A brief introduction to genetic algorithms
1 the introduction 
Two, some source code
% this program is designed foroptimal substation placement %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %function SP_main(a)
clear; clc; pack; tic; display('______________________________________ RESULTS STARTED _____________________________________');
global T L FinalTransPow FinalLoad FinalTransCap TransTypes AuxTransCap AuxTransPow K2 K3 MaxT
global SelCaseRow FinalTrans_x FinalTrans_y FinalLoad_x FinalLoad_x FinalLoad_y BrTransIndex
global AuxFinalTrans_x AuxFinalTrans_y AuxFinalLoad_x AuxFinalLoad_x AuxFinalLoad_y AuxFinalLoad
global FinalTLDistances VarCheckPrg
global finaltranspow finaltranscap
global PowerFactor UtilizationFactor TransformersTypes KWTransformersTypes
global InstallCosts OpenCircuitLosses ShortCircuitLosses
global CurrentTr_x CurrentTr_y
K2 = 0.0035 e-3;
K3 = 0.64;
% determination of load centers & the vector of load values
DATA = xlsread('DATA.xls'.'Loads');
CANDIDATES = xlsread('DATA.xls'.'Candidates');
CURRENT_TRANSFORMERS = xlsread('DATA.xls'.'Current_Transformers');
DESIGN_CONSTANTS = xlsread('DATA.xls'.'Design_Constants');
TRANSFORMERS_TYPES = xlsread('DATA.xls'.'Transformers_Types');
ExcelLoad_x = DATA(:,1);
ExcelLoad_y = DATA(:,2);
ExcelLoads = DATA(:,3);
ExcelCandidates_x = CANDIDATES(:,1);
ExcelCandidates_y = CANDIDATES(:,2);
PowerFactor = DESIGN_CONSTANTS(1.1);
UtilizationFactor = DESIGN_CONSTANTS(1.2) /100;
TransformersTypes(1,:) = sort(TRANSFORMERS_TYPES(:,1));
KWTransformersTypes = ceil(UtilizationFactor*PowerFactor*TransformersTypes);
InstallCosts(1,:) = sort(TRANSFORMERS_TYPES(:,2));
OpenCircuitLosses(1,:) = sort(TRANSFORMERS_TYPES(:,3));
ShortCircuitLosses(1,:) = sort(TRANSFORMERS_TYPES(:,4));
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Loads(1,:) = ExcelLoads(:,1);
Load_x(1,:) = ExcelLoad_x(:,1);
Load_y(1,:) = ExcelLoad_y(:,1);
Candidates_x(1,:) = ExcelCandidates_x(:,1);
Candidates_y(1,:) = ExcelCandidates_y(:,1);
if length(CURRENT_TRANSFORMERS) ~= 0
CurrentTr_x = CURRENT_TRANSFORMERS(:,1)'; CurrentTr_y = CURRENT_TRANSFORMERS(:,2)';
CurrentTrCap = CURRENT_TRANSFORMERS(:,3)'; CurrentTrPow = ceil(UtilizationFactor*PowerFactor*CurrentTrCap); else CurrentTr_x = []; CurrentTr_y = []; CurrentTrCap = []; CurrentTrPow = []; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % initialize transformer locations and powers % one transformer in every load center. initially we assume the first % transformer for all candidate points. TransTypes = length(TransformersTypes); LoadCenters = length(ExcelLoads); CurrentTrNo = length(CurrentTr_x); CandidateNo = length(ExcelCandidates_x); for count1=1:CurrentTrNo, if CurrentTrPow(1,count1) >= ceil((400*UtilizationFactor*PowerFactor)) LimitedCurrentTrPow(1,count1) = KWTransformersTypes (1, 6); The else LimitedCurrentTrPow (1, count1) = KWTransformersTypes (1, 1); end; end; Trans_x = [CurrentTr_x Candidates_x]; Trans_y = [CurrentTr_y Candidates_y]; TransCap = [LimitedCurrentTrPow (KWTransformersTypes(1,1) + Zeros (1, Length (ExcelCandidates_x)))]; CandidateCenters = length(TransCap); % current + candidate transformers TransPow = zeros(1,CandidateCenters); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % calculation of the distances between transformers % this is a matrice with dimensions: (LoadCenters)*(CandidateCenters) Distances = zeros(LoadCenters,CandidateCenters); for count1=1:LoadCenters, for count2=1:CandidateCenters, Distances(count1,count2) = sqrt((Load_x(1,count1)-Trans_x(1,count2))^2 + (Load_y(1,count1)-Trans_y(1,count2))^2); end; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CanDistances = zeros(CandidateCenters); for count1=1:CandidateCenters, for count2=1:count1, CanDistances(count1,count2) = sqrt((Trans_x(1,count1)-Trans_x(1,count2))^2 + (Trans_y(1,count1)-Trans_y(1,count2))^2); CanDistances(count2,count1) = CanDistances(count1,count2); end; end; % the distances are pairly compared with 100, if they are smaller than 100 % the transformer with smaller value of load is detached. for count1=1:CandidateCenters, for count2=1:CandidateCenters, if (CanDistances(count1,count2) <= 100) & (count1 ~= count2) & (count1 > CurrentTrNo) TransCap(1,count1) = 0; TransPow(1,count1) = 0; end; end; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % this function step-up the transformers size until it can feed the total % loads connected to it. % for count1=1:TransTypes, % for count2=1:LoadCenters, % if (TransCap(1,count2) < Loads(1,count2)) && (TransCap(1,count2) ~= 0) % TransCap(1,count2) = SP_stepup(TransCap(1,count2)); % end; % end; % end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % in this subsection, the coordinations of the final possible transformers % are saved in FinalTrans_x & FinalTrans_y and their values in % FinalTransCap. similarly, the coordinations of the loadcenters to be % attached to transformers are saved in FinalLoad_x & FinalLoad_y and their % values in FinalLoad. T = 1; L = LoadCenters; for count1 = 1:CandidateCenters, if (TransCap(1,count1) ~= 0) FinalTransCap(1,T) = TransCap(1,count1); FinalTransPow(1,T) = 0; FinalTrans_x(1,T) = Trans_x(1,count1); FinalTrans_y(1,T) = Trans_y(1,count1); T = T+1; end; end; MaxT = T-1; % MinL = L-1; % if ((MaxT > 23) & (VarCheckPrg == 1)) % warndlg('MATLAB unable to solve! Try smaller number of loads'.' DSP Warning');
% display('MATLAB unable to solve! Try smaller number of loads');
% return; % end; AuxTransCap = FinalTransCap; AuxTransPow = FinalTransPow; AuxFinalTrans_x = FinalTrans_x; AuxFinalTrans_y = FinalTrans_y; AuxFinalLoad_x = Load_x; AuxFinalLoad_y = Load_y; AuxFinalLoad = Loads; % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %calculation of Distances beetween transformers and loads in a (MinL*MaxT) matrice.
for count1=1:LoadCenters,
for count2=1:MaxT,
TLDistances(count1,count2) = sqrt((AuxFinalLoad_x(1,count1)-AuxFinalTrans_x(1,count2))^2 + (AuxFinalLoad_y(1,count1)-AuxFinalTrans_y(1,count2))^2);
end;
end;
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% HERE, THE OPERATION OF GENETIC ALGORITHM IS STARTED.
TotalLevels = 0;
LowLim = CurrentTrNo;
MaxLim = LowLim + (MaxT-CurrentTrNo);
for count5=LowLim:MaxLim,
TotalLevels = TotalLevels + ceil(nchoosek(MaxT,count5));
end;
ScalingFactor = ceil(TotalLevels/20);
TotalLevels = ceil(TotalLevels/ScalingFactor);
Index = 0;
TMat = [(CurrentTrNo+1):MaxT];
% if ((TotalLevels < 20) & (VarCheckPrg == 1))
% warndlg('Try smaller Scaling Factor! '.' DSP Warning');
% display('Try smaller Scaling Factor! ');
% return;
% end;
% if ((TotalLevels > 300) & (VarCheckPrg == 1))
% warndlg('Try bigger Scaling Factor! '.' DSP Warning');
% display('Try bigger Scaling Factor! ');
% return;
% end;
% if ((VarCheckPrg == 1) & ((TotalLevels <= 300) & (TotalLevels >= 20)))
% warndlg('No problem in running program. Push "Run DSP"'.' DSP Warning');
% LEVELS = TotalLevels;
% LEVELS
% display('No problem in running program. Push "Run DSP"');
% return;
% end;
close all;
pack;
cfinaltranscap = cell(TotalLevels,1);
cfinaltranspow = cell(TotalLevels,1);
cfinaltrans_x = cell(TotalLevels,1);
cfinaltrans_y = cell(TotalLevels,1);
cfinalload = cell(TotalLevels,1);
cfinalload_x = cell(TotalLevels,1);
cfinalload_y = cell(TotalLevels,1);
pack;
h = waitbar(0.'Please wait... ');
for count1=0:(MaxLim-LowLim), % MAIN for. NOTE: "count1" stands for the number of new trans.
T = LowLim + count1; % "LowLim" stands for the number of current transformers.
numberOfVariables = LoadCenters;
L = numberOfVariables;
SelCaseMat = nchoosek(TMat,count1);
SIZE = size(SelCaseMat);
RowNumber = SIZE(1.1);
for count2=1:ScalingFactor:RowNumber,
Index = Index + 1;
Level = Index;
SelCaseRow = [[1:CurrentTrNo] SelCaseMat(count2,:)]; % SelCaseRow should be sent to SP_create.m. It is a selection of transformers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % modifying FinalTrans_x,y & FinalLoad_x,y & FinalLoad & % FinalTransPow & FinalTransCap finaltranscap = zeros(1,MaxT) - 1;
finaltranspow = zeros(1,MaxT) - 1;
finaltrans_x = zeros(1,MaxT) - 1;
finaltrans_y = zeros(1,MaxT) - 1;
for count3=1:T,
finaltranscap(1,SelCaseRow(1,count3)) = AuxTransCap(1,SelCaseRow(1,count3));
finaltranspow(1,SelCaseRow(1,count3)) = AuxTransPow(1,SelCaseRow(1,count3));
finaltrans_x(1,SelCaseRow(1,count3)) = AuxFinalTrans_x(1,SelCaseRow(1,count3));
finaltrans_y(1,SelCaseRow(1,count3)) = AuxFinalTrans_y(1,SelCaseRow(1,count3));
end;
FinalTransCap = finaltranscap;
FinalTransPow = finaltranspow;
FinalTrans_x = finaltrans_x;
FinalTrans_y = finaltrans_y;
cfinaltranscap{Index} = finaltranscap;
cfinaltranspow{Index} = finaltranspow;
cfinaltrans_x{Index} = finaltrans_x;
cfinaltrans_y{Index} = finaltrans_y;
finalload = Loads;
finalload_x = Load_x;
finalload_y = Load_y;
% Li = 0;
% for count3=1:LoadCenters,
% if (size(find(FinalTrans_x==Load_x(1,count3)))==[1 0] | size(find(FinalTrans_y==Load_y(1,count3)))==[1 0])
% Li = Li + 1;
% finalload(1,Li) = Loads(1,count3);
% finalload_x(1,Li) = Load_x(1,count3);
% finalload_y(1,Li) = Load_y(1,count3);
% end;
% end;
Copy the code3. Operation results
Matlab version and references
1 matlab version 2014A
[1] Yang Baoyang, YU Jizhou, Yang Shan. Intelligent Optimization Algorithm and Its MATLAB Example (2nd Edition) [M]. Publishing House of Electronics Industry, 2016. [2] ZHANG Yan, WU Shuigen. MATLAB Optimization Algorithm source code [M]. Tsinghua University Press, 2017.