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⛄ 内容介绍
纵横交叉算法（Vertical and Horizontal Cross Algorithm）是一种用于解决迷宫问题的启发式搜索算法。该算法的思想基于深度优先搜索和广度优先搜索。
在纵横交叉算法中，搜索者从起点开始，按照一定的规则进行搜索。首先，搜索者会向前移动一步，然后依次向左、向右、向上、继续四个方向移动一步，形成十个字形的搜索路径。接下来，对每个搜索路径上的节点，再次按照相同的规则进行搜索。这样，不断纵向和水平地交叉搜索，直到找到终点或者无法继续移动轨迹。
纵横交叉算法在搜索迷宫时具有极高的效率和准确性。它能够利用深度优先搜索的特点，在保证搜索效率的同时，覆盖整个迷宫空间。同时，它也能够利用广度优先搜索的特点特点是，在搜索过程中逐步扩大搜索范围，增加找到终极的可能性。
⛄ 部分代码
function Fit=BenFunctions(X,FunIndex,Dim)global nfe;nfe=nfe+1; switch FunIndex %%%%%%%%%%%%%%%%%%%%%%%%%%unimodal function%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Sphere case 1 Fit=sum(X.^2); %Schwefel 2.22 case 2 Fit=sum(abs(X))+prod(abs(X)); %Schwefel 1.2 case 3 Fit=0; for i=1:Dim Fit=Fit+sum(X(1:i))^2; end %Schwefel 2.21 case 4 Fit=max(abs(X)); %Rosenbrock case 5 Fit=sum(100*(X(2:Dim)-(X(1:Dim-1).^2)).^2+(X(1:Dim-1)-1).^2); %Step case 6 Fit=sum(floor((X+.5)).^2); %Quartic case 7 Fit=sum([1:Dim].*(X.^4))+rand; %%%%%%%%%%%%%%%%%%%%%%%%%%multimodal function%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Schwefel case 8 Fit=sum(-X.*sin(sqrt(abs(X)))); %Rastrigin case 9 Fit=sum(X.^2-10*cos(2*pi.*X))+10*Dim; %Ackley case 10 Fit=-20*exp(-.2*sqrt(sum(X.^2)/Dim))-exp(sum(cos(2*pi.*X))/Dim)+20+exp(1); %Griewank case 11 Fit=sum(X.^2)/4000-prod(cos(X./sqrt([1:Dim])))+1; %Penalized case 12 a=10;k=100;m=4; Dim=length(X); Fit=(pi/Dim)*(10*((sin(pi*(1+(X(1)+1)/4)))^2)+sum((((X(1:Dim-1)+1)./4).^2).*... (1+10.*((sin(pi.*(1+(X(2:Dim)+1)./4)))).^2))+((X(Dim)+1)/4)^2)+sum(k.*... ((X-a).^m).*(X>a)+k.*((-X-a).^m).*(X<(-a))); %Penalized2 case 13 a=10;k=100;m=4; Dim=length(X); Fit=.1*((sin(3*pi*X(1)))^2+sum((X(1:Dim-1)-1).^2.*(1+(sin(3.*pi.*X(2:Dim))).^2))+... ((X(Dim)-1)^2)*(1+(sin(2*pi*X(Dim)))^2))+sum(k.*... ((X-a).^m).*(X>a)+k.*((-X-a).^m).*(X<(-a))); %%%%%%%%%%%%%%%%%%%%%%%%%%fixed-dimensionalmultimodalfunction%%%%%%%%%%%%%% %Foxholes case 14 a=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,... -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32]; for j=1:25 b(j)=sum((X'-a(:,j)).^6); end Fit=(1/500+sum(1./([1:25]+b))).^(-1); %Kowalik case 15 a=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246]; b=[.25 .5 1 2 4 6 8 10 12 14 16];b=1./b; Fit=sum((a-((X(1).*(b.^2+X(2).*b))./(b.^2+X(3).*b+X(4)))).^2); %Six Hump Camel case 16 Fit=4*(X(1)^2)-2.1*(X(1)^4)+(X(1)^6)/3+X(1)*X(2)-4*(X(2)^2)+4*(X(2)^4); %Branin case 17 Fit=(X(2)-(X(1)^2)*5.1/(4*(pi^2))+5/pi*X(1)-6)^2+10*(1-1/(8*pi))*cos(X(1))+10; %GoldStein-Price case 18 Fit=(1+(X(1)+X(2)+1)^2*(19-14*X(1)+3*(X(1)^2)-14*X(2)+6*X(1)*X(2)+3*X(2)^2))*... (30+(2*X(1)-3*X(2))^2*(18-32*X(1)+12*(X(1)^2)+48*X(2)-36*X(1)*X(2)+27*(X(2)^2))); %Hartman 3 case 19 a=[3 10 30;.1 10 35;3 10 30;.1 10 35];c=[1 1.2 3 3.2]; p=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828]; Fit=0; for i=1:4 Fit=Fit-c(i)*exp(-(sum(a(i,:).*((X-p(i,:)).^2)))); end %Hartman 6 case 20 af=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14]; cf=[1 1.2 3 3.2]; pf=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;... .2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381]; Fit=0; for i=1:4 Fit=Fit-cf(i)*exp(-(sum(af(i,:).*((X-pf(i,:)).^2)))); end %Shekel 5 case 21 a=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; c=[0.1 0.2 0.2 0.4 0.4 0.6 0.3 0.7 0.5 0.5]; Fit=0; for i=1:5 Fit=Fit-1/((X-a(i,:))*(X-a(i,:))'+c(i)); end %Shekel 7 case 22 a=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; c=[0.1 0.2 0.2 0.4 0.4 0.6 0.3 0.7 0.5 0.5]; Fit=0; for i=1:7 Fit=Fit-1/((X-a(i,:))*(X-a(i,:))'+c(i)); end %Shekel 10% otherwise% a=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];% c=[0.1 0.2 0.2 0.4 0.4 0.6 0.3 0.7 0.5 0.5];% Fit=0;% for i=1:10% Fit=Fit-1/((X-a(i,:))*(X-a(i,:))'+c(i));% end case 23 % ESTIMATION OF SOLAR PV PARAMETERS % SINGLE DIODE MODEL % DATA FROM GWO PAPER PROVIDED BY PACHAURI SIR % SEQUENCE OF VALUES: Iph(A), Isd(A),Rs(ohm), Rsh(ohm),a1 (IDEALITY FACTOR OF DIODE) % S IS THE IRRADIANCE, TEMP IS THE TEMPRATURE % S=1000 W/m2; TEMP=33 0C=306 KELVIN % I-V DATA: 57mm diameter industrial silicon solar cell (R.T.C. France) % VE EXPERIMENTED DATA OF VOLTAGE % IE EXPERIMENTED DATA OF CURRENT TEMP=306.15; VE=[-0.2057,-0.1291,-0.0588,0.0057,0.0646,0.1185,0.1678,0.2132,0.2545,0.2924,0.3269,0.3585,0.3873,0.4137,0.4373,0.459,0.4784,0.496,0.5119,0.5265,0.5398,0.5521,0.5633,0.5736,0.5833,0.59]; IE=[0.764,0.762,0.7605,0.7605,0.76,0.759,0.757,0.757,0.7555,0.754,0.7505,0.7465,0.7385,0.728,0.7065,0.6755,0.632,0.573,0.499,0.413,0.3165,0.212,0.1035,-0.01,-0.123,-0.21]; PE=VE.*IE; k=1.3806503*10^-23; % k: BOLTZMANN CONSTANT (J/K) q=1.60217646*10^-19; % q: CHARGE ON ELECTRON (COULOMB) NCS=1; % NCS: NUMBER OF CELLS CONNECTED IN SERIES VT=(NCS*k*TEMP)/q; Iph=X(1);Isd=X(2);Rs=X(3);Rsh=X(4);a1=X(5); for i=1:length(IE) t1=Isd*(exp((VE(i)+IE(i)*Rs)/a1*VT)-1); t2=(VE(i)+IE(i)*Rs)/Rsh;% IC(i)=Iph-t1-t2;% IC(i)=(Iph-t1-t2)-IE(i); IC(i)=IE(i)-(Iph-t1-t2); end N=length(IE); %RMSE Fit=sqrt((1/N)*sum((IC-IE).^2)); % NRMSE% Fit=sqrt((1/N)*sum((IC-IE).^2))/sqrt((1/N)*sum((IE).^2)); % target=abs(sum(IC-IE)); end
⛄ 运行结果
⛄ 参考文献
[1] 方宏伟.基于多智能体纵横交叉算法的热电联产经济调度研究[D].广东工业大学[2023-07-29].
[2] 李正硕.纵横交叉算法的优化及其在电力系统调度中的应用[J].[2023-07-29].
[3] 刘凯.纵横交叉算法在地区电网无功优化中的研究与应用[D].广东工业大学,2015.
