 0 0 3 7 0 0 0 6 0 0 0 0 0 0 0 
10 10 10 10 10 10 10 1 22 22 1 1 1 1 1 2 2 2 2 2 2 6 6 6 6 6 6 13 8 8 8 8 13 8 10 2 2 17 14 22 18 12 2 22 17 14 18 17 13 18 10 13 13 22 2 14 13 18 18 14 12 12 22 18 14 13 14 13 12 18 
p47: 6468 0.03173s
12 5 13 8 12 7 12 9 7 5 
0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 6 7 6 0 7 7 7 7 7 7 8 8 6 8 8 8 8 8 6 9 0 2 9 9 9 9 
p48: 5849 0.040644s
12 0 0 6 0 13 0 0 8 6 0 6 0 9 7 0 0 13 0 0 
0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 9 9 5 9 5 5 5 8 8 8 8 8 8 8 9 8 9 9 11 11 11 11 11 11 13 13 13 13 13 13 13 14 14 13 14 13 0 14 14 14 14 17 17 17 17 17 17 17 17 17 17 17 17 17 0 0 
p49: 6476 0.037012s
9 0 6 0 0 5 4 11 0 0 0 0 8 5 0 0 0 7 0 0 0 0 6 0 0 9 0 0 0 0 
0 0 2 2 2 2 2 2 5 5 5 5 5 6 6 6 7 7 7 7 7 7 7 7 7 7 7 12 12 12 13 13 13 6 13 13 17 17 17 17 17 17 12 25 17 12 12 12 22 12 22 25 0 22 22 22 22 25 25 25 25 25 25 25 0 0 0 0 0 0 
p50: 9345 0.027264s
12 8 11 15 9 11 9 13 0 12 
3 6 3 0 2 1 5 5 3 7 7 4 1 9 6 9 9 2 5 3 6 0 0 4 0 0 7 4 4 7 7 7 3 3 3 5 9 9 0 6 0 9 9 1 5 5 5 5 5 3 3 5 6 4 0 0 9 6 1 2 2 7 7 7 3 3 0 4 7 7 3 6 6 0 0 4 4 3 3 4 3 5 2 2 2 2 6 7 2 7 9 1 2 2 1 1 1 9 9 9 
p51: 8204 0.024044s
8 8 0 0 0 16 9 0 0 0 7 0 10 15 5 10 0 0 0 12 
15 6 19 10 12 12 5 5 15 1 5 14 6 13 6 13 12 5 5 15 0 0 10 14 14 14 1 19 19 15 1 1 15 19 15 5 13 13 10 0 0 13 13 13 12 5 5 5 5 19 15 5 0 14 10 10 6 6 13 12 13 5 1 5 15 15 10 19 1 1 15 0 0 0 10 19 19 19 19 19 19 5 12 12 13 13 6 5 5 1 13 12 12 6 13 13 6 13 12 6 
p52: 9236 0.028758s
0 0 0 20 15 15 18 16 8 8 
7 7 7 7 7 7 7 7 3 4 4 4 4 4 4 4 4 3 3 8 8 3 8 8 8 9 9 9 9 9 9 9 9 5 6 6 6 6 6 6 6 6 6 6 7 7 4 8 8 5 5 3 4 6 7 5 3 3 3 4 6 5 5 3 3 3 5 7 4 7 6 6 4 3 3 5 3 4 7 6 6 3 8 5 5 3 3 7 5 3 5 5 6 5 5 6 3 4 3 7 
p53: 9408 0.030053s
0 6 0 11 0 12 8 9 0 10 0 0 7 6 0 15 0 0 16 0 
5 5 5 5 5 5 5 5 1 7 7 7 1 7 7 7 7 12 13 12 12 13 12 12 3 9 9 9 9 9 15 9 9 15 18 18 18 18 18 18 18 18 18 18 5 5 7 12 12 15 15 3 7 18 6 15 3 3 1 6 18 9 15 13 3 13 15 18 6 5 9 18 6 3 3 15 3 6 6 13 18 1 13 15 15 3 1 6 15 3 15 15 9 15 15 18 1 6 3 5 
p54: 9289 0.031193s
11 0 15 19 9 6 17 8 8 7 
7 7 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 6 6 8 8 6 8 8 8 8 8 8 6 3 6 6 6 6 6 6 6 6 6 5 5 6 5 5 5 6 6 0 0 6 0 5 7 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 9 4 9 9 9 2 9 9 9 
p55: 9249 0.026301s
9 0 0 0 8 0 15 14 6 8 4 0 0 6 6 10 0 0 14 0 
18 18 4 18 4 4 4 4 4 8 4 8 4 8 18 8 8 6 8 6 14 6 14 14 6 14 14 6 6 6 6 14 6 6 6 6 6 6 6 7 10 7 0 7 0 0 0 0 0 0 0 0 7 7 7 7 10 7 7 7 7 9 13 7 9 7 10 7 10 9 13 9 9 13 18 13 9 13 9 9 13 15 15 15 15 15 15 15 15 15 15 18 18 18 18 18 18 18 18 18 
p56: 22598 0.029667s
8 0 8 7 13 11 7 7 0 9 10 7 7 8 4 0 8 4 7 12 11 10 4 0 9 8 0 9 12 0 
18 19 21 27 2 12 21 27 22 28 4 28 13 13 28 18 3 20 22 0 18 16 5 24 10 18 27 14 4 2 19 19 4 16 27 6 20 9 24 16 18 9 6 4 20 19 13 21 19 14 24 16 24 16 20 6 11 9 18 7 4 0 7 20 13 11 5 14 28 25 18 12 19 9 5 10 20 5 20 16 10 0 9 25 4 13 6 5 27 7 28 6 25 25 2 3 28 6 0 28 28 21 25 7 4 0 4 24 22 3 19 4 27 12 12 20 28 7 17 20 9 11 17 19 9 16 2 11 19 17 28 24 25 20 5 9 3 3 28 10 12 22 11 11 25 5 24 21 27 25 24 17 10 0 13 11 2 16 3 13 13 27 10 24 5 27 5 4 3 21 5 20 19 14 4 2 0 10 4 10 5 21 2 19 12 9 28 10 0 21 2 21 6 4 7 12 7 21 10 19 
p57: 29956 0.024212s
9 0 7 0 12 8 8 0 13 0 7 13 9 14 3 0 8 9 0 14 5 10 6 6 9 13 5 12 0 0 
27 19 21 27 2 12 21 27 22 17 4 19 13 13 19 11 13 20 22 0 27 16 5 24 10 27 27 19 4 2 19 19 4 16 27 6 20 8 24 16 25 8 6 4 8 19 13 21 19 14 24 16 24 16 8 6 12 8 22 25 4 0 25 8 13 11 5 14 19 25 22 12 6 8 5 23 20 23 8 16 10 0 26 25 4 13 19 5 27 25 17 6 25 25 0 13 11 6 0 17 17 21 12 11 4 0 4 24 22 13 19 4 27 12 12 8 11 25 17 8 26 11 17 19 26 16 2 11 26 17 11 24 11 20 23 8 13 13 17 10 12 22 11 11 25 5 24 21 27 25 24 17 23 0 8 11 2 16 13 13 13 27 10 24 23 27 5 4 13 21 5 20 19 14 26 2 0 10 4 10 5 21 2 6 12 8 11 23 0 21 2 21 6 4 25 12 25 21 10 19 
p58: 44019 0.0257s
11 0 12 7 13 11 0 5 14 0 0 8 11 10 7 0 15 3 7 13 0 0 4 10 0 9 6 12 12 0 
18 19 2 27 2 12 2 27 22 28 4 28 13 13 28 27 3 13 22 0 18 16 5 0 23 18 27 19 4 5 19 19 4 16 27 12 14 8 27 16 18 8 12 4 8 26 13 16 19 14 0 16 2 16 8 12 11 8 18 25 4 0 7 8 13 11 5 14 28 25 18 12 19 8 23 23 13 23 8 16 23 0 26 25 4 13 4 5 27 7 28 19 25 25 2 3 11 12 0 28 28 16 25 18 4 0 4 27 22 3 19 4 27 12 12 8 28 7 17 8 26 11 28 19 26 16 5 11 26 17 28 2 25 13 23 8 3 3 28 14 12 22 11 11 25 5 16 16 27 25 0 17 23 0 8 11 5 16 3 13 13 27 23 2 5 27 5 4 3 16 5 8 19 14 26 2 0 14 4 14 5 2 2 19 12 8 28 23 0 16 2 16 19 4 7 12 7 2 23 19 
p59: 33436 0.023092s
7 0 8 8 0 8 8 0 0 14 10 9 6 6 7 6 0 4 9 13 0 10 0 7 12 13 0 13 11 11 
18 19 21 27 2 11 15 27 27 28 29 28 23 3 28 18 3 10 24 27 18 21 5 24 10 18 27 14 29 2 19 19 19 21 27 6 14 9 24 15 18 9 6 29 9 19 13 21 19 14 24 24 24 21 9 6 11 9 18 25 29 0 18 9 13 11 5 14 28 25 18 12 19 9 23 23 10 23 9 24 10 0 9 25 29 13 6 5 27 25 28 6 25 25 2 3 11 6 0 28 28 15 25 18 29 0 29 24 27 3 19 29 27 12 12 9 28 25 17 9 14 11 17 19 9 21 2 11 19 17 28 24 25 10 23 9 3 3 28 14 12 27 11 11 25 5 24 15 27 25 24 17 23 0 13 11 2 15 3 13 13 27 10 24 5 27 5 29 3 21 5 10 19 14 29 2 0 10 29 10 5 21 2 19 12 9 28 23 0 21 2 21 6 6 25 12 25 15 10 19 
p60: 23326 0.022809s
10 0 11 6 7 7 8 6 12 0 8 8 7 8 0 4 9 5 8 11 7 8 4 6 0 8 6 11 11 4 
18 19 21 27 2 12 15 27 22 28 4 28 13 13 19 18 3 20 22 0 18 16 5 0 10 18 27 28 29 2 19 19 4 16 27 6 20 8 16 16 18 8 6 26 8 19 13 21 19 20 0 16 2 16 8 6 11 8 18 7 29 0 7 8 13 11 5 17 28 25 18 12 19 8 23 23 20 23 8 16 10 0 26 25 29 13 6 2 27 7 28 6 25 25 2 3 11 6 0 28 28 15 25 18 4 0 4 27 22 3 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 17 28 21 25 20 23 20 3 3 28 10 12 22 11 11 25 5 16 15 27 25 27 17 23 0 8 11 2 15 13 13 13 27 10 2 5 27 5 4 3 21 5 20 19 10 26 2 0 10 29 10 5 21 2 6 12 8 28 23 0 21 2 21 6 4 7 12 7 21 10 19 
p61: 29336 0.02241s
7 0 8 0 10 8 7 0 13 0 9 7 8 14 0 0 9 6 9 12 5 9 0 6 9 13 7 13 11 0 
18 19 21 27 2 12 21 27 27 28 4 28 13 13 28 18 13 20 27 0 18 16 5 24 10 18 27 19 4 2 19 19 4 16 27 6 20 8 24 16 18 8 6 26 8 19 13 21 19 20 24 16 24 16 8 6 11 8 18 25 19 0 18 8 13 11 5 17 28 25 18 12 19 8 23 23 20 23 8 16 10 0 26 25 4 13 6 5 27 25 28 6 25 25 2 13 11 6 17 28 28 21 25 18 4 0 4 24 27 13 26 4 27 12 12 8 28 25 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 10 23 8 13 13 28 10 12 27 12 11 25 5 24 16 27 25 24 17 23 0 8 11 2 16 13 13 13 27 10 24 5 27 5 4 13 21 5 20 19 10 26 2 0 10 4 10 5 21 2 19 12 8 28 23 0 21 2 21 6 4 25 12 25 21 10 19 
p62: 42170 0.022819s
10 0 8 0 0 7 0 0 13 6 8 8 11 0 0 0 8 0 9 17 11 10 0 12 11 14 14 11 12 0 
18 19 21 27 2 12 21 27 18 28 26 28 20 23 28 18 23 20 27 24 18 16 5 24 10 18 27 19 26 2 19 19 26 16 27 12 20 8 24 16 18 9 12 26 8 19 20 21 19 20 24 16 24 16 8 12 11 9 18 25 26 0 25 8 20 11 23 19 28 25 18 12 19 9 23 23 20 23 8 16 10 0 9 25 26 10 19 5 27 25 28 19 25 25 2 8 11 12 0 28 28 21 25 18 26 0 26 24 24 8 19 26 27 12 12 8 28 25 0 8 9 11 28 19 26 16 2 11 26 0 28 24 25 20 23 9 23 8 28 10 12 27 11 11 25 5 24 21 27 25 24 0 23 0 8 11 2 16 8 20 23 27 10 24 5 27 5 26 23 21 5 20 19 10 26 2 0 10 26 20 5 21 2 19 12 8 28 23 0 21 2 21 19 19 25 12 25 21 10 19 
p63: 30281 0.023375s
8 0 11 0 12 0 7 0 11 0 7 0 9 14 0 0 9 5 9 12 8 9 0 12 9 17 5 13 13 0 
18 19 21 27 2 12 21 27 27 28 4 28 13 13 28 18 13 20 27 0 18 16 23 24 10 18 27 19 4 2 19 19 4 16 27 6 20 8 24 16 18 8 6 4 8 19 13 21 19 20 24 16 24 16 8 6 25 8 18 25 4 0 18 8 13 25 23 17 28 25 18 12 19 20 23 23 20 23 8 16 23 0 26 25 4 13 6 2 27 25 28 6 25 25 2 13 28 6 0 28 28 21 25 18 4 0 4 24 27 13 19 4 27 12 12 8 28 25 17 8 26 25 17 19 26 16 2 12 26 17 28 24 25 20 23 20 13 13 28 10 12 27 12 25 25 2 24 16 27 25 24 17 23 0 8 28 2 16 13 13 13 27 10 24 23 27 23 4 13 21 23 20 19 10 26 2 0 10 4 10 2 21 2 19 12 8 28 23 0 21 2 21 6 4 25 12 25 21 10 19 
p64: 22837 0.023797s
8 0 9 6 8 11 7 0 10 5 13 9 7 8 5 0 8 4 9 11 0 9 4 0 9 12 4 9 11 4 
18 19 2 27 2 12 21 27 22 28 4 28 13 13 28 18 13 10 22 0 18 16 5 24 10 18 27 14 29 2 19 19 4 16 27 6 14 8 24 16 18 9 6 4 8 19 13 21 19 14 24 16 24 16 8 6 11 9 18 25 29 0 18 8 13 11 5 14 28 25 18 12 19 9 5 10 10 5 8 16 10 0 9 25 29 13 6 5 27 25 28 6 11 25 2 3 11 6 0 28 28 21 25 18 4 0 4 24 22 3 19 4 27 12 12 8 28 25 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 10 5 9 3 3 28 10 12 22 11 11 25 5 24 21 27 25 24 17 10 0 8 11 2 16 3 13 13 27 10 24 5 27 5 4 3 21 5 8 19 14 26 2 0 10 29 10 5 21 2 19 12 8 28 10 0 21 2 21 6 4 25 12 25 21 10 19 
p65: 28885 0.024375s
11 0 11 0 9 0 8 10 9 7 9 7 8 14 0 0 8 0 0 13 5 10 5 11 9 8 0 11 13 4 
7 19 21 27 2 12 21 27 22 28 4 28 13 13 19 7 13 20 22 0 27 16 23 24 10 27 27 19 29 2 19 19 4 16 27 6 20 8 24 16 7 9 6 4 8 19 13 21 19 20 24 16 24 16 8 6 11 9 22 25 29 0 7 8 13 11 23 28 28 25 7 12 19 9 23 23 20 23 8 16 10 0 9 25 29 13 6 2 27 7 28 6 25 25 2 13 28 6 0 28 28 21 12 7 4 0 4 24 22 13 19 4 27 12 12 8 28 7 0 8 9 25 28 19 9 16 2 11 19 0 28 24 11 10 23 9 13 13 28 10 12 22 11 11 25 2 24 21 27 25 24 0 23 0 8 11 2 16 13 13 13 27 10 24 23 27 23 4 13 21 23 20 19 10 4 2 0 10 29 10 2 21 2 6 12 8 28 23 0 21 2 21 6 4 7 12 7 21 10 19 
p66: 41820 0.022734s
8 0 14 0 12 0 0 10 14 5 20 8 11 0 0 0 0 4 0 16 11 16 5 0 11 9 4 11 11 0 
7 19 21 27 2 12 21 27 22 28 4 28 20 10 28 7 10 20 22 0 27 21 2 24 10 27 27 19 4 2 19 19 4 21 27 12 20 8 24 21 7 9 12 4 8 19 8 21 19 20 24 24 24 21 20 12 11 9 22 25 4 0 7 8 20 11 2 19 28 25 7 12 19 9 10 10 20 10 8 24 10 0 9 25 4 10 19 2 27 7 28 19 25 25 2 8 11 12 0 28 28 21 25 7 4 0 4 24 22 8 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 21 2 11 26 17 28 24 25 20 10 9 8 20 28 10 12 22 11 11 25 2 24 21 27 25 24 17 10 0 8 11 2 21 8 20 10 27 10 24 10 27 2 4 8 21 10 20 19 10 26 2 0 10 4 10 2 21 2 19 12 8 28 10 0 21 2 21 19 4 7 12 7 21 10 19 
p67: 31928 0.023798s
0 0 12 6 15 8 7 5 12 0 7 0 9 8 4 11 0 8 10 13 7 0 0 6 16 11 0 13 12 0 
18 19 2 24 2 12 15 27 27 28 4 28 13 13 28 18 3 20 27 27 18 24 5 24 10 18 27 19 4 2 19 19 4 15 27 6 20 8 24 15 18 8 6 4 8 19 13 2 19 14 24 24 24 24 8 6 18 8 18 25 4 2 7 8 13 12 5 14 28 25 18 12 19 20 23 23 20 23 8 24 10 17 8 25 4 13 4 5 27 7 28 6 25 25 2 3 27 6 17 28 28 15 25 18 4 24 4 24 27 13 19 4 27 12 12 8 28 7 17 8 14 25 17 19 4 15 2 12 19 17 28 24 25 20 23 20 3 3 28 10 12 18 6 25 25 5 24 15 27 25 24 17 23 17 8 28 2 15 3 13 13 27 10 24 5 27 5 4 3 15 5 20 19 14 4 2 24 10 4 10 5 15 2 19 12 8 28 23 17 2 2 15 6 4 7 12 7 15 10 19 
p68: 23250 0.024028s
9 0 11 7 8 6 6 6 9 5 8 8 8 7 0 0 8 3 9 13 6 10 0 6 8 8 4 12 11 4 
18 19 21 27 2 12 21 27 27 28 4 28 13 13 28 18 3 20 27 0 18 16 5 24 10 18 27 19 29 2 19 19 4 16 27 6 20 8 24 16 18 9 12 4 8 19 13 21 19 20 24 16 2 16 8 6 11 9 18 7 29 0 7 8 13 11 5 19 28 25 18 12 6 9 23 23 20 23 8 16 10 0 9 25 29 13 19 2 27 7 28 6 25 25 2 3 28 6 0 28 28 21 25 18 4 0 4 24 18 3 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 0 11 24 25 20 23 9 3 3 28 10 12 27 11 11 25 2 24 21 27 25 24 17 23 0 8 11 2 16 3 13 13 27 10 24 5 27 5 4 3 21 5 20 19 10 26 2 0 10 29 10 5 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 21 10 19 
p69: 31113 0.025707s
9 0 10 0 8 7 8 10 17 0 10 8 7 0 3 6 6 3 0 12 7 5 5 11 9 9 5 11 10 4 
7 19 2 27 2 12 15 27 22 28 4 28 10 23 19 7 23 20 22 0 27 16 5 24 10 27 27 19 29 2 19 19 4 16 27 6 20 8 24 15 7 8 6 4 8 19 8 21 19 14 24 16 24 16 8 6 11 8 22 25 29 0 7 8 20 11 5 14 28 25 7 12 19 8 23 23 20 23 8 16 10 0 26 25 29 10 6 2 27 7 28 6 25 25 2 8 11 6 0 28 28 15 25 7 4 0 4 24 22 8 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 0 28 24 11 20 23 20 23 8 28 10 12 22 11 25 25 5 24 15 27 25 24 17 23 0 8 11 2 15 8 10 23 27 10 24 5 27 5 4 23 21 5 20 19 14 26 2 0 10 29 10 5 21 2 6 12 8 28 23 0 21 2 21 6 4 7 12 7 15 10 19 
p70: 42229 0.029573s
0 0 8 12 13 8 12 0 0 8 8 11 0 0 5 0 7 9 9 11 11 10 0 8 12 14 0 13 11 0 
18 19 21 27 2 6 21 27 18 28 4 28 10 3 28 18 3 20 27 27 18 16 5 24 10 18 27 19 4 2 19 19 4 16 27 6 20 9 24 16 18 9 6 4 20 19 3 21 19 14 24 16 24 16 20 6 11 9 18 25 4 17 25 20 3 11 5 14 28 25 18 6 6 9 23 23 20 23 20 24 23 17 9 25 4 10 6 5 27 25 28 6 25 25 2 3 11 6 17 28 28 21 25 18 4 24 4 24 27 3 19 4 27 6 11 20 28 25 17 20 14 11 17 19 9 16 2 11 14 17 28 24 25 20 23 9 3 3 28 10 11 27 11 11 25 5 24 21 27 25 24 17 23 17 3 11 2 16 3 3 23 27 10 24 5 27 5 4 3 21 5 20 19 14 4 2 24 10 4 10 5 21 2 19 11 9 28 23 17 21 2 21 6 4 25 6 25 21 10 19 
p71: 29922 0.024978s
0 0 11 0 10 7 8 0 0 0 7 0 9 14 4 0 9 7 10 12 19 10 0 6 11 16 0 13 13 4 
18 19 21 27 2 12 21 27 27 28 4 28 13 13 28 18 13 20 27 27 18 16 5 24 10 18 27 19 29 2 19 19 4 16 27 6 20 20 24 16 18 20 6 4 20 19 13 21 19 14 24 16 24 16 20 6 18 20 18 25 29 2 18 20 13 25 5 14 28 25 18 12 6 20 23 23 20 23 20 16 10 2 20 25 29 13 6 2 27 25 28 6 25 25 2 13 28 6 17 28 28 21 25 18 4 24 4 24 16 13 19 4 27 12 12 20 28 25 17 20 14 25 17 19 4 16 2 12 19 17 28 24 25 20 23 20 13 13 28 10 12 27 12 25 25 5 24 21 27 25 24 17 23 17 20 28 2 16 13 13 13 27 10 24 5 27 5 4 13 21 5 20 19 14 4 2 24 10 29 10 5 21 2 19 12 20 28 23 17 21 2 21 6 4 25 12 25 21 10 19

解決方案二：禁忌搜尋法

演算法描述

  1. 給定演算法引數，隨機產生初始解S，置禁忌表為空。
  2. 判斷演算法終止條件是否滿足，若是，則結束演算法，輸出最優解，否則繼續以下步驟。
  3. 利用當前解的領域函式產生所有領域解，並從中確定若干候選解。
  4. 對候選解判斷是否能特赦準則，若成立，則用這個解S’替代S為新的當前解，並把S’放進禁忌表，然後更新禁忌表，然後進入步驟2，否則進入步驟5。
  5. 判斷候選解對應的各物件的禁忌屬性，選擇候選解中非禁忌物件對應的最佳狀態S’為新的當前解，並把S’放進禁忌表，然後更新禁忌表，進行步驟2。

流程圖

在這裡插入圖片描述

領域解和候選解

跟前面的一樣，把所有的領域解當成候選解，最多有factory_num * customer_num - 1種可能。

禁忌操作

當使用了某個解時，在一段時間內不能再恢復。即把customer i 從 factory 1 分配給 factory 2後，在一段時間內不能把customer i 從 factory 2 分配給factory 1。禁忌表用一個二維陣列結構來存，記錄著每個操作禁忌的迭代次數。

禁忌表的長度

如果禁忌表長度過小，那麼搜尋過程就可能進入死迴圈，整個搜尋將圍繞著相同的幾個解徘徊;相反，如果禁忌表長度過大，那它將在相當大的程度上限制了搜尋區域，好的解就有可能被跳過，同時，不會改進解的效果而增加演算法運算時間。禁忌表的長度為 n \sqrt{n} ，n為領域解的大小。

停止準則

要有停止的準則才能終止演算法，這裡設為一定次數之後，最優解沒有更新。

特赦準則

某個解在禁忌表中，但如果它能產生比歷史最優解更好的解時，就依然能使用這個解。

中期記憶與集中搜索（Intensification）

如果當前搜尋出現了比較好的解，則進一步對當前區域進行更集中的搜尋，這樣可以發現更多更好的解。採用的策略是，如果最好的解被更新，就把禁忌表清空。

完整程式碼

#include<iostream>
#include<fstream>
#include<stdlib.h>
#include<cmath>
using namespace std;
#define FILE_NUM 71
#define INT_MAX 10000

int factory_num;
int customer_num;
int* origin_capactity;
int* capacity;
int* fixed_cost;
double* demand;
double** allocating_cost;

int** tabu_list;
int** frequence;

// how many customer to allocate
int* open_list;
// witch factory to allocate
int* allocating_list;



double get_total_cost(){
	double cost = 0;

	for(int i = 0; i < factory_num; i++){
		if(open_list[i] != 0){
			cost += fixed_cost[i];
		}
	}
	for(int i = 0; i < customer_num; i++){
		cost += allocating_cost[allocating_list[i]][i];
	}
	return cost;
}

void generate_random_solution(){
	for(int i = 0; i < customer_num; i++){
		while(true){
			int allocated = rand() % factory_num;
			if(capacity[allocated] >= demand[i]){
				open_list[allocated] += 1;
				allocating_list[i] = allocated;
				capacity[allocated] -= demand[i];
				break;
			}
		}
		
	}
}

void update_tabu_list(){
	for(int i = 0; i < factory_num; i++){
		for(int j = 0; j < customer_num; j++){
			if(tabu_list[i][j] > 0){
				tabu_list[i][j]--;
			}
		}
	}
}


double calculate_delta_cost(int customer, int factory){
	int result = 0;
	//open new factory
	if(open_list[factory] == 0){
		result += fixed_cost[factory];
	}
	int f = allocating_list[customer];
	if(open_list[f] == 1){
		result -= fixed_cost[f];
	}
	result += allocating_cost[factory][customer] - allocating_cost[f][customer];
	return result;

}

void accept(int customer, int factory){
	int f = allocating_list[customer];
	capacity[f] += demand[customer];
	capacity[factory] -= demand[customer];
	allocating_list[customer] = factory;
	open_list[f] -= 1;
	open_list[factory] += 1;
}

void clear_tabu_list(){
	for(int i = 0; i < factory_num; i++){
		for(int j = 0; j < customer_num; j++){
			tabu_list[i][j] = 0;
		}
	}
}

int main(){
	int file_num = 0;
	ofstream result("TABUresult");
	srand((int)time(0));
	while(file_num != FILE_NUM){
		file_num++;
		string file_name = "Instances/p" + to_string(file_num);	
		ifstream file(file_name);
		if(!file.is_open()){
			cout << "open error" << endl;
			return -1;
		}
		file >> factory_num >> customer_num;
		capacity = new int[factory_num];
		origin_capactity = new int[factory_num];
		fixed_cost = new int[factory_num];

		for(int i = 0; i < factory_num; i++){
			file >> capacity[i] >> fixed_cost[i];
			origin_capactity[i] = capacity[i];
		}

		demand = new double[customer_num];
		for(int i = 0; i < customer_num; i++){
			file >> demand[i];
		}

		//allocating_cost[i][j] means the cost allocating of 
		//customer j to facity i
		allocating_cost = new double*[factory_num];
		
		for(int i = 0; i < factory_num; i++){
			allocating_cost[i] = new double[customer_num];		
		}
		for(int i = 0; i < factory_num; i++){
			for(int j = 0; j < customer_num; j++){
				file >> allocating_cost[i][j];
			}		
		}

		open_list = new int[factory_num];
		allocating_list = new int[customer_num];
		for(int i = 0; i < factory_num; i++){
			open_list[i] = 0;
		}

		tabu_list = new int*[factory_num];
		frequence = new int*[factory_num];
		for(int i = 0; i < factory_num; i++){
			tabu_list[i] = new int[customer_num];
			frequence[i] = new int[customer_num];
		}
		for(int i = 0; i < factory_num; i++){
			for(int j = 0; j < customer_num; j++){
				tabu_list[i][j] = 0;
				frequence[i][j] = 0;
			}
		}

		//tabu
		clock_t start = clock();
		generate_random_solution();	
		int best_ever = get_total_cost();
		int best_current = get_total_cost();
		int neibor_num = customer_num * factory_num - 1;
		int len = (int)sqrt(neibor_num);
		int repeat = 0;

		while(repeat <= customer_num){
			//generate neibor

			int best_in_neibor = INT_MAX;
			int factory = factory_num;
			int customer = customer_num;
			int f = factory_num;
			int c = customer_num;
			for(int i = 0; i < customer_num; i++){
				for(int j = 0; j < factory_num; j++){
					//invalid solution
					if(capacity[j] < demand[i]) continue;
					if(allocating_list[i] == j) continue;
					int delta = calculate_delta_cost(i, j);
					//find the best in neibor
					if(delta < best_in_neibor && tabu_list[j][i] == 0){
						best_in_neibor = delta;
						factory = j;
						customer = i;
					}else if(best_current + delta < best_ever){
						//best_ever = best_current + delta;
						f = j;
						c = i;
					}

				}
			}
			update_tabu_list();
			if(f != factory_num){
				//aspiration		
				clear_tabu_list();		
				int old_factory = allocating_list[customer];
				tabu_list[old_factory][c] = len;
				frequence[f][c]++;
				accept(c, f);
				best_current = get_total_cost();
				best_ever = best_current;
				//cout << "aspiration" << endl;
				repeat = 0;
			}else if(best_in_neibor != INT_MAX){
				//select the best in the neibor
				int old_factory = allocating_list[customer];
				tabu_list[old_factory][customer] = len;
				frequence[factory][customer]++;
				accept(customer, factory);
				best_current = get_total_cost();
				if(best_current < best_ever){
					repeat = 0;
					best_ever = best_current;
					clear_tabu_list();
					tabu_list[old_factory][customer] = len;
				} 			

			}			
			repeat++;
		}
		//get result
		clock_t end = clock();
		result << "p" << file_num << ": ";
		result << best_ever << ' ';
		result << (end - start) * 1.0 / CLOCKS_PER_SEC << "s" << endl;		
		for(int i = 0; i < factory_num; i++){
			result << open_list[i] << ' ';
		}
		result << endl;
		for(int i = 0; i < customer_num; i++){
			result << allocating_list[i] << ' ';
		}
		result << endl;
		

		
		//release
		delete capacity;
		delete fixed_cost;
		delete demand;
		delete open_list;
		for(int i = 0; i < factory_num; i++){
			delete allocating_cost[i];
		}
		delete allocating_list;
		delete allocating_cost;

	}
	result.close();

	
}

結果

p1: 9324 0.001898s
7 5 7 6 9 3 4 2 5 2 
0 2 1 6 3 8 2 4 4 1 9 8 3 2 8 3 4 0 9 7 3 2 6 4 2 5 1 5 8 1 2 6 0 3 4 4 4 3 0 4 5 8 1 6 7 0 2 0 4 0 
p2: 8010 0.001979s
9 5 3 5 8 4 4 4 5 3 
7 0 1 6 3 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 8 6 4 5 5 1 5 0 1 2 6 0 3 4 4 4 3 0 4 5 8 1 6 7 0 9 0 7 0 
p3: 10010 0.001769s
9 5 3 5 8 4 4 4 5 3 
7 0 1 6 3 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 8 6 4 5 5 1 5 0 1 2 6 0 3 4 4 4 3 0 4 5 8 1 6 7 0 9 0 7 0 
p4: 11483 0.001665s
8 0 8 7 10 6 0 2 5 4 
0 4 5 2 3 8 2 4 4 5 9 8 0 2 8 3 4 0 9 7 3 2 9 4 2 5 3 5 8 5 2 9 0 3 4 4 4 3 0 4 2 8 3 5 7 0 2 0 4 0 
p5: 9204 0.001943s
6 7 6 7 6 0 5 4 6 3 
8 8 1 6 3 8 2 4 2 1 9 8 3 2 8 3 2 0 9 7 1 7 6 4 2 6 1 1 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 7 0 9 3 7 0 
p6: 7809 0.001827s
7 7 5 7 7 0 5 2 6 4 
8 8 1 6 3 8 2 4 2 1 9 8 0 2 8 3 4 0 9 7 1 2 6 4 1 6 3 1 8 1 2 6 0 3 9 4 4 3 0 4 3 0 1 6 7 0 9 3 4 0 
p7: 9609 0.002642s
7 6 5 6 8 0 5 3 6 4 
8 0 1 6 1 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 1 4 9 4 2 6 1 6 0 1 2 6 0 3 9 4 7 3 8 4 3 0 3 6 7 8 2 3 4 0 
p8: 11409 0.001986s
7 7 5 7 7 0 5 2 6 4 
8 8 1 6 3 8 2 4 2 1 9 8 0 2 8 3 4 0 9 7 1 2 6 4 1 6 3 1 8 1 2 6 0 3 9 4 4 3 0 4 3 0 1 6 7 0 9 3 4 0 
p9: 8847 0.00171s
9 7 5 6 9 0 5 2 5 2 
8 0 1 6 3 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 2 6 4 1 6 1 1 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 7 0 4 0 2 0 
p10: 7855 0.001259s
8 6 6 4 8 6 0 2 7 3 
8 8 1 2 1 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 8 9 4 1 5 1 5 0 5 2 5 0 3 4 4 4 3 0 4 5 8 1 5 7 0 2 0 2 0 
p11: 9448 0.001916s
9 7 5 6 9 0 5 2 5 2 
8 0 1 6 3 8 2 4 4 1 9 8 0 2 8 3 4 0 9 7 3 2 6 4 1 6 1 1 0 1 2 6 0 3 4 4 4 3 0 4 3 8 1 6 7 0 4 0 2 0 
p12: 10817 0.001376s
8 7 7 5 9 0 6 2 6 0 
8 0 1 6 3 8 2 4 4 1 4 8 0 2 8 3 4 0 6 7 3 2 6 4 1 6 1 1 8 1 2 6 0 3 4 4 4 3 0 4 2 8 1 6 7 0 2 0 2 0 
p13: 8840 0.003711s
0 3 0 0 0 5 0 0 0 5 6 3 0 6 5 0 5 6 0 6 
16 17 10 10 19 1 17 13 14 17 16 19 1 10 13 9 5 10 17 9 14 5 14 19 9 11 16 17 1 17 13 5 13 16 11 10 11 19 19 13 14 5 5 16 9 13 14 10 19 9 
p14: 7510 0.005134s
0 0 0 0 0 0 3 0 0 2 5 2 0 5 6 6 6 6 0 9 
16 14 10 10 19 19 17 13 14 17 15 19 19 6 13 14 15 10 19 9 14 15 15 19 6 17 16 17 14 17 13 16 13 16 17 10 11 19 19 13 6 16 15 16 11 15 14 10 19 9 
p15: 9859 0.004145s
0 0 0 0 4 0 4 0 0 0 6 6 5 5 0 7 6 0 0 7 
16 12 10 10 19 15 11 13 15 4 15 4 19 6 13 11 15 10 4 6 12 15 15 19 6 19 16 11 12 4 13 10 13 16 11 10 11 19 19 13 12 16 16 16 11 15 12 10 19 6 
p16: 12247 0.005167s
0 0 0 4 0 2 4 0 3 0 5 0 4 0 0 5 5 6 7 5 
16 3 10 10 12 18 17 18 8 17 15 19 19 6 18 3 15 10 17 6 12 15 15 19 6 17 16 17 12 17 18 15 18 16 3 10 3 18 19 18 6 16 5 16 8 5 12 10 19 8 
p17: 8517 0.006122s
0 5 0 0 0 0 4 0 2 2 5 0 4 6 0 6 5 6 0 5 
16 12 10 10 1 13 17 13 6 17 15 19 1 6 13 12 15 10 17 9 12 15 15 19 6 17 16 17 1 17 13 12 19 16 1 10 8 1 19 13 6 16 15 16 8 13 15 10 19 9 
p18: 8198 0.004017s
0 4 5 0 0 3 4 3 0 2 3 4 0 0 0 6 5 6 2 3 
16 1 10 10 1 18 17 18 15 17 15 19 1 6 2 11 15 7 17 9 15 15 7 2 6 17 16 17 1 17 2 7 2 16 11 10 11 19 19 5 6 16 5 16 11 5 15 6 2 9 
p19: 9626 0.005439s
0 0 6 5 0 0 4 0 0 0 6 0 0 0 3 7 5 7 0 7 
16 3 10 10 17 2 17 2 14 17 15 19 19 6 2 3 15 10 17 10 14 15 15 19 6 19 16 3 17 17 2 15 2 16 3 10 3 19 19 2 6 16 15 16 17 15 14 10 19 6 
p20: 12442 0.004016s
0 0 0 6 3 3 5 5 0 0 4 2 5 6 0 0 5 0 0 6 
16 3 10 10 12 12 3 13 7 4 7 4 19 6 13 12 5 7 4 6 12 5 7 19 6 19 16 3 3 3 13 7 13 16 3 10 11 19 19 13 6 16 5 16 11 13 12 10 19 6 
p21: 8749 0.004007s
0 0 0 0 0 0 0 0 0 4 6 2 2 6 6 5 6 7 0 6 
16 12 10 10 12 13 17 13 14 17 15 19 19 10 13 14 15 10 17 9 14 15 15 19 9 17 16 17 14 17 13 14 13 16 17 10 11 19 19 13 9 16 16 16 11 15 14 10 19 9 
p22: 7706 0.003843s
0 0 0 7 4 0 3 4 0 3 4 0 0 5 4 4 4 0 0 8 
16 3 10 10 19 19 3 13 14 4 7 4 19 6 13 3 15 14 4 9 14 15 7 19 6 19 16 3 3 4 13 7 13 16 3 10 3 19 19 13 6 16 7 15 9 15 14 10 19 9 
p23: 9541 0.005277s
0 0 0 4 0 0 3 0 0 3 5 0 0 6 3 4 7 7 2 6 
16 3 10 10 13 18 17 13 14 17 15 19 19 6 13 3 15 10 17 9 14 15 15 19 6 17 16 17 3 17 13 16 13 16 3 10 17 19 19 13 6 16 16 16 9 18 14 10 19 9 
p24: 11298 0.005883s
0 0 0 8 4 0 0 5 0 2 7 0 0 6 0 6 5 0 0 7 
16 3 10 10 19 15 3 13 7 3 15 4 19 10 13 3 15 7 4 9 7 15 15 19 10 19 16 4 3 4 13 7 13 16 3 10 3 19 19 13 10 16 15 16 3 13 7 10 19 9 
p25: 13448 0.079611s
10 0 9 0 0 16 0 8 12 0 0 14 0 6 17 2 0 11 0 0 16 0 0 0 20 9 0 0 0 0 
20 11 13 14 13 5 2 24 14 17 24 8 8 20 2 14 14 0 5 11 14 7 5 17 5 8 2 24 5 24 5 25 13 25 20 20 24 15 0 14 0 14 15 13 24 14 11 20 11 8 5 14 14 5 20 20 17 0 11 14 0 5 20 11 11 11 24 0 5 24 13 20 11 0 24 8 24 20 14 24 20 7 20 17 2 17 17 7 20 5 2 24 17 11 17 24 2 25 25 8 8 17 17 25 2 25 7 11 14 8 14 14 2 11 11 7 24 24 24 24 5 8 25 13 20 7 5 24 7 0 0 11 24 24 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 
p26: 12259 0.07608s
16 0 9 3 0 10 0 0 12 0 0 14 0 4 16 2 0 10 0 0 18 0 0 0 20 10 0 0 0 6 
20 11 13 2 20 5 2 24 14 0 24 8 8 20 3 14 14 17 25 11 14 0 29 3 29 8 2 24 5 24 25 25 20 25 20 20 24 15 0 14 0 14 15 13 24 14 3 20 11 8 29 14 14 5 20 20 17 29 11 14 0 5 20 11 11 11 24 0 25 24 20 20 11 17 24 8 24 20 14 24 20 0 13 0 2 17 17 0 20 5 2 24 17 11 17 24 2 29 25 8 8 17 17 25 2 29 0 11 14 8 14 14 2 11 11 0 24 24 24 24 5 8 25 13 20 0 5 24 0 11 0 11 24 24 8 14 0 5 20 17 0 8 20 14 8 25 25 5 2 5 
p27: 13514 0.100328s
17 0 10 0 0 18 0 0 12 0 0 17 0 0 18 2 0 10 0 0 21 0 0 0 16 9 0 0 0 0 
20 11 20 14 20 5 2 24 14 17 5 20 8 20 0 14 14 0 5 11 2 11 11 0 25 8 2 24 5 24 5 25 20 25 20 20 24 15 25 14 0 14 15 14 24 14 11 20 11 8 5 14 14 5 20 20 17 0 0 14 0 5 20 11 11 11 24 0 0 5 20 20 11 17 24 8 24 20 14 24 20 0 20 17 2 17 2 0 20 5 2 24 17 11 17 5 2 14 11 8 8 17 17 25 2 25 0 11 14 8 14 14 2 11 11 5 24 24 24 24 5 8 25 20 8 11 5 24 0 5 0 0 24 11 8 14 0 5 20 17 0 8 20 14 8 25 25 5 2 5 
p28: 17181 0.080334s
19 0 9 0 0 11 0 0 12 0 0 13 0 6 17 2 0 10 0 0 17 0 0 0 19 9 0 0 0 6 
20 11 20 14 20 5 2 24 14 0 24 8 8 20 2 14 14 17 25 11 14 0 29 0 29 8 2 24 5 24 29 25 13 25 20 20 24 15 0 14 0 14 15 13 24 14 0 20 11 8 29 14 14 5 13 20 17 29 0 14 0 5 20 11 11 11 24 0 25 24 20 20 11 17 24 8 24 20 14 24 20 0 13 0 2 17 17 0 20 5 2 24 17 11 17 5 2 13 25 8 8 17 17 25 2 29 0 11 14 8 14 14 2 11 11 0 24 24 24 24 5 8 25 13 20 0 5 24 0 11 0 11 24 24 8 14 0 5 20 17 0 8 20 14 8 25 25 5 2 5 
p29: 14742 0.075452s
9 0 9 0 0 15 0 4 10 0 0 15 0 8 14 2 0 16 0 0 14 0 6 0 14 8 0 0 4 2 
20 11 13 2 13 5 2 24 28 17 22 20 8 20 0 14 14 17 5 11 2 7 5 17 5 8 2 24 5 24 29 25 13 25 20 20 24 15 0 14 0 14 15 28 24 14 0 13 11 8 5 14 14 5 13 20 17 25 11 14 0 5 20 11 11 11 22 0 5 22 13 20 11 17 24 8 22 20 14 24 20 7 13 17 17 17 17 7 20 5 2 24 17 11 17 22 2 14 25 8 8 17 17 25 2 29 7 11 28 28 14 14 2 11 11 11 24 24 24 24 5 8 25 13 20 17 5 24 0 11 0 11 24 22 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p30: 11879 0.076014s
15 0 11 0 0 15 0 0 11 8 0 13 0 8 14 0 0 15 0 0 13 0 0 0 14 10 0 0 3 0 
20 11 13 2 13 5 2 24 14 17 9 8 8 20 2 14 14 17 5 11 2 0 9 17 9 8 2 24 5 9 5 25 20 25 20 20 24 24 0 14 0 14 24 28 24 14 11 20 11 8 25 14 14 5 13 20 17 0 0 14 0 5 20 11 11 11 9 0 5 5 13 13 11 17 24 8 24 20 14 9 20 0 13 17 17 17 2 17 20 5 2 24 17 11 17 5 2 25 25 8 8 17 17 25 2 25 0 11 28 28 14 14 2 11 11 0 24 24 24 24 5 8 25 13 13 11 5 9 0 0 0 0 24 9 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p31: 15916 0.070015s
8 0 9 0 0 15 0 6 10 5 0 15 0 8 14 2 0 16 0 0 15 0 0 0 14 8 0 0 3 2 
20 11 13 2 20 5 2 24 28 17 9 20 8 20 0 14 14 17 5 11 2 7 9 17 5 8 2 24 5 24 29 25 13 25 20 20 24 15 7 14 0 14 15 8 24 14 7 13 11 8 5 14 14 5 13 20 17 25 0 14 0 5 20 11 11 11 9 0 5 24 20 13 11 17 24 8 9 20 14 24 20 7 13 17 17 17 17 7 20 5 2 24 17 11 17 5 2 14 25 13 8 17 17 25 2 29 7 11 28 28 14 14 2 11 11 11 24 24 24 24 5 8 25 13 20 17 5 9 0 11 0 11 24 11 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p32: 17903 0.096698s
13 0 13 0 0 15 3 0 15 7 0 14 0 0 14 2 0 15 0 0 14 0 0 0 14 8 0 0 3 0 
8 11 8 2 20 5 2 24 14 17 5 8 8 8 2 14 14 17 5 11 2 0 9 2 9 8 2 24 5 9 5 25 6 25 20 20 24 15 0 14 0 14 15 28 24 14 0 20 11 8 5 14 14 5 6 20 17 0 11 14 0 5 20 11 11 11 9 0 24 9 20 6 11 17 24 8 9 20 14 24 20 0 20 17 2 17 2 17 20 5 2 24 17 11 17 5 2 17 25 8 8 17 17 25 2 25 17 11 28 28 14 14 2 11 11 0 24 24 24 24 5 8 25 20 8 11 5 9 0 11 0 0 24 24 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p33: 12990 0.0991s
12 0 8 0 0 15 0 0 13 0 0 15 0 6 16 2 0 18 0 0 16 0 0 0 19 10 0 0 0 0 
20 11 20 14 13 5 2 24 14 17 24 8 8 20 17 14 14 17 5 11 2 17 5 17 5 8 2 24 5 24 5 25 13 25 20 20 24 15 11 14 0 14 15 13 24 14 11 20 11 8 25 14 14 5 13 20 17 0 0 14 0 5 20 11 11 11 24 0 5 24 13 20 11 17 24 8 24 20 14 24 20 0 20 17 17 17 17 0 20 5 2 24 17 11 17 24 2 8 25 8 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 0 24 24 24 24 5 8 25 13 20 11 5 24 0 11 0 0 24 25 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 
p34: 11535 0.093005s
11 0 9 0 0 15 0 0 13 0 0 17 0 6 16 2 0 17 0 0 16 0 0 0 19 9 0 0 0 0 
20 11 20 14 13 5 2 24 14 17 24

相關推薦

使用模擬退火與禁忌搜尋解決Capacitated Facility Location Problem

Capacitated Facility Location Problem 問題描述 Suppose there are n facilities and m customers. We wish to choose: (1) which of the n facilities to

Capacitated Facility Location Problem

文章目錄 [Problem Description](https://en.wikipedia.org/wiki/Facility_location_problem) [遺傳演算法（genetic algorithm）](https://en.wiki

Capacitated Facility Location Problem貪心演算法實現

1. 問題描述 給定n個工廠和m個顧客，開工廠需要一定的費用，一個工廠有一定的容量限制，每個顧客也有一定的需求，而每個顧客要選取某個工廠也需要一定的分配費用，現在要求找出一個分配方案，把顧客分配給不同的工廠，然後在可以滿足所有顧客需求的前提下讓所有的花費（開工廠的花費和分配的花費）最小。 問

模擬退火演算法理論+Python解決函式極值+C++實現解決TSP問題

簡述 演算法設計課這周的作業： 趕緊寫了先，不然搞不完了。 文章目錄 簡述 演算法理論部分 變數簡單分析 從狀態轉移概率到狀態概率 推導 理解當溫度收斂到接近0的時候，收斂到結果 理論

[Luogu3959] [NOIP2017] 寶藏 Treasure [狀態壓縮+子集+dp/搜尋+剪枝/模擬退火]

[ L i n

【模擬退火】解決【TSP】問題

TSP問題求解     n個城市之間有一定距離,現在讓選擇一個城市出發，然後到達所有的城市,最後回到原點每個城市只到達一次,求出一條路徑並且求出最短的距離    TSP問題是一個NP問題，但是可以求近似解，通過模擬退火演算法實現， 源：https:

模擬退火演算法與C語言實現（TSP問題）

1簡介： 模擬退火來自冶金學的專有名詞退火。退火是將材料加熱後再經特定速率冷卻，目的是增大晶粒的體積，並且減少晶格中的缺陷。材料中的原子原來會停留在使內能有區域性最小值的位置，加熱使能量變大，原子會離開原來位置，而隨機在其他位置中移動。退火冷卻時速度較慢，使得原子有較多可能

模擬退火演算法解決TSP（python實現 110+行程式碼）【gif生成】

簡述 程式碼我是基於我之前寫的兩篇，一篇是遺傳演算法TSP的Python實現，一篇是模擬退火演算法的解決TSP的C++實現。 模擬退火演算法理論+Python解決函式極值+C++實現解決TSP問題 遺傳演算法解決TSP問題 Python實現【160行以內程式碼】

2018華為軟挑--模擬退火+FF解決裝箱問題【C++程式碼】

演算法簡介：        裝箱問題是一個NP完全問題，求解全域性最優解有很多種方法：遺傳演算法、禁忌搜尋演算法、蟻群演算法、模擬退火演算法等等，本次使用模擬退火，它的優點是在引數合適的情況下基本上可以100%得到全域性最優解，缺點是相較於其他演算法，其穩定速度較慢。    

模擬退火(Simulated Annealing, SA)演算法簡介與MATLAB實現

目錄 演算法步驟 演算法特點 模擬退火演算法概述 模擬退火演算法(Simulated Annealing，簡稱SA)的思想最早是由Metropolis等提出的。其出發點是基於物理中固體物質的退火過程與一般的組合優化問題之間的相似性。模擬退火法是一種

模式識別九--模擬退火演算法的設計與實現

本文轉自：http://www.kancloud.cn/digest/prandmethod/102851         本節的目的是記錄以下學習和掌握模擬退火(Simulated Annealing，簡稱SA演算法)過程。模擬退火演算法是一種通用概率演算法，用來在一個大的搜尋空間內尋找命題的最優解。這裡

禁忌搜尋演算法解決圖著色問題

禁忌搜尋演算法原理及實現 圖著色問題 對給定圖G=(V,E)的每個頂點著色,要求每個相鄰的頂點不同色，求最小需要的顏色數。 禁忌搜尋演算法 禁忌搜尋演算法，是一種區域性搜尋演算法，通過採用禁忌表，逃脫了區域性最優解，得到全域性最優解。禁忌搜尋

集體智慧程式設計——優化搜尋演算法：爬山法，模擬退火演算法，遺傳演算法-Python實現

在優化問題中，有兩個關鍵點 代價函式：確定問題的形式和規模之後，根據不同的問題，選擇要優化的目標。如本文涉及的兩個問題中，一個優化目標是使得航班選擇最優，共計12個航班，要使得總的票價最少且每個人的等待時間之和最小。第二個問題是學生選擇宿舍的問題，每個學生可

模擬退火演算法解決TSP問題+Python實現

網上看見的比喻： 爬山演算法：兔子朝著比現在高的地方跳去。它找到了不遠處的最高山峰。但是這座山不一定是珠穆朗瑪峰。這就是爬山演算法，它不能保證區域性最優值就是全域性最優值。 模擬退火：兔子喝醉了。它隨機地跳了很長時間。這期間，它可能走向高處，也可能踏入平地。但是，它漸漸清

用模擬退火演算法解決0-1揹包問題

clear clc a = 0.95 k = [5;10;13;4;3;11;13;10;8;16;7;4]; k = -k; % 模擬退火演算法是求解最小值，故取負數 d = [2;5;18;3;2;5;10;4;11;7;14;6]; restriction = 46;

模擬退火 (poj 2420, poj 2069)

mes 全局 poj include using div tracking out amp 模擬退火基本知識 其偽代碼例如以下： Let s = s0 For k = 0 through k_max (exclusive): T := temperature(k /

Atitit.angular.js 使用最佳實踐 原理與常見問題解決與列表顯示案例 attilax總結

依賴 實現 http dsi 概念 模板 style ctr net Atitit.angular.js 使用最佳實踐 原理與常見問題解決與列表顯示案例 attilax總結 1. 本文範圍 1 2. Angular的長處 1 2.1. 雙向數據綁定 1 2.2. d

爬山算法和模擬退火算法簡介

出了 搜索算法 旅行 www cnblogs 所有 發的 圖1 貪心 轉自：http://www.cnblogs.com/chaosimple/archive/2013/06/10/3130664.html 一. 爬山算法 ( Hill Climbing )

【BZOJ3680】吊打XXX 模擬退火

esc 題解 ret 爬山 能量 truct style namespace ngx 【BZOJ3680】吊打XXX Description gty又虐了一場比賽，被虐的蒟蒻們決定吊打gty。gty見大勢不好機智的分出了n個分身，但還是被人多勢眾的蒟蒻抓住了。蒟蒻們

【BZOJ1844/2210】Pku1379 Run Away 模擬退火

tro pku str sqrt mes tchar 矩形 ron run 【BZOJ1844/2210】Pku1379 Run Away 題意：矩形區域中有一堆點，求矩形中一個位置使得它到所有點的距離的最小值最大。 題解：模擬退火的裸題，再調調調調調參就行了~