算法Project（变种背包问题）-白红宇

算法Project（变种背包问题）

阅读量：2395 次

发布时间：2019-05-10

本文共 61600 字，大约阅读时间需要 205 分钟。

问题描述：

假设有n个商店和m位顾客，我们希望计算得到：

（1）开放那些商店

（2）安排哪位顾客去哪位商店

来使得开销最小。

其中：如果商店有安排到至少一位顾客，则商店需要开放营业，而这需要开销opening cost（每个商店的opening cost不同），另外安排某位顾客去某位商店的这一过程也需要开销assigning cost，且因商店的不同和顾客的不同而变化。

也即：总开销 = 所有商店的opening cost + 所有顾客的assigning cost

除此之外，还需要考虑到商店的容量，每位顾客会占据一定的空间(demand of customer)，安排到一个商店的顾客不能超过商店的容量。

输入格式：

共71个输入，格式为：

解法一：

使用局部搜索的思想（爬山法）：

（1）随机生成一个合法的解

关于这个随机，需要考虑到商店是否开放的问题。当商店开放的开销非常大时，商店开放的选择将对最终的结果产生较大的影响。我采用的方式是：随机选择一个商店，顺序安排顾客，容量满了之后再随机选择另一个商店，重复这个过程。(如果这样的策略导致最终无法安排完所有的顾客，则重新再生成一个合法初始解)。

（2）对一个初始解进行n次迭代（如果迭代一段时间仍然得不到更优的解，则认为已经得到了局部最优解，停止迭代）：

找到当前解的邻域，在邻域中找出开销最小的解，如果这个解比原来的解要好，则将它作为新的解，重复这个过程。

（3) 为了避免一开始商店不完全开放产生的不好的影响，每次随机生成多个合法的初始解，重复以上过程。并且保证第一个初始解开放了所有的商店。

其中找邻域的算法为：

随机选择一个顾客，再随机选择一个商店，将这个顾客分配到这个商店。（保证这个商店不是这个顾客原来分配的商店，且分配过去之后不会超过商店的容量，如果不满足就重新执行）并在一次迭代中同时找到十个这样的随机更改（都是以当前的解为起点），作为邻域进行判断。

这个思想很简单，但是存在问题：

1. 可能最终得到的解是局部最优，而不是全局最优（可以理解为到达了一个小山峰，通过邻域无法在找到更好的解，但实际上有更高的山峰）。

2. 可能遇到平顶，邻域中的解相同，无法确定要搜索的最佳方向。

代码：

定义数据结构

#ifndef DEFINE_HPP#define DEFINE_HPP#include 
   
    using namespace std;struct data {  int facility_num;  // 商店数量  int customer_num;  // 顾客数量  vector
    
      facility_capacity;  // 商店容量  vector
     
       facility_opening_cost; // 商店开放开销  vector
      
        customer_demand;    // 顾客占的空间  vector
       
        
         > assignment_cost; // [facility][customer] 安排顾客的开销 data(int facility_num, int customer_num, vector
         
          
           > init_assignment_cost) { this->facility_num = facility_num; this->customer_num = customer_num; this->assignment_cost = init_assignment_cost; } vector
           
             assignment; // 最终的安排方式 vector
            
              facility_used; // 最终各个商店消耗的容量};#endif

核心代码：

int get_random(int range) {  return rand()%range;}// 根据顾客的安排计算总开销int evaluation(vector
   
    & assignment, data& m_data) {  int result = 0; // 要记得初始化  vector
    
      facility_status(m_data.facility_num, 0);  for(int i = 0; i < assignment.size(); i++) {    facility_status[assignment[i]] = 1;  }  for(int i = 0; i < facility_status.size(); i++) {    if(facility_status[i] != 0)      result += m_data.facility_opening_cost[i];  }  for(int i = 0; i < assignment.size(); i++) {    result += m_data.assignment_cost[assignment[i]][i];  }  return result;}// 随机得到一个初始的合法解bool init_solution(vector
     
      & assignment, vector
      
       & facility_used, data& m_data, vector
       
        & m_random) {  // 随机选择一个商店，顺序安排顾客，容量满了之后再随机选择另一个商店，重复这个过程  // 初始解中未开放的商店意味着永远关闭，后续不会安排顾客过去  int p = get_random(m_data.facility_num);  m_random.push_back(p);  for(int i = 0; i < m_data.customer_num; i++) {    while(true) {      int facility = p;      if(m_data.facility_capacity[facility]-facility_used[facility] >= m_data.customer_demand[i]) {        assignment[i] = facility;        facility_used[facility] += m_data.customer_demand[i];        break;      } else {        while(true) {          p = get_random(m_data.facility_num);          if(find(m_random.begin(), m_random.end(), p) == m_random.end()) {            m_random.push_back(p);            break;          }          if(m_random.size() == m_data.facility_num)            return false; // 当前的策略导致无法安排完所有顾客，抛弃此次初始解        }      }    }  }  return true;}bool can_open(int facility, vector
        
         & m_random) { // 初始时开放的商店才能继续使用，其余的商店不再开放 if(find(m_random.begin(), m_random.end(), facility) != m_random.end()) return true; else return false;}// 爬山法int local_search(data& m_data) { int final_result = 100000; int final_times; int final_last_update; for(int x = 0; x < 10; x++) { int result = 0; vector
         
           facility_status(m_data.facility_num, 0); vector
          
            assignment(m_data.customer_num, 0); vector
           
             facility_used(m_data.facility_num, 0); vector
            
              m_random; // 获得一个初始解 // 如果求解异常，跳过这次执行 if(!init_solution(assignment, facility_used, m_data, m_random)) { x--; continue; } result = evaluation(assignment, m_data); int last_update = -1; int times = 500; for(int i = 0; i < times; i++) { int cur = 0; int customer1, customer2; int facility1, facility2; int type; // 确定邻域中的最优解是用哪种策略找到的 for(int j = 0; j < 10; j++) { // int choice = get_random(100); // 修改一个顾客的安排得到一个邻域，同时找10个邻域，从中选出最好的 int tmp_customer, tmp_facility; while(true) { // 得到一个可执行的调整（不超过最大容量） tmp_customer = get_random(m_data.customer_num); tmp_facility = get_random(m_data.facility_num); // 不选取关闭的商店 // 第一个初始解开放所有的商店 if(facility_used[tmp_facility] == 0 && !can_open(tmp_facility, m_random) && x != 0) continue; if(m_data.facility_capacity[tmp_facility]-facility_used[tmp_facility] >= m_data.customer_demand[tmp_customer] && tmp_facility != assignment[tmp_customer]) // 要避开调度到同一个商店的情况(相当于没调动，而且会出bug) break; } int tmp_result = m_data.assignment_cost[tmp_facility][tmp_customer]-m_data.assignment_cost[assignment[tmp_customer]][tmp_customer]; if(facility_used[tmp_facility] == 0) { // 变动需要开启新的商店 tmp_result += m_data.facility_opening_cost[tmp_facility]; } if(facility_used[assignment[tmp_customer]] == m_data.customer_demand[tmp_customer]) { // 变动会关闭旧的商店 tmp_result -= m_data.facility_opening_cost[assignment[tmp_customer]]; } // 求出10个邻域中的最优解 if(tmp_result < cur) { cur = tmp_result; customer1 = tmp_customer; facility1 = tmp_facility; } } // 如果邻域中有更优的解，将这个解作为新解 if(cur < 0) { facility_used[assignment[customer1]] -= m_data.customer_demand[customer1]; assignment[customer1] = facility1; facility_used[facility1] += m_data.customer_demand[customer1]; result += cur; last_update = i; } if(i == times-1) { if(i-last_update < 500) // 如果迭代一段时间仍然得不到更优的解，则认为已经得到了局部最优解，停止迭代 times += 500; } } if(result < final_result) { final_result = result; final_times = times; final_last_update = last_update; m_data.assignment = assignment; m_data.facility_used = facility_used; } } cout << "HC final cost: " << final_result << " total times: " << final_times << " last update: " << final_last_update << " check: " << evaluation(m_data.assignment, m_data) << endl; return final_result;}

运行结果：

Result Time(s)p1  9501  0.054185p2  8389  0.045538p3  10238 0.050825p4  12130 0.051824p5  9439  0.017958p6  7962  0.017928p7  10032 0.018934p8  11857 0.020096p9  9115  0.034581p10 8123  0.033655p11 9677  0.034299p12 10914 0.036240p13 9661  0.135806p14 8191  0.166471p15 9945  0.242802p16 13097 0.228588p17 10134 0.152015p18 8015  0.128695p19 10536 0.116270p20 12680 0.110996p21 10074 0.077413p22 8881  0.082733p23 9860  0.077299p24 12351 0.091676p25 13234 0.209495p26 12969 0.241355p27 15095 0.263315p28 18475 0.254944p29 16332 0.218115p30 14259 0.198850p31 19712 0.231230p32 20131 0.219975p33 14405 0.334967p34 13089 0.306140p35 16172 0.342267p36 22645 0.322351p37 14907 0.173000p38 12751 0.176526p39 15464 0.189599p40 16619 0.181526p41 7388  0.052925p42 6544  0.171739p43 6032  0.210609p44 8467  0.047902p45 8258  0.100014p46 6932  0.262841p47 8181  0.082714p48 7223  0.134204p49 6815  0.197290p50 10577 0.053424p51 9268  0.131023p52 12332 0.045207p53 13069 0.088564p54 10441 0.041415p55 11832 0.149901p56 25263 0.124397p57 29976 0.119811p58 42407 0.131893p59 32655 0.121115p60 22848 0.172864p61 30155 0.166056p62 37719 0.165686p63 30824 0.170274p64 25597 0.204970p65 33459 0.242885p66 40494 0.222066p67 32434 0.165219p68 25102 0.176221p69 32597 0.176730p70 41367 0.204037p71 35552 0.191322

具体信息：

（依次为：总开销，商店是否开放，各个顾客的安排）

[p1]95011 1 1 1 1 0 1 1 1 0 8 2 3 6 3 0 2 4 4 1 4 0 3 2 8 3 4 0 6 7 3 8 6 4 2 6 1 6 0 1 2 6 0 0 4 4 4 3 0 4 1 8 1 6 7 0 4 0 4 3 [p2]83891 1 0 1 1 1 1 1 1 1 7 8 1 6 3 8 4 4 4 1 9 8 3 4 8 3 9 0 9 7 3 4 6 4 5 5 1 5 0 5 9 6 0 3 9 4 4 3 0 4 1 8 1 5 7 0 9 0 4 0 [p3]102381 1 1 1 1 0 1 1 0 0 0 2 1 6 3 0 2 4 2 1 4 0 3 2 7 3 4 2 6 7 3 4 6 4 2 6 1 6 0 1 2 6 0 3 4 4 4 3 0 4 1 0 3 6 7 3 4 0 4 0 [p4]121301 1 0 1 1 1 0 1 0 1 7 4 5 5 3 0 5 4 4 1 9 0 3 7 0 3 4 0 9 7 1 4 9 4 5 5 1 5 0 5 9 5 0 3 9 4 4 3 0 4 1 3 3 5 7 0 4 3 4 0 [p5]94391 1 1 1 1 0 1 1 1 1 8 0 1 6 3 8 2 4 4 1 9 8 3 2 0 3 2 0 9 7 3 8 6 4 2 6 1 1 0 1 2 6 0 3 9 4 7 3 0 4 1 8 1 6 7 0 4 3 4 8 [p6]79621 1 1 1 1 0 1 1 1 1 8 8 1 6 3 8 2 4 4 1 9 8 3 2 8 3 4 0 9 7 3 4 6 7 2 6 1 1 8 1 2 6 0 3 9 4 7 3 0 4 1 8 1 6 7 0 4 0 4 0 [p7]100321 1 1 1 1 1 1 1 1 0 8 8 1 6 3 8 2 4 4 1 4 8 0 2 8 0 4 0 6 7 3 8 6 7 2 5 1 5 0 5 6 6 0 3 2 4 4 3 0 4 1 8 1 5 7 0 2 3 4 3 [p8]118571 1 1 1 1 1 1 1 1 0 8 8 1 6 3 8 2 4 4 1 4 8 3 2 8 3 4 0 6 7 3 8 6 7 2 5 1 5 0 5 2 6 0 3 2 4 7 3 0 4 1 8 1 5 7 0 4 0 4 1 [p9]91150 1 1 1 1 0 1 0 1 0 8 8 1 6 3 8 2 4 4 1 4 8 3 2 8 3 4 8 6 4 3 4 6 2 2 6 1 1 8 1 2 6 3 3 2 4 4 3 8 4 1 8 1 6 4 8 4 3 2 3 [p10]81231 1 1 1 1 1 0 1 1 0 8 8 1 5 3 8 2 4 4 1 4 8 3 2 8 3 4 0 4 7 3 8 5 4 2 5 1 5 0 5 2 5 0 3 4 4 7 3 0 4 1 8 1 5 7 0 4 0 4 0 [p11]96771 0 1 1 1 0 1 0 1 1 8 8 3 6 3 8 2 4 4 3 9 8 3 2 8 3 4 0 9 4 3 8 6 9 2 6 3 6 0 2 2 6 0 3 9 4 4 3 0 4 3 8 3 6 4 0 4 0 4 0 [p12]109141 0 0 1 1 1 0 0 1 1 8 8 5 5 3 8 3 4 4 5 9 8 3 4 8 3 4 0 9 4 3 8 9 9 5 5 3 5 0 5 9 5 0 3 9 4 9 3 0 4 3 8 3 5 4 0 4 0 4 0 [p13]96610 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 16 12 10 10 12 12 1 13 14 19 15 19 19 6 13 12 15 10 19 9 12 15 15 19 6 1 16 1 1 1 13 15 13 16 12 10 9 19 19 13 6 16 5 16 9 5 14 10 19 9 [p14]81911 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 16 1 10 10 1 18 17 18 14 17 15 4 1 6 13 11 15 10 4 6 14 15 15 13 6 17 16 17 1 17 13 15 13 16 11 10 11 1 1 13 6 0 0 0 8 13 14 10 4 8 [p15]99450 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 7 14 10 10 19 13 17 13 14 17 7 19 19 6 13 11 5 10 19 6 14 5 5 19 6 17 7 17 17 17 13 7 13 7 11 10 11 19 19 13 6 7 5 7 11 5 14 10 19 6 [p16]130970 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 10 11 10 10 1 15 1 7 7 4 15 4 1 6 2 11 7 10 4 6 1 7 7 2 6 4 7 11 1 4 2 15 2 15 1 10 11 2 4 2 6 15 7 15 11 15 10 6 2 6 [p17]101340 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 16 12 16 16 1 18 17 18 14 17 15 19 1 9 18 12 15 14 17 9 12 15 15 19 9 17 16 17 1 17 18 15 18 15 1 14 8 19 19 18 9 16 16 14 8 15 14 14 19 9 [p18]80151 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 16 1 10 10 1 18 17 18 14 17 15 19 1 6 18 3 15 10 17 6 14 15 15 19 6 17 16 17 1 17 18 15 18 16 3 10 3 19 19 18 6 0 5 0 3 5 14 10 19 6 [p19]105360 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 16 1 7 7 1 18 17 13 7 17 15 4 1 9 13 8 15 7 4 9 18 15 15 13 9 17 16 17 1 17 13 7 13 16 1 7 8 1 1 13 9 16 15 16 8 13 7 9 4 9 [p20]126800 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 16 12 15 7 19 12 17 15 12 17 15 19 12 9 19 3 7 7 17 9 12 15 15 19 9 3 16 17 3 17 19 7 19 16 3 7 3 12 17 12 9 7 16 16 3 15 12 9 19 9 [p21]100740 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 16 1 16 6 1 12 17 13 12 17 16 1 1 6 13 12 16 6 17 9 12 12 12 13 6 17 16 17 1 17 13 16 13 16 1 6 17 1 1 13 6 13 12 12 9 13 12 6 1 9 [p22]88810 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 5 12 6 6 12 12 17 13 12 17 15 17 12 6 13 12 15 6 17 9 12 15 15 13 6 17 5 17 12 17 13 15 13 15 12 6 17 12 13 13 6 5 5 15 9 5 12 6 13 9 [p23]98600 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 16 1 10 10 1 18 3 18 3 3 15 1 1 6 18 3 15 10 1 6 18 15 15 18 6 3 16 1 1 3 18 15 18 16 3 10 3 1 1 18 6 16 15 16 6 15 15 10 18 6 [p24]123511 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 12 10 10 12 12 11 5 12 11 5 1 1 10 5 11 5 10 11 9 12 5 5 1 9 1 0 1 1 11 12 10 12 0 11 10 11 1 1 5 10 0 5 0 11 0 12 10 1 9 [p25]132341 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 20 11 20 2 20 5 2 24 14 17 24 20 28 20 2 14 14 17 5 11 14 0 5 2 5 20 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 28 24 14 7 20 11 28 5 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 24 0 24 24 20 20 11 17 24 20 24 20 14 24 20 7 20 0 2 17 17 7 20 5 17 24 17 11 17 24 2 14 21 20 28 7 17 25 14 25 7 11 14 28 14 14 2 11 11 21 24 24 24 24 5 28 25 20 20 0 5 24 0 25 0 11 24 5 28 14 7 5 20 0 0 28 20 14 20 25 25 5 2 5 [p26]129691 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 20 11 13 2 20 5 2 24 14 17 24 16 8 20 19 14 14 17 5 11 2 0 5 17 5 8 19 24 5 24 5 25 13 25 20 20 24 15 0 14 0 14 15 8 24 14 7 13 11 8 29 14 14 5 20 20 17 11 11 14 0 5 20 11 11 11 24 0 24 24 20 20 11 17 24 8 24 20 14 24 20 7 20 0 19 0 2 7 20 5 14 24 17 11 17 5 2 2 25 16 8 17 14 25 2 29 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 16 0 5 24 0 29 0 11 24 5 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 [p27]150951 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 20 11 13 2 20 5 2 9 14 17 24 8 8 20 19 14 14 17 5 11 2 0 5 19 5 8 19 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 28 24 14 0 13 11 8 5 14 14 5 13 20 17 11 0 14 0 5 20 11 11 11 9 0 9 24 20 20 11 0 24 8 24 20 14 24 20 0 13 0 19 17 17 0 20 5 2 24 17 11 17 5 2 19 25 20 8 17 14 25 2 25 17 11 14 28 14 14 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 9 0 25 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p28]184751 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 20 11 13 2 20 5 2 9 14 0 9 8 8 20 19 14 14 0 25 11 2 0 9 17 9 8 19 5 5 9 5 25 20 25 20 20 5 15 0 14 0 14 15 8 5 14 0 13 11 8 5 14 14 5 13 20 17 11 11 14 0 5 20 11 11 11 9 0 5 9 20 20 11 17 9 8 9 20 14 9 20 7 20 17 19 0 17 7 20 5 2 9 17 11 17 9 2 19 25 20 8 17 17 25 2 25 7 11 14 8 14 14 2 11 11 25 5 15 5 5 5 8 25 13 8 0 5 9 0 25 0 11 5 25 8 14 7 25 20 17 0 8 20 14 8 25 25 5 2 5 [p29]163320 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 20 11 20 2 20 5 2 9 14 17 24 8 8 20 19 14 14 11 5 11 2 7 5 17 24 8 19 24 5 9 5 25 20 25 20 20 24 24 7 14 17 14 24 8 24 14 4 13 11 8 29 14 14 5 13 20 17 11 11 14 17 5 8 11 17 11 24 17 5 9 20 13 11 7 24 8 9 20 14 24 20 7 20 17 19 17 17 4 20 5 2 9 17 11 7 9 2 2 21 13 8 17 17 25 2 29 17 11 14 8 14 14 2 11 11 21 5 24 24 24 5 8 25 13 8 7 5 9 7 29 17 11 24 5 8 8 17 5 13 17 11 8 13 14 8 25 25 11 2 5 [p30]142591 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 8 11 20 2 20 5 2 24 14 17 22 8 28 14 19 14 14 17 5 0 2 0 5 17 5 8 19 24 5 24 5 11 20 11 20 20 24 24 0 14 0 14 24 8 5 17 7 20 11 8 29 14 17 5 20 20 17 11 11 14 0 5 20 11 11 11 22 0 22 22 20 8 11 17 9 8 22 20 14 24 8 7 28 17 17 17 17 7 20 5 2 24 17 11 17 9 2 2 21 8 8 7 14 11 2 29 17 0 14 28 14 14 2 11 11 21 24 24 24 24 11 8 11 20 8 0 5 9 0 21 0 11 24 5 28 8 7 5 8 17 0 8 20 14 8 29 11 5 2 24 [p31]197121 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 16 11 16 2 16 5 19 9 2 17 24 16 16 8 17 17 14 0 5 11 2 0 5 17 5 8 19 24 5 24 5 25 16 25 8 14 5 24 0 14 0 14 24 16 24 14 7 8 11 8 5 2 17 11 8 2 2 11 11 14 0 5 14 11 11 11 9 0 9 9 8 8 11 0 24 2 24 14 2 9 8 7 8 0 19 0 17 7 8 25 2 9 7 11 17 9 14 19 21 16 16 17 17 25 2 25 17 11 14 14 17 14 2 11 11 25 24 24 24 24 5 8 25 2 16 0 5 24 0 21 0 11 24 5 16 2 17 5 8 0 0 8 14 17 14 25 25 5 17 11 [p32]201311 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 20 11 13 2 20 5 2 9 28 17 22 8 8 20 19 8 17 0 5 11 2 0 5 19 5 8 19 24 24 24 5 25 20 25 20 13 24 24 0 2 0 8 24 28 24 17 7 13 11 8 5 28 17 5 13 20 2 11 11 17 0 5 8 11 11 11 22 0 22 22 13 20 11 0 24 8 9 20 2 24 20 7 20 17 19 0 17 7 20 25 2 9 17 11 17 9 2 2 25 20 8 17 17 25 2 25 17 11 28 28 17 2 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 9 0 25 0 11 24 5 8 8 7 5 20 17 0 8 20 17 8 25 25 5 2 5 [p33]144051 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 20 11 20 2 20 5 2 24 14 17 24 16 14 20 19 14 14 17 5 11 2 0 5 17 5 20 19 24 5 24 5 25 13 25 20 20 24 24 0 14 0 14 24 16 24 14 0 13 27 14 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 20 5 20 14 24 13 7 13 17 19 17 17 7 20 5 2 24 17 11 17 24 2 2 25 16 16 17 17 25 2 25 17 11 14 14 14 14 2 11 11 27 24 24 24 24 5 16 25 13 16 0 5 24 0 25 0 11 5 5 16 14 7 5 20 17 0 20 20 14 14 25 25 5 2 5 [p34]130891 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 20 11 13 2 20 5 2 24 14 17 24 16 8 20 19 14 14 17 5 11 2 0 5 17 5 8 19 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 13 27 8 29 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 9 0 24 24 20 20 11 17 24 8 9 20 14 24 20 7 13 17 17 17 17 7 20 5 2 24 17 11 17 24 2 19 25 16 8 17 17 25 2 29 17 11 14 8 14 14 2 11 11 27 24 24 24 5 5 8 25 13 16 0 5 24 0 29 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p35]161721 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 20 11 20 2 20 11 2 24 14 17 29 20 28 13 19 14 14 17 25 11 2 0 24 17 24 20 19 24 25 24 29 25 20 25 20 20 24 25 0 14 0 14 24 28 24 14 0 13 11 28 29 14 14 11 20 20 17 11 0 14 0 24 20 11 11 11 29 0 24 24 20 20 11 17 24 28 29 20 14 24 20 7 20 17 17 17 17 7 20 29 2 24 17 11 17 24 2 19 25 13 28 17 17 25 2 29 17 11 14 28 14 14 2 11 11 25 24 24 24 24 11 28 25 13 20 0 25 29 0 25 0 11 24 29 28 14 17 25 20 17 0 28 13 14 14 25 25 11 2 11 [p36]226451 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 6 11 16 14 16 5 19 24 14 17 24 16 14 14 19 14 17 17 5 11 19 0 5 17 5 17 19 24 5 24 5 25 6 25 17 14 5 24 0 14 0 0 24 16 24 0 7 14 27 17 5 19 14 5 6 17 17 11 11 14 0 5 17 11 11 11 24 0 24 24 16 6 11 0 24 19 24 14 14 24 6 7 14 0 19 17 17 7 14 5 14 24 17 11 7 5 17 19 25 16 16 17 17 25 19 25 7 11 14 14 17 19 0 11 11 27 24 24 24 24 5 16 25 14 16 0 5 5 0 25 0 11 24 5 16 17 7 5 14 0 0 14 17 17 0 25 25 5 0 5 [p37]149071 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 8 11 6 14 8 5 19 24 14 17 24 8 8 8 19 14 14 17 5 11 14 0 5 17 5 8 19 24 5 24 5 25 6 25 8 8 24 15 0 14 0 14 15 28 24 14 7 8 25 8 5 14 14 5 6 8 17 11 0 14 0 5 8 11 11 11 24 0 24 24 8 6 11 17 24 8 24 8 14 24 8 7 8 17 17 17 17 7 8 5 17 24 17 11 17 24 14 19 25 8 8 17 17 25 19 25 17 11 14 28 14 14 17 11 11 25 24 24 24 24 5 8 25 8 8 0 5 24 0 25 0 11 24 5 8 14 17 5 8 17 0 8 8 14 8 25 25 5 17 5 [p38]127511 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 20 11 13 2 20 5 2 24 14 17 24 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 19 24 5 24 5 25 6 25 20 20 24 24 0 14 0 14 24 28 24 14 0 13 11 8 5 14 14 5 13 20 17 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3 4 6 9 5 5 0 5 5 6 0 4 6 6 4 3 3 1 3 4 4 9 1 3 8 5 5 4 3 4 9 3 5 9 9 5 5 6 3 4 3 6 [p53]130690 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 3 3 3 3 3 3 3 3 9 9 15 15 15 3 3 9 3 5 16 16 16 16 16 16 16 16 16 5 16 7 15 3 9 4 4 7 15 16 9 4 4 3 7 16 15 15 15 3 4 9 16 7 5 16 15 7 3 3 15 3 7 5 15 16 7 3 15 15 3 3 7 15 4 15 15 9 15 15 15 7 7 4 16 [p54]104411 0 1 1 1 1 1 0 1 0 2 2 2 2 2 4 2 2 2 2 4 2 2 2 2 4 2 2 2 3 3 2 2 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 6 6 8 8 6 8 3 8 8 8 8 8 3 6 6 6 6 6 6 6 6 6 5 5 6 5 5 5 6 6 4 0 6 0 0 2 0 0 4 0 0 0 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 [p55]118320 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 17 17 16 17 16 17 16 16 18 16 18 17 17 18 17 18 18 18 18 16 16 16 14 14 16 14 16 16 14 16 14 7 16 16 14 7 7 16 7 7 7 18 14 14 7 7 7 7 16 7 14 7 7 7 7 7 7 7 18 7 7 7 18 14 18 7 7 7 14 13 13 13 13 13 17 13 13 13 13 13 13 13 13 17 18 13 18 17 18 18 18 18 18 18 18 17 18 18 18 18 [p56]252631 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 18 19 21 27 21 19 15 27 22 0 29 6 13 13 19 18 3 20 22 0 18 21 5 24 10 18 27 26 29 21 6 26 26 21 27 6 20 8 27 15 18 9 6 26 8 19 13 21 6 20 24 24 21 15 8 19 25 9 18 25 29 24 7 8 13 25 5 10 0 25 18 25 19 9 5 13 20 5 8 24 10 0 9 7 29 13 6 0 27 7 27 19 25 25 0 3 27 19 0 19 19 15 25 18 29 24 29 24 22 3 19 29 18 6 25 8 27 7 0 8 26 18 0 19 26 15 21 6 26 10 27 24 7 20 5 9 3 3 0 10 6 22 6 25 25 5 24 15 27 7 27 0 10 0 8 25 5 15 3 13 13 27 10 21 5 24 5 29 3 21 5 20 6 10 26 5 24 10 29 10 5 21 24 19 25 8 6 10 0 21 21 21 6 29 7 6 7 15 20 6 [p57]299760 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 27 19 21 27 21 25 2 27 22 17 29 28 13 13 28 7 10 20 22 27 27 21 5 24 10 27 24 14 29 2 26 26 26 21 27 28 20 20 27 21 7 20 19 26 13 26 13 21 19 14 24 24 2 24 20 28 25 26 22 7 29 2 7 20 13 25 5 14 19 25 7 19 19 20 5 13 20 5 10 24 10 17 26 7 29 13 19 5 27 25 17 19 25 25 2 20 28 28 17 28 17 21 25 7 29 24 29 24 22 13 19 29 22 25 19 20 28 7 17 20 26 7 17 14 26 21 2 25 26 17 28 24 25 20 5 26 13 13 28 10 28 22 28 25 7 5 21 21 27 7 24 17 10 17 20 27 2 21 13 13 13 27 10 24 5 27 5 29 13 21 5 20 19 14 26 2 24 10 29 10 5 2 2 19 28 20 28 10 17 21 2 21 19 29 7 19 7 21 10 19 [p58]424070 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 18 19 21 22 21 6 15 18 22 17 4 17 8 3 19 18 3 20 22 17 18 21 2 2 20 18 22 19 4 2 19 19 26 21 18 6 20 8 21 15 18 8 6 4 8 26 3 21 19 14 2 22 15 15 8 19 18 8 22 7 4 2 7 8 3 11 5 14 19 7 18 6 6 8 20 5 20 5 8 22 20 17 26 7 4 3 6 5 22 7 17 19 7 11 2 3 11 6 17 17 17 15 11 7 4 17 4 22 22 3 19 4 22 6 11 8 11 7 17 20 26 11 14 19 26 21 2 11 26 17 11 21 7 20 5 8 3 3 11 14 11 18 6 11 11 5 21 15 18 11 22 17 5 17 8 11 2 15 3 3 3 17 14 21 2 18 5 4 3 21 5 8 19 14 26 2 2 20 4 20 2 21 5 19 6 8 6 5 2 21 2 21 6 4 7 4 7 15 20 19 [p59]326551 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 18 6 21 27 2 6 2 27 18 27 4 28 23 3 28 18 3 20 27 0 18 21 23 24 20 18 27 28 4 2 6 26 4 21 27 6 8 8 24 21 18 9 6 4 8 26 3 21 6 20 24 24 24 21 8 6 11 9 18 25 4 24 18 8 3 11 0 28 6 11 18 11 6 9 0 23 20 20 8 24 23 0 9 25 26 20 6 23 27 25 28 4 25 25 2 3 11 6 0 28 0 21 25 18 4 0 4 24 27 3 26 4 27 6 11 8 28 25 0 20 26 11 28 4 26 21 21 11 26 0 28 24 25 8 23 9 3 3 28 20 25 27 11 11 25 2 24 21 18 25 24 0 20 28 8 28 2 21 3 3 3 27 20 2 23 27 2 4 3 21 23 20 28 8 26 2 0 23 4 8 23 2 2 6 11 8 28 23 0 21 2 21 6 4 25 11 25 21 23 6 [p60]228480 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 18 6 21 27 2 12 21 27 22 17 4 17 13 13 6 18 3 13 22 27 18 16 23 27 23 18 27 17 29 2 6 4 4 16 27 6 8 8 16 16 18 8 6 4 8 4 13 21 6 17 27 16 2 16 8 6 11 8 18 11 29 2 18 8 13 11 23 17 6 12 18 12 6 8 23 23 8 23 8 16 23 17 8 11 29 13 6 2 27 18 17 6 11 11 2 3 11 6 17 17 17 21 12 18 4 2 4 27 22 3 6 4 27 12 12 8 11 11 17 8 8 11 17 6 4 16 2 11 4 17 11 21 11 8 23 8 3 3 17 17 12 22 11 11 11 2 16 21 27 11 27 17 23 17 8 11 2 16 3 13 13 27 23 2 23 27 23 4 3 21 23 8 17 17 4 2 27 23 29 23 2 21 2 6 12 8 11 23 17 21 2 21 6 4 18 12 18 21 23 6 [p61]301551 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 7 6 2 27 0 25 0 27 27 17 4 17 13 13 6 7 13 10 0 0 27 2 23 0 10 27 0 17 4 2 6 4 4 2 27 6 10 13 27 0 7 10 6 4 10 4 13 2 6 10 0 27 0 27 13 25 25 10 7 25 4 17 7 10 13 25 23 17 6 25 7 25 6 13 23 23 10 23 10 27 10 0 4 25 4 13 6 23 27 7 17 6 25 7 0 23 27 17 0 17 17 2 25 7 4 0 4 2 27 13 6 4 27 6 6 13 17 7 17 13 10 25 17 4 4 2 0 6 4 17 27 2 25 10 23 13 13 13 17 10 25 27 6 25 25 2 2 2 27 25 27 17 23 0 13 25 2 2 13 13 13 27 23 2 23 27 23 4 13 2 23 10 17 10 4 0 0 23 6 10 2 2 2 6 6 13 6 23 0 2 2 2 6 4 7 25 7 2 10 6 [p62]377190 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 18 19 2 22 2 12 15 11 22 18 26 19 3 3 19 18 3 9 22 18 18 15 23 2 23 18 22 19 26 2 19 26 26 15 18 12 9 9 22 15 18 9 12 26 9 19 3 15 19 19 2 22 15 15 9 12 18 9 18 11 26 22 18 9 3 11 2 19 19 12 18 12 19 9 3 23 23 23 9 22 23 2 9 11 26 23 19 23 22 11 11 19 11 11 15 3 11 12 2 11 11 15 12 18 26 22 26 22 22 3 19 26 18 12 12 9 11 11 19 9 26 11 19 26 26 15 2 12 26 23 11 2 11 23 3 9 3 3 11 23 12 22 11 11 12 2 22 15 22 12 22 23 23 2 3 11 2 15 3 3 3 18 23 15 23 18 2 26 3 15 3 9 19 19 26 2 2 23 26 23 2 15 2 19 12 9 11 23 11 2 2 2 12 19 18 12 18 15 3 19 [p63]308240 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 18 28 16 27 5 12 5 27 18 28 4 28 1 1 28 18 1 20 27 27 18 16 5 27 20 18 27 28 4 5 4 26 4 16 27 12 20 26 16 16 27 20 12 4 20 26 20 16 28 20 27 16 16 16 26 12 27 26 18 18 4 17 18 20 1 28 5 17 28 18 18 12 4 20 5 5 17 5 26 16 20 17 26 12 4 20 4 5 27 18 28 4 18 12 5 1 28 28 17 28 28 16 12 18 4 17 4 27 27 1 26 4 18 12 12 20 28 18 17 26 26 18 17 4 26 16 16 12 26 17 28 16 28 20 1 26 1 1 28 17 12 27 12 12 12 17 27 5 27 12 27 17 1 17 20 28 5 16 20 1 1 27 20 16 5 27 5 4 1 16 1 20 28 20 26 5 17 20 4 20 5 16 16 28 12 20 28 5 17 16 5 16 12 4 18 12 18 5 17 28 [p64]255970 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 24 6 21 24 21 12 15 28 21 24 4 28 23 3 28 28 3 8 24 24 28 21 5 24 23 28 24 28 4 21 6 4 4 21 28 6 8 8 24 15 28 9 6 4 8 4 3 21 6 9 24 24 24 21 8 6 12 9 24 12 4 24 12 8 3 12 5 28 28 6 28 12 6 9 23 23 8 23 8 24 23 5 9 12 4 23 6 5 24 12 28 6 12 12 5 3 28 6 5 28 28 15 12 12 4 24 4 24 21 3 6 4 28 12 12 8 28 12 23 8 9 12 28 6 9 21 21 12 4 28 28 24 12 8 23 9 3 3 28 23 12 24 12 12 12 5 24 15 21 12 24 23 23 24 8 28 5 15 3 3 3 28 23 21 5 24 5 4 3 21 5 8 28 23 4 21 24 23 4 23 5 21 21 6 12 8 12 23 24 21 21 21 6 4 28 6 12 15 23 6 [p65]334591 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 7 19 21 21 21 6 21 19 7 0 26 19 14 5 19 7 5 14 21 0 7 21 5 0 0 7 21 19 26 5 19 19 26 21 0 6 14 14 21 0 7 26 6 26 26 19 14 21 19 19 0 21 0 21 14 6 7 26 7 7 26 21 7 14 14 6 5 14 19 7 7 6 19 26 14 5 14 5 14 21 5 0 26 7 26 14 6 5 0 7 0 6 7 6 5 5 6 6 0 19 19 21 7 7 26 0 26 21 0 5 19 26 0 6 6 26 19 6 14 14 26 7 0 19 26 21 0 6 26 0 6 21 7 14 5 26 5 5 19 14 6 21 6 7 7 5 21 21 7 7 14 19 0 14 14 6 5 5 14 5 5 21 19 0 5 0 5 26 5 21 5 26 19 14 26 5 0 14 26 14 5 21 21 19 6 26 6 5 0 0 21 21 6 6 7 6 7 21 14 19 [p66]404940 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 22 6 21 22 21 6 21 6 22 21 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10 24 16 18 25 24 28 20 0 20 11 0 16 3 3 3 24 20 24 10 18 10 26 3 16 3 20 28 10 26 0 0 10 25 10 0 16 24 28 25 20 28 10 0 16 0 16 11 26 25 25 25 24 10 28 [p68]251021 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 7 19 16 22 5 28 15 28 22 28 19 28 20 1 28 7 1 20 22 0 7 16 5 0 20 7 22 19 4 5 19 19 4 16 28 19 20 8 16 16 7 9 19 9 8 4 3 16 19 20 0 16 0 16 8 19 25 9 22 25 4 5 7 8 3 25 5 19 0 25 7 25 4 9 5 5 20 5 8 16 20 0 9 7 4 20 19 5 22 7 28 19 25 25 0 3 28 19 0 28 0 15 7 7 4 0 4 16 22 3 19 4 22 19 25 8 7 7 0 8 9 25 0 9 9 16 5 25 19 0 28 16 25 20 1 9 3 3 28 20 28 22 28 7 25 5 16 15 22 25 0 28 5 0 8 25 5 15 3 3 1 0 20 16 5 0 5 4 3 15 1 20 19 20 4 0 0 20 4 20 5 15 0 19 25 8 25 5 28 16 5 16 19 4 7 19 7 15 20 19 [p69]325970 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 7 12 21 24 21 12 21 11 16 11 4 17 23 23 11 7 8 5 16 17 11 16 21 21 8 11 16 17 4 21 12 8 12 16 24 12 8 8 16 16 7 8 11 4 8 4 8 21 12 8 24 16 21 16 8 12 11 8 7 7 8 17 7 8 8 11 5 17 11 12 7 12 4 23 5 23 23 5 5 16 23 5 8 7 4 8 4 5 24 7 17 12 7 11 5 8 11 11 17 17 17 21 12 7 12 24 4 16 16 8 4 12 11 12 12 8 11 7 17 8 23 11 17 4 8 16 21 11 12 17 11 24 11 8 5 4 8 5 17 23 12 24 11 11 11 5 24 21 24 7 24 5 5 23 5 11 5 16 8 8 23 24 5 24 5 24 23 17 23 21 5 8 12 5 4 21 24 5 8 5 5 21 21 12 12 8 11 23 24 21 21 21 12 4 7 11 7 21 23 12 [p70]413670 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 18 28 21 18 21 25 21 28 18 17 29 28 5 13 28 18 13 13 16 17 7 16 5 21 13 18 18 17 29 21 28 9 29 16 18 28 9 9 16 16 18 9 25 29 9 29 13 21 28 9 21 16 21 16 9 17 7 9 18 7 9 5 7 9 9 25 13 28 28 7 7 25 25 9 5 13 9 5 9 16 13 17 9 25 29 5 29 5 18 7 7 28 7 25 5 5 28 25 17 28 9 21 7 18 25 21 29 16 16 13 28 29 18 25 25 13 18 7 28 9 9 18 5 29 9 16 21 28 29 17 28 21 7 9 5 13 13 5 17 17 25 16 17 25 25 5 16 21 7 25 21 17 5 17 13 18 5 16 13 13 13 18 5 21 5 7 5 9 5 21 5 13 28 5 9 21 21 13 29 9 5 21 16 28 25 9 7 13 17 21 21 21 29 29 7 7 7 21 17 9 [p71]355521 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 22 28 16 22 1 12 0 28 22 0 8 28 8 1 28 11 1 8 22 0 22 16 1 0 13 11 22 26 26 1 26 26 26 16 11 12 26 8 22 16 11 8 12 8 8 8 13 16 26 8 0 16 16 22 8 12 28 8 22 12 26 0 11 8 13 11 0 28 12 12 22 12 12 8 13 1 8 1 8 16 13 0 26 12 26 13 26 0 22 12 11 12 12 11 16 13 11 12 0 28 28 16 12 11 26 0 26 16 22 13 28 26 22 12 12 8 28 11 0 8 26 11 28 26 26 16 0 11 8 0 11 16 11 8 1 1 1 8 0 13 12 22 11 11 11 0 16 16 22 11 22 11 13 11 13 28 0 16 13 13 13 0 13 16 0 22 1 26 1 16 1 8 28 8 26 1 0 8 26 13 1 16 0 28 11 8 11 13 0 16 0 16 12 26 11 11 11 16 13 28

解法二：

使用模拟退火算法：

模拟退火法是克服爬山法缺点的有效方法，所谓退火是冶金专家为了达到某些特种晶体结构重复将金属加热或冷却的过程，该过程的控制参数为温度T。模拟退火法的基本思想是，在系统朝着能量减少的趋势这样一个变化过程中，偶尔允许系统跳到能量较高的状态，以避开局部极小点，最终稳定到全局极小点。

算法步骤如下：

（1）随机生成一个合法的解 P_k

（2）随机挑选一单元k，并给它一个随机的位移，求出系统因此而产生的能量变化 $\Delta E_K$ 。

（3）若 $\Delta E_K$ $\leq$ 0，该位移可采纳，而变化后的系统状态可作为下次变化的起点；若 $\Delta E_K$ >0，位移后的状态可采纳的概率为：

$P_k=e^{-\Delta E_k/T}$

式中T为温度，然后从(0,1)区间均匀分布的随机数中挑选一个数R，若 R<P_k ,则将变化后的状态作为下次的起点；否则，将变化前的状态作为下次的起点。

关于温度：

温度越高，系统越容易达到平衡状态，然而在平衡状态下处于能量较小状态的可能性也越小。温度越低，系统达到平衡状态的速度虽慢，但系统更容易达到能量较小的平衡状态。对于搜索问题中的爬山法，利用模拟退火法，不但可以使变化的随机选择大一些的步长，而且可以跨过局部极小点。通常的做法是：最初阶段倾向于取大步，后阶段倾向于取小步。

可以采用如下的方式设置温度：设置一个初始温度T，一个最终温度min_T, 一个降温系数f(如0.9)。每次迭代 T = T*f，使得温度逐渐降下来，当温度低于最终温度时，迭代停止。

算法的应用：

产生能量变化的方式：与上文爬山法一致。

$\Delta E_K$ 即新解的开销减去旧解的开销。

初始时温度较高， P_k 较大，容易接受差解，但随着温度的降低，接受差解将成为小概率事件，大部分时候都是朝着优解的方向搜索的，偶尔接受差解，使得能够跳出局部最小值。

代码：

int SA(data& m_data) {  int final_result = 100000;  int final_times;  int final_last_update;  for(int x = 0; x < 5; x++) {    int result = 0;    float T = 10000;        // 初温    float min_T = 0.00001;  // 末温    float factor = 0.9999;  // 降温系数    vector
   
     facility_status(m_data.facility_num, 0);    vector
    
      assignment(m_data.customer_num, 0);    vector
     
       facility_used(m_data.facility_num, 0);    vector
      
        m_random;    if(!init_solution(assignment, facility_used, m_data, m_random)) {      x--;      continue;    }     result = evaluation(assignment, m_data);    // cout << "init cost: " << result << endl;    float last_update = -1;    int i = 1;    while(T > min_T) {      int customer;      int facility;      // 随机挑选一个顾客，并给他一个随机的位移，求出系统因此而产生的能量变化      while(true) {        // 得到一个可执行的调整（不超过最大容量）        customer = get_random(m_data.customer_num);        facility = get_random(m_data.facility_num);        // 不选取关闭的商店        // 第一个初始解开放所有的商店        if(facility_used[facility] == 0 && !can_open(facility, m_random) && x != 0)          continue;                if(m_data.facility_capacity[facility]-facility_used[facility] >= m_data.customer_demand[customer]        && facility != assignment[customer]) // 要避开调度到同一个商店的情况(相当于没调动，而且会出bug)          break;      }      int E = m_data.assignment_cost[facility][customer]-m_data.assignment_cost[assignment[customer]][customer];      if(facility_used[facility] == 0) {        // 当前调整如果需要开启新的商店        E += m_data.facility_opening_cost[facility];      }       if(facility_used[assignment[customer]] == m_data.customer_demand[customer]) {        // 当前调整如果会关闭旧的商店        E -= m_data.facility_opening_cost[assignment[customer]];      }      if(E <= 0) { // 如果是优的解，接受        facility_used[assignment[customer]] -= m_data.customer_demand[customer];        assignment[customer] = facility;        facility_used[assignment[customer]] += m_data.customer_demand[customer];        result += E;        last_update = i;        // cout << i << " : " << result << endl;      } else {  // 如果是差的解，以一定概率接受        float R = get_random(10000)/(float)10000;        float P = exp(-E/T);        if(R < P) {          facility_used[assignment[customer]] -= m_data.customer_demand[customer];          assignment[customer] = facility;          facility_used[assignment[customer]] += m_data.customer_demand[customer];          result += E;          last_update = i;                }      }      T *= factor; // 降温      i++;    }    if(result < final_result) {      final_result = result;      final_times = i;      final_last_update = last_update;      m_data.assignment = assignment;      m_data.facility_used = facility_used;    }  }  cout << "SA final cost: " << final_result << " total times: " << final_times << " last update: " << final_last_update << " check: " << evaluation(m_data.assignment, m_data) << endl;  return final_result;  // cout << "check result..." << endl;  // check(assignment, m_data);}

运行结果：

Result  Time(s)p1  8958  0.542318p2  7977  0.574981p3  9521  0.456748p4  11335 0.434649p5  9037  0.222143p6  7781  0.216178p7  9602  0.231183p8  11377 0.233821p9  8576  0.332075p10 7648  0.358680p11 9226  0.336261p12 10826 0.324133p13 8798  1.668732p14 7435  1.281751p15 10185 1.042824p16 12255 1.464110p17 8719  1.065602p18 7519  1.008021p19 9319  1.221803p20 11606 0.977873p21 8567  0.679936p22 7332  0.649653p23 10187 0.642594p24 11057 0.796385p25 12995 2.124665p26 11353 2.373364p27 14023 1.998778p28 15730 1.702998p29 13257 1.971333p30 12171 1.774540p31 14723 1.401018p32 17377 2.267692p33 13366 2.080220p34 11325 1.964321p35 13981 2.501082p36 15039 2.642908p37 12793 1.685629p38 11280 1.486809p39 13540 1.251547p40 14984 1.465966p41 6628  0.485934p42 6976  1.455323p43 6098  2.149522p44 7160  0.493512p45 6910  6.036019p46 7409  2.324937p47 6309  0.581589p48 6459  1.213418p49 5625  1.343800p50 9343  0.356038p51 8180  0.739496p52 9403  0.462276p53 10375 1.207710p54 9207  0.483871p55 9195  1.347166p56 23371 0.605247p57 29942 0.714306p58 42494 0.614179p59 32929 0.643699p60 22875 1.437787p61 29571 1.117360p62 41236 1.174382p63 32934 1.109773p64 22970 1.780464p65 29930 1.659472p66 36962 1.782220p67 32720 1.151957p68 23150 1.530568p69 30626 1.938921p70 39355 1.266474p71 33590 1.367931

具体信息：

（依次为：总开销，商店是否开放，各个顾客的安排）

[p1]89581 1 1 1 1 1 0 0 1 1 8 2 1 5 3 8 2 4 4 1 9 0 3 2 8 3 4 0 9 4 3 4 9 4 2 5 1 5 0 5 2 5 0 3 9 4 4 3 0 4 1 8 1 5 4 0 2 0 4 0 [p2]79771 1 1 1 1 1 1 1 1 0 8 2 1 6 3 8 2 4 4 1 4 8 3 2 0 3 4 0 6 7 3 4 6 4 2 5 1 5 0 5 2 6 0 3 4 4 4 3 0 4 1 8 1 5 7 0 2 0 4 0 [p3]95211 1 1 1 1 1 1 0 1 0 8 2 1 6 3 8 2 4 4 1 4 0 3 2 8 3 2 0 6 4 3 4 6 4 2 5 1 5 0 5 2 6 0 3 4 4 4 3 0 4 1 8 1 5 4 0 2 0 4 0 [p4]113351 0 1 1 1 1 1 0 1 1 2 8 5 6 3 8 2 4 4 5 9 8 3 2 8 3 4 0 9 4 3 4 6 4 2 5 3 5 0 5 2 6 0 3 9 4 4 3 0 4 5 8 3 5 4 0 2 0 4 0 [p5]90371 1 1 1 1 1 1 0 1 1 8 8 1 6 1 8 2 4 4 1 9 8 0 2 8 3 2 0 9 9 3 8 6 4 2 5 1 5 0 5 2 6 0 3 9 4 4 3 0 4 1 8 1 5 4 0 9 0 4 3 [p6]77811 1 1 1 1 0 1 1 1 1 8 8 1 6 3 8 2 4 4 1 9 8 3 2 8 3 2 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 9 3 4 0 [p7]96021 1 1 1 1 0 1 0 1 1 8 8 1 6 3 8 2 4 4 1 9 8 3 2 8 3 2 0 9 9 3 2 6 4 2 6 1 1 8 1 9 6 0 3 9 4 4 3 0 4 1 8 1 6 4 0 9 0 4 0 [p8]113771 1 1 1 1 0 1 1 1 1 8 8 1 6 3 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]85761 1 1 1 1 0 1 0 1 1 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]76481 1 1 1 1 0 1 1 1 1 8 8 1 6 3 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 4 0 4 0 [p11]92261 1 1 1 1 0 1 0 1 1 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 [p12]108261 1 1 1 1 0 1 0 1 1 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 [p13]87981 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 16 1 10 10 1 15 17 13 14 17 15 19 1 10 13 3 15 10 17 9 14 15 15 19 9 17 16 17 1 17 13 15 13 16 3 10 3 19 19 13 9 0 0 0 3 13 14 10 19 9 [p14]74350 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 16 12 10 10 1 12 17 13 12 17 15 19 1 6 13 3 15 10 17 9 12 15 15 19 6 17 16 17 1 17 13 15 13 16 3 10 3 19 19 13 6 16 15 16 3 13 12 10 19 9 [p15]101850 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 16 3 10 10 18 18 3 18 7 4 7 4 4 10 2 3 7 7 4 8 18 18 7 2 10 4 16 3 3 4 2 7 2 16 3 10 3 18 4 2 8 16 16 16 8 18 7 10 2 8 [p16]122551 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 14 7 7 19 19 17 2 14 17 7 19 19 9 2 14 2 7 19 9 14 7 7 19 9 17 0 17 17 17 2 7 2 0 17 14 8 19 19 2 8 7 0 0 8 2 14 9 19 9 [p17]87190 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 16 14 10 10 1 15 17 13 14 17 15 1 1 10 13 14 15 10 17 9 14 15 15 13 9 1 16 17 14 17 13 15 13 16 17 10 8 1 1 13 9 16 15 16 8 13 14 10 1 9 [p18]75191 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 10 10 1 15 17 13 7 17 15 19 1 10 13 3 15 10 17 9 15 15 15 19 9 17 0 17 1 17 13 7 13 0 3 10 3 19 19 13 9 0 15 0 3 13 7 10 19 9 [p19]93191 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 3 10 10 1 1 17 13 3 17 15 1 1 6 13 3 15 10 17 6 15 15 15 13 6 17 0 17 1 17 13 15 13 0 3 10 3 1 1 13 6 0 15 0 3 13 10 10 1 6 [p20]116060 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 16 1 10 10 1 18 17 18 14 17 15 19 1 10 18 11 15 10 17 11 14 15 15 19 10 17 16 17 1 17 18 15 18 16 1 10 11 19 19 18 14 16 15 16 11 15 14 14 19 11 [p21]85670 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7 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 24 0 25 0 11 24 5 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 [p28]157301 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 14 20 5 2 24 14 17 24 8 8 20 2 14 14 17 5 11 14 0 5 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 20 11 8 5 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 24 0 5 24 20 20 11 17 24 8 24 20 14 24 20 7 20 17 17 17 2 7 20 5 2 24 17 11 7 5 2 14 25 20 8 17 14 25 2 25 7 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 20 8 0 5 24 0 25 0 11 24 5 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 [p29]132571 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 2 20 5 2 9 14 17 9 8 8 20 2 14 14 17 5 11 2 0 9 17 5 8 2 24 24 9 5 25 6 25 20 20 24 24 0 14 0 14 24 8 24 14 0 20 11 8 5 14 14 5 6 20 17 11 11 14 0 5 20 11 11 11 9 0 9 9 8 6 11 17 24 8 9 20 2 24 20 0 20 17 2 17 17 0 20 5 2 24 17 11 17 5 2 2 25 8 8 17 17 25 2 25 0 11 14 17 14 14 2 11 11 25 24 24 24 24 5 8 25 20 8 0 5 9 0 25 0 11 24 5 8 14 17 5 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1 0 0 1 0 0 0 1 1 0 1 0 0 20 11 13 2 20 5 2 24 14 17 24 8 8 20 17 14 14 17 25 11 2 0 5 17 25 8 2 24 24 24 5 25 13 25 20 20 24 5 0 14 0 14 24 8 24 14 0 13 27 8 25 2 14 5 13 20 17 27 0 14 0 5 20 11 11 11 25 0 5 25 20 20 11 17 24 8 24 20 14 25 20 7 13 17 2 17 17 7 20 25 2 24 17 11 17 5 2 2 25 13 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 27 24 24 5 5 5 8 25 13 8 0 5 24 0 25 0 11 24 27 8 14 7 5 20 17 0 8 20 14 8 27 25 5 2 5 [p33]133661 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 2 20 5 2 9 14 17 24 8 8 20 17 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 13 11 8 5 14 14 5 13 20 17 11 11 14 0 5 20 11 11 11 9 0 5 24 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 20 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 24 0 25 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p34]113251 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 13 2 20 5 2 5 14 17 24 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 13 11 8 5 14 14 5 13 20 17 11 0 14 0 5 20 11 11 11 24 0 24 5 20 20 11 17 24 8 24 20 14 24 20 0 13 17 17 17 17 0 20 5 2 24 17 11 17 5 2 2 25 13 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 24 0 25 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p35]139811 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 2 20 5 2 24 14 17 5 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 13 11 8 5 14 14 5 13 20 17 11 11 14 0 5 20 11 11 11 24 0 24 5 20 20 11 17 24 8 24 20 14 24 20 7 13 17 17 17 17 7 20 5 2 24 17 11 17 5 2 2 25 13 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 13 8 0 5 24 0 25 0 11 24 5 8 14 7 5 20 17 0 8 20 14 8 25 25 5 2 5 [p36]150391 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 2 20 5 2 24 14 17 24 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 25 8 25 20 20 24 24 0 14 0 14 24 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24 20 20 11 17 24 8 24 20 14 24 20 7 20 17 17 17 17 7 20 5 2 24 17 11 17 5 2 2 25 20 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 20 8 0 5 24 0 25 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p39]135401 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 20 11 13 2 20 5 2 24 14 17 24 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 11 20 11 20 20 24 24 0 14 0 14 24 8 24 14 0 13 27 8 5 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 24 0 5 24 20 20 11 17 24 8 24 20 14 24 20 0 13 17 17 17 17 0 20 5 2 24 17 11 17 24 2 2 27 20 8 17 17 11 2 5 17 11 14 8 14 14 2 11 11 27 24 24 24 24 5 8 11 13 8 0 5 24 0 27 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 27 11 5 2 5 [p40]149841 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 20 11 20 2 20 5 2 24 14 17 24 8 8 20 17 14 14 17 5 11 2 0 5 17 5 8 2 24 5 24 5 25 20 25 20 20 24 24 0 14 0 14 24 8 24 14 0 20 11 8 5 14 14 5 20 20 17 11 0 14 0 5 20 11 11 11 24 0 24 24 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 20 8 17 17 25 2 25 17 11 14 8 14 14 2 11 11 25 24 24 24 24 5 8 25 20 8 0 5 24 0 25 0 11 24 5 8 14 17 5 20 17 0 8 20 14 8 25 25 5 2 5 [p41]66281 0 1 1 0 1 1 0 0 1 5 6 0 6 2 9 3 3 5 3 5 6 2 6 2 2 5 3 0 6 6 6 6 6 6 5 5 0 5 5 5 0 0 0 3 9 2 6 6 9 2 3 3 3 3 5 0 5 6 6 6 6 6 6 9 9 2 3 3 3 0 0 6 5 0 6 6 6 5 5 0 0 5 0 3 9 2 2 2 5 5 2 2 2 9 9 9 9 9 2 [p42]69760 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 17 14 9 9 7 18 17 17 17 17 9 18 18 14 18 18 18 17 14 14 14 9 9 17 18 18 9 17 17 17 7 18 18 14 14 18 14 7 7 7 7 17 17 18 9 14 18 18 18 18 17 17 7 17 17 9 17 18 14 14 18 17 9 17 9 17 7 18 18 18 18 18 18 18 18 18 18 18 18 18 [p43]60980 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 29 7 11 29 7 7 7 7 29 29 29 29 7 7 11 11 11 11 7 7 7 7 7 11 7 7 29 11 29 29 29 29 29 7 7 7 7 7 11 11 29 7 29 29 29 7 7 7 7 11 11 7 7 11 11 11 7 11 7 29 29 29 7 29 29 29 29 29 29 29 [p44]71601 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 6 6 0 0 0 0 0 0 1 1 1 7 1 7 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 0 1 1 2 8 7 5 3 7 7 6 5 5 8 8 7 7 9 5 5 5 9 3 0 6 6 8 1 0 4 9 9 7 7 8 6 6 5 8 7 9 9 9 9 9 6 5 7 5 [p45]69101 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 18 1 1 1 1 1 18 2 2 2 2 2 2 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 0 0 2 2 11 11 18 17 18 13 18 5 13 13 11 18 18 18 5 1 2 2 2 2 0 17 13 13 11 11 13 1 18 2 13 17 17 17 17 17 13 13 [p46]74091 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 10 0 10 10 10 0 10 1 1 18 1 1 1 1 19 2 2 2 2 2 2 27 27 27 27 27 27 8 8 27 8 8 8 8 10 2 2 14 14 1 0 19 19 0 14 14 18 27 26 18 0 26 27 0 2 26 27 18 18 14 19 19 0 18 26 27 14 27 19 18 [p47]63091 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 1 2 1 1 1 1 2 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 9 2 9 9 9 9 9 0 [p48]64591 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 2 3 2 2 3 3 5 5 5 5 5 5 5 5 5 9 5 5 9 5 5 5 8 8 8 8 8 8 8 9 9 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 0 17 0 0 [p49]56250 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 2 2 2 2 2 2 2 2 2 2 2 2 2 6 6 6 6 6 6 6 6 6 9 9 9 9 9 13 13 14 13 13 13 14 13 14 13 13 13 13 13 13 20 20 20 20 20 20 21 20 21 20 2 21 21 21 21 26 26 26 26 26 26 26 26 28 28 28 28 28 [p50]93431 1 1 1 1 1 1 1 0 1 3 6 3 0 2 9 5 5 3 7 7 4 6 9 9 2 9 2 5 3 6 6 0 4 0 6 7 4 4 7 7 7 3 3 3 5 9 9 0 6 0 9 9 9 5 5 5 5 5 3 3 5 6 0 0 0 9 6 1 2 9 7 7 7 3 3 0 4 7 7 3 0 6 6 0 4 4 3 3 4 3 5 2 2 2 2 1 7 2 7 9 1 2 2 2 1 1 9 1 1 [p51]81801 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 15 0 19 10 12 13 5 5 15 1 5 14 18 13 13 13 12 5 5 15 0 0 10 14 14 14 1 19 19 15 1 1 19 19 15 5 13 13 10 0 0 13 13 13 12 5 5 5 5 15 15 5 0 14 14 10 13 0 18 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 18 5 12 1 13 13 13 18 18 18 18 18 13 13 [p52]94030 1 0 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7 3 4 4 4 3 4 4 4 4 8 3 8 8 8 3 8 3 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 5 3 3 5 6 4 7 6 6 4 3 3 5 3 4 7 1 6 3 3 5 5 3 3 7 5 3 5 5 1 1 5 1 3 4 3 7 [p53]103750 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 5 5 5 5 5 5 5 5 19 19 19 7 7 7 7 7 7 12 13 12 12 13 13 12 12 9 9 9 15 9 15 9 15 9 18 18 18 18 18 18 18 18 18 18 5 5 7 12 12 15 15 3 7 18 5 15 3 3 1 6 18 2 15 13 3 13 2 18 6 5 18 18 6 3 3 15 3 6 6 2 18 19 13 15 15 3 1 6 15 3 15 2 9 2 15 18 1 6 1 5 [p54]92071 0 1 1 1 1 1 1 0 1 7 7 7 7 7 7 7 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 3 2 3 3 2 3 3 3 3 3 3 3 3 3 3 3 6 6 3 6 6 6 3 6 6 3 3 3 3 6 6 6 6 6 6 6 6 6 5 5 6 5 5 5 6 5 0 0 0 0 5 7 0 0 0 0 0 0 4 0 4 4 4 4 4 4 4 4 9 4 9 9 9 2 9 9 9 [p55]91951 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 17 18 17 18 18 18 17 2 8 8 8 8 2 8 8 2 2 2 8 6 12 12 2 6 12 12 12 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 0 7 0 0 0 0 0 0 0 0 7 7 7 7 7 7 7 7 11 11 11 11 11 11 11 7 11 9 9 11 9 11 17 13 9 13 9 9 13 15 15 15 15 15 15 15 15 15 15 18 18 18 18 17 18 18 18 18 [p56]233711 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 19 21 27 2 12 15 27 22 28 4 28 13 13 28 18 3 20 22 0 18 16 5 24 10 18 27 19 29 2 19 19 4 16 27 6 20 8 24 16 18 8 6 4 8 19 13 21 19 14 24 16 24 16 8 6 11 8 18 25 29 0 7 8 13 11 5 14 28 25 18 12 19 8 23 23 20 23 8 16 10 0 26 25 29 13 6 5 27 7 28 6 25 25 2 3 11 6 0 28 28 15 25 18 4 0 4 24 22 3 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 20 23 8 3 3 28 10 12 22 11 11 25 5 24 15 27 25 24 17 23 0 8 11 2 15 3 13 13 27 10 24 5 27 5 4 3 21 5 20 19 14 26 2 0 10 29 10 5 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 15 10 19 [p57]299420 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 18 19 21 27 21 28 21 27 22 27 4 28 13 13 28 18 13 20 22 27 18 16 10 24 10 18 22 28 29 21 19 19 4 16 27 19 20 8 24 16 18 8 12 4 8 4 13 16 19 20 24 16 24 16 8 19 18 8 18 7 29 27 7 8 13 12 23 19 28 12 18 12 4 8 23 23 20 23 8 16 23 23 8 7 29 13 19 21 27 7 27 19 7 7 23 8 28 12 10 28 19 21 7 18 4 27 4 16 22 13 19 29 27 28 12 8 27 7 10 8 20 18 10 19 4 16 16 18 4 28 28 24 12 20 23 8 13 13 28 10 12 22 28 12 7 23 16 16 22 7 24 20 23 28 8 18 21 16 13 13 13 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8 24 10 0 9 25 4 13 6 2 27 7 28 6 25 25 2 13 11 6 0 28 28 21 25 18 4 0 4 24 27 13 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 21 2 11 26 17 28 24 25 10 23 9 13 13 28 10 12 27 11 11 25 2 24 21 27 25 24 17 23 0 8 11 2 21 13 13 13 27 10 24 23 27 23 4 13 21 23 8 19 14 26 2 0 10 4 10 2 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 21 10 19 [p60]228751 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 7 19 21 27 2 12 21 27 22 28 4 28 13 1 28 7 1 20 22 0 27 16 5 24 10 27 27 19 4 2 19 19 4 16 27 6 20 8 24 16 7 9 6 4 8 19 13 21 19 14 24 16 24 16 8 6 11 9 22 25 4 0 7 8 13 11 5 14 28 25 7 12 19 9 5 13 20 5 8 16 10 0 9 25 4 13 6 5 27 7 28 6 25 25 2 13 11 6 0 28 28 21 25 7 4 0 4 24 22 13 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 20 1 9 1 13 28 10 12 22 11 11 25 5 24 21 27 25 24 17 10 0 8 11 2 16 13 13 13 27 10 24 5 27 5 4 1 21 1 20 19 14 26 2 0 10 4 10 5 21 2 19 12 8 28 10 0 21 2 21 6 4 7 12 7 21 10 19 [p61]295711 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 18 6 2 22 0 6 2 0 22 14 4 14 8 13 6 18 3 8 22 0 18 22 2 0 13 18 22 14 4 2 6 4 4 22 0 6 8 8 22 2 18 8 6 4 8 4 13 2 14 14 2 22 22 2 8 6 11 8 18 18 4 0 18 8 13 11 13 14 6 11 18 11 6 8 13 13 8 13 8 22 13 0 8 18 4 13 4 3 22 18 11 6 11 11 0 3 6 6 0 11 14 0 11 18 4 0 4 22 22 3 14 4 18 6 11 8 11 18 14 8 14 11 0 6 4 22 2 18 4 0 11 2 11 8 13 8 3 3 6 14 11 22 6 11 11 2 22 2 22 11 0 14 13 0 8 6 2 2 3 13 13 18 13 0 13 22 13 4 3 2 13 8 14 14 4 22 0 14 4 14 2 2 2 6 6 8 11 13 0 2 2 2 6 4 18 11 18 2 14 14 [p62]412361 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 18 26 0 27 10 4 0 27 22 27 4 0 13 13 12 18 3 20 22 27 18 22 10 27 10 18 27 26 4 13 4 4 4 22 27 12 20 20 22 22 22 26 4 26 13 26 13 0 26 20 27 22 27 22 20 4 18 26 18 18 4 0 18 20 13 12 10 10 4 12 18 12 26 20 10 13 20 10 20 22 10 0 26 12 4 13 4 13 27 18 20 4 18 12 10 3 27 12 0 27 26 0 12 18 4 0 4 22 22 3 26 4 18 12 27 20 0 18 10 20 26 18 0 26 26 22 10 12 26 0 27 0 12 20 13 20 3 3 27 10 12 22 12 12 18 0 22 22 27 18 27 0 10 0 13 12 0 22 3 13 13 27 10 27 10 27 13 26 3 0 13 20 26 20 26 13 27 20 4 20 10 0 22 12 12 20 4 13 0 22 0 22 4 4 18 12 18 0 10 26 [p63]329341 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 18 19 2 27 2 12 2 27 18 28 29 28 13 13 28 18 13 20 27 0 18 16 5 24 10 18 27 19 29 2 19 19 26 16 27 6 20 8 24 16 18 9 6 26 8 19 13 2 19 20 24 16 24 16 8 6 11 9 18 25 29 0 25 8 13 11 5 17 28 25 18 12 19 9 23 23 20 23 8 16 10 0 9 25 29 13 6 5 27 25 28 6 25 25 2 13 11 6 0 28 28 16 25 18 29 0 29 24 27 13 19 29 27 12 12 8 28 25 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 20 23 9 13 13 28 10 12 27 11 11 25 5 24 16 27 25 24 17 23 0 8 11 2 16 13 13 13 27 10 24 5 27 5 29 13 2 5 20 19 10 26 2 0 10 29 10 5 16 2 19 12 8 28 23 0 2 2 2 6 29 25 12 25 2 10 19 [p64]229701 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 18 19 21 27 2 12 15 27 22 28 4 28 13 13 28 18 3 20 22 0 18 21 23 24 10 18 27 19 29 2 19 19 4 21 27 6 20 8 24 15 18 8 6 4 8 19 13 21 19 14 24 24 24 21 8 6 11 8 18 25 29 0 7 8 13 11 23 14 28 25 18 12 19 8 23 23 20 23 8 24 10 0 8 25 29 13 6 2 27 7 28 6 25 25 2 3 11 6 0 28 28 15 25 18 4 0 4 24 22 3 19 4 27 12 12 8 28 7 17 8 14 11 17 19 4 21 2 11 19 17 28 24 25 20 23 8 3 3 28 10 12 22 11 11 25 2 24 15 27 25 24 17 23 0 8 11 2 15 3 13 13 27 10 24 23 27 23 4 3 21 23 20 19 14 4 2 0 10 29 10 2 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 15 10 19 [p65]299301 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 18 19 21 27 2 12 15 27 22 28 4 28 13 13 28 18 13 20 22 0 18 16 5 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 14 24 16 24 16 8 6 11 8 18 7 4 0 7 8 13 11 5 14 28 25 18 12 19 8 5 13 20 5 8 16 10 0 8 25 4 13 6 5 27 7 28 6 25 25 2 13 11 6 0 28 28 15 25 18 4 0 4 24 22 13 19 4 27 12 12 8 28 7 17 8 14 11 17 19 4 16 2 11 19 17 28 24 25 20 5 8 13 13 28 10 12 22 11 11 25 5 24 15 27 25 24 17 10 0 8 11 2 15 13 13 13 27 10 24 5 27 5 4 13 21 5 20 19 14 4 2 0 10 4 10 5 21 2 19 12 8 28 10 0 21 2 21 6 4 7 12 7 15 10 19 [p66]369620 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 18 19 2 22 22 11 2 28 22 28 28 28 3 3 28 18 3 14 22 28 18 22 3 22 14 18 22 19 19 2 19 19 19 2 18 11 14 3 22 2 18 14 19 14 3 19 3 2 19 14 2 22 22 2 14 19 11 14 18 11 19 28 18 14 3 11 2 14 28 11 18 11 28 14 14 3 14 2 14 22 14 2 14 11 19 3 19 2 22 18 28 19 11 11 2 3 11 11 28 28 28 22 11 18 19 22 19 22 22 3 14 19 18 11 11 3 28 11 14 3 19 11 28 19 19 22 2 11 28 28 28 2 11 14 3 14 3 3 28 14 11 22 11 11 11 2 22 22 18 11 22 28 3 28 3 28 2 2 3 3 3 18 3 22 2 18 2 19 3 2 3 3 19 14 19 2 28 14 19 14 2 2 2 28 11 14 28 3 28 2 2 2 19 19 18 11 18 2 14 19 [p67]327201 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 18 19 2 22 2 12 15 27 22 28 4 28 10 3 28 18 3 20 22 0 18 16 23 24 10 18 27 19 4 2 19 19 4 16 27 6 20 8 24 15 18 8 6 26 8 19 3 16 19 10 24 16 24 16 8 6 11 8 18 25 4 0 18 8 8 11 23 17 28 25 18 12 19 20 23 23 20 23 8 16 10 0 26 25 4 10 19 2 27 25 28 6 25 25 2 3 27 6 0 28 28 15 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 20 23 8 3 3 28 10 12 22 11 11 25 2 24 15 27 25 24 17 23 0 8 11 2 15 3 3 23 27 10 24 23 27 23 4 3 16 23 20 19 10 26 2 0 10 4 10 2 15 2 19 12 8 28 23 0 2 2 16 6 4 25 12 25 15 10 19 [p68]231501 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 18 19 21 27 2 12 15 27 22 28 4 28 10 1 28 18 1 20 22 0 18 16 5 24 10 18 27 19 4 2 19 19 4 16 27 6 20 8 24 16 18 8 6 4 8 19 3 21 19 14 24 16 24 16 8 6 11 8 18 7 4 0 7 8 3 11 5 14 28 25 18 12 19 8 23 23 20 23 8 16 10 0 26 25 4 10 6 5 27 7 28 6 25 25 2 3 11 6 0 28 28 15 25 18 4 0 4 24 22 3 19 4 27 12 12 8 28 7 17 8 26 11 17 19 26 16 2 11 26 17 28 24 25 20 23 8 3 3 28 10 12 22 11 11 25 5 24 15 27 25 24 17 23 0 8 11 2 15 3 3 1 27 10 24 5 27 5 4 3 21 1 20 19 14 26 2 0 10 4 10 5 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 15 10 19 [p69]306261 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 7 19 21 27 2 12 15 27 22 28 4 28 13 13 28 7 3 20 22 0 27 16 5 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 7 29 0 7 8 13 11 5 17 28 25 7 12 19 9 23 23 20 23 8 16 10 0 9 25 29 13 6 5 27 7 28 6 25 25 2 3 11 6 0 28 28 15 25 7 4 0 4 24 22 3 19 4 27 12 12 8 28 7 17 8 9 11 17 19 9 16 2 11 19 17 28 24 25 20 23 9 3 3 28 10 12 22 11 11 25 5 24 15 27 25 24 17 23 0 8 11 2 15 3 13 13 27 10 24 5 27 5 4 3 21 5 20 19 10 4 2 0 10 29 10 5 21 2 19 12 8 28 23 0 21 2 21 6 4 7 12 7 15 10 19 [p70]393550 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 24 19 21 24 21 11 21 24 16 14 14 28 13 13 28 11 13 8 16 24 24 16 21 24 8 11 24 19 4 2 19 19 4 16 24 19 8 8 24 16 11 8 19 4 8 4 13 21 19 14 24 16 21 16 8 4 11 8 16 11 4 2 24 8 13 11 2 14 19 11 16 11 19 8 2 13 8 2 8 16 14 2 8 11 14 13 19 2 24 11 11 4 11 28 2 13 28 19 14 28 14 21 28 11 4 21 4 24 16 13 19 4 16 11 28 8 11 11 14 8 14 28 14 19 14 16 2 28 19 2 28 21 28 8 13 8 8 8 28 14 28 16 28 11 11 2 16 21 24 19 24 14 13 2 8 11 2 16 13 13 13 24 8 21 2 28 2 4 8 21 13 8 19 14 4 2 21 14 4 8 2 21 21 19 11 8 11 13 21 21 2 21 19 4 11 19 28 21 13 19 [p71]335900 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 18 19 21 24 2 12 21 28 18 28 4 28 13 1 28 18 1 20 24 17 18 21 5 24 10 18 24 19 29 2 19 19 4 21 28 6 20 8 24 21 18 9 6 4 8 19 13 21 19 14 24 24 2 21 8 6 11 9 18 7 29 2 7 8 13 11 5 14 28 25 18 12 19 9 23 23 20 23 8 24 10 17 9 25 29 13 6 5 24 7 28 6 25 25 2 13 11 6 17 28 28 21 25 18 4 24 4 24 18 13 19 4 18 12 12 8 28 7 17 8 9 11 17 19 9 21 2 11 19 17 28 24 25 20 23 9 1 13 28 10 12 18 11 11 25 5 24 21 18 25 24 17 23 17 8 11 2 21 13 13 13 28 10 24 5 18 5 4 1 21 1 20 19 14 4 2 24 10 29 10 5 21 2 19 12 8 28 23 17 21 2 21 6 4 7 12 7 21 10 19

结果分析：

从总体来看，模拟退火算法运行的效果地比爬山法要好，但需要更长的执行时间。

代码链接:

转载地址：http://pwwob.baihongyu.com/

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