位面之子演算法 - The Chosen One Algorithm

最近書荒，想找點小說看，卻發現沒有什么能夠耐心看下去的，
想要自己去寫小說，卻又發現動筆寫大綱，塑造人物，建立劇情的前后關系，又是極其麻煩，
寫游戲嘛？嘛，算了算了，代碼塊太多，本喵太懶
怎么辦！干脆直接Simulation好了！說干就干！咱們這就模擬一個小說里強者為尊的世界！
實作語言，當然是簡單便捷的Matlab！

宣告：本代碼為本人提出，僅供娛樂之用，歡迎轉載，但請保留頭部簽名協議，感謝！

首先，這個世界需要規定一些引數：

%%% @author: RaZNeo
%%% @license: MIT License
%%% @contact: raznexo@gmail.com
%%% @file: main.m
%%% @time: 2021/7/21 13:28
%%% @desc: Happy Coding

%%% 清理門戶：一屋不掃，何以掃天下？
close all; clear; clc;
%%% 位面指標
dim = 20;
%%% 位面人口
npop = 1000;
%%% 強者數量,能力范圍,初始化強者身份資料庫
numPowerfull = 20;
numAbilityRange = 0.15;
powerFullLibrary = zeros(numPowerfull,1);
%%% 位面年代
currentYear = 1650;
%%% 位面之子產生間隔
intervalOccur = 16; %每16年產生一位位面之子帶領位面走向繁榮
%%% 凡人學習能力
aveAbility = 0.4;
%%% 凡人榜樣數量
target = 3;
%%% 位面淘汰概率
elimiProb = 0.3;
%%% 位面發展值上下限
upp =  20 * ones(1,dim);
low = -20 * ones(1,dim);

然后高階文明開始了游戲（他們規定了一個目標函式，大家為了這個目標而紛爭不斷）

%%% 高維度文明在本位面展開的游戲
objFun = @(x) sum(x.^2 + 3.*x - 15);

%%% 高維度文明灑下原始文明的種子
historyRec = zeros(currentYear,1);
bestManHistory = zeros(currentYear,dim);
x = ones(npop,1)*low + ...
    (ones(npop,1)*(upp-low)).*rand(npop,dim);
for i=1:1:npop
    fit(i) = objFun(x(i,:));
end
[historyRec(1),idxPowerMax] = min(fit);
powerMan = x(idxPowerMax,:);
fit = Inf * ones(npop,1);
newFit = Inf * ones(npop,1);

歷史的車輪滾滾向前！（就是主回圈啦！）

%%% 位面發展仿真
for year = 1:currentYear
    
    %%% 隨機產生新的“Chosen One”,
    %%% 位于歷史最優點附近，即獲得較優歷史資源，
    %%% 且為高斯分布，
    if mod(year,intervalOccur) == 0 || year == 1
        chosenList = randperm(npop,numPowerfull);
        x(chosenList,:) = repmat(powerMan * normrnd(1,0.01),numPowerfull,1);
    end
    
    for people = 1:npop        
        %%% 如果此人是位面之子，
        %%% 則隨機指定位面之子的特殊技能值（維度、指標）
        if ismember(people,chosenList)
            abilityList = randperm(dim,floor(numAbilityRange*dim));
            newAbility = low + (upp-low).*rand();
            new_x = x(i,:);
            new_x(abilityList) = newAbility(abilityList);
        else
            %%% 若此人為凡人，隨機以target位面之子為榜樣，增進能力
            new_x = x(people,:) + aveAbility .* ...
                mean(x(chosenList(randperm(numPowerfull,target)),:));
        end        
        %%% 檢查是否有能力越界者，若有，超階文明予以抹除
        new_x = max(min(new_x, upp), low);        
        %%% 對此人進行能力評估
        newFit(people) = objFun(new_x);        
        %%% 如果習得上乘模因，則保留記憶，否則放棄無用模因
        if newFit(people) < fit(people) && ~ismember(people,chosenList)
            fit(people) = newFit(people);
            x(people,:) = new_x;
        elseif ismember(people,chosenList)
            fit(people) = newFit(people);
            x(people,:) = new_x;
        end        
    end
    
    %%% 眾人排出實力強弱，有時會殺出黑馬
    [fit, fitIdx] = sort(fit);
    x = x(fitIdx,:);
    
    %%% 弱者末尾淘汰
    numElimi = floor(elimiProb*npop);
    x(end-numElimi:end,:) = x(1:numElimi+1,:);
    
    %%% 記錄強者歷史
    [historyRec(year),recIdx] = min(fit);
    bestManHistory(year,:) = x(recIdx,:);
    
    if mod(year,100) == 0
        disp("Year " + num2str(year) + " history record finished !");
    end
    
end

歷史學家們對神明游戲的情況進行了統計！（其實就是繪個圖啦）

%%% 展示歷史的曲折發展道路
figure(1101);
title('歷史的車輪滾滾向前 ');
xlabel('迭代次數');
ylabel('目標函式值');
plot(historyRec,'LineWidth',3);

嗯，咱們研究這個高階文明的游戲，發現它的分數軌跡是這樣的（居然能收斂！？驚！）

[ 重要 ] 代碼最侄訓總：

%%% @author: RaZNeo
%%% @license: MIT License
%%% @contact: raznexo@gmail.com
%%% @file: main.m
%%% @time: 2021/7/21 13:28
%%% @desc: Happy Coding

%%% 清理門戶：一屋不掃，何以掃天下？
close all; clear; clc;

%%% 位面指標
dim = 20;

%%% 位面人口
npop = 1000;

%%% 強者數量,能力范圍,初始化強者身份資料庫
numPowerfull = 20;
numAbilityRange = 0.15;
powerFullLibrary = zeros(numPowerfull,1);

%%% 位面年代
currentYear = 1650;

%%% 位面之子產生間隔
intervalOccur = 16; %每16年產生一位位面之子帶領位面走向繁榮

%%% 凡人學習能力
aveAbility = 0.4;

%%% 凡人榜樣數量
target = 3;

%%% 位面淘汰概率
elimiProb = 0.3;

%%% 位面發展值上下限
upp =  20 * ones(1,dim);
low = -20 * ones(1,dim);

%%% 高維度文明在本位面展開的游戲
objFun = @(x) sum(x.^2 + 3.*x - 15);

%%% 高維度文明灑下原始文明的種子
historyRec = zeros(currentYear,1);
bestManHistory = zeros(currentYear,dim);
x = ones(npop,1)*low + ...
    (ones(npop,1)*(upp-low)).*rand(npop,dim);
for i=1:1:npop
    fit(i) = objFun(x(i,:));
end
[historyRec(1),idxPowerMax] = min(fit);
powerMan = x(idxPowerMax,:);
fit = Inf * ones(npop,1);
newFit = Inf * ones(npop,1);

%%% 位面發展仿真
for year = 1:currentYear
    
    %%% 隨機產生新的“Chosen One”,
    %%% 位于歷史最優點附近，即獲得較優歷史資源，
    %%% 且為高斯分布，
    if mod(year,intervalOccur) == 0 || year == 1
        chosenList = randperm(npop,numPowerfull);
        x(chosenList,:) = repmat(powerMan * normrnd(1,0.01),numPowerfull,1);
    end
    
    for people = 1:npop
        
        %%% 如果此人是位面之子，
        %%% 則隨機指定位面之子的特殊技能值（維度、指標）
        if ismember(people,chosenList)
            abilityList = randperm(dim,floor(numAbilityRange*dim));
            newAbility = low + (upp-low).*rand();
            new_x = x(i,:);
            new_x(abilityList) = newAbility(abilityList);
        else
            %%% 若此人為凡人，隨機以target位面之子為榜樣，增進能力
            new_x = x(people,:) + aveAbility .* ...
                mean(x(chosenList(randperm(numPowerfull,target)),:));
        end
        
        %%% 檢查是否有能力越界者，若有，超階文明予以抹除
        new_x = max(min(new_x, upp), low);
        
        %%% 對此人進行能力評估
        newFit(people) = objFun(new_x);
        
        %%% 如果習得上乘模因，則保留記憶，否則放棄無用模因
        if newFit(people) < fit(people) && ~ismember(people,chosenList)
            fit(people) = newFit(people);
            x(people,:) = new_x;
        elseif ismember(people,chosenList)
            fit(people) = newFit(people);
            x(people,:) = new_x;
        end
        
    end
    
    %%% 眾人排出實力強弱，有時會殺出黑馬
    [fit, fitIdx] = sort(fit);
    x = x(fitIdx,:);
    
    %%% 弱者末尾淘汰
    numElimi = floor(elimiProb*npop);
    x(end-numElimi:end,:) = x(1:numElimi+1,:);
    
    %%% 記錄強者歷史
    [historyRec(year),recIdx] = min(fit);
    bestManHistory(year,:) = x(recIdx,:);
    
    if mod(year,100) == 0
        disp("Year " + num2str(year) + " history record finished !");
    end
    
end

%%% 展示歷史的曲折發展道路
figure(1101);
title('歷史的車輪滾滾向前 ');
xlabel('迭代次數');
ylabel('目標函式值');
plot(historyRec,'LineWidth',3);