figure(1);
fplot('variable.*sin(10*pi*variable)+2.0',[-1,2]); %畫出函數曲線
%定義遺傳演算法參數
NIND=40; %個體數目(Number of individuals)
MAXGEN=25; %最大遺傳代數(Maximum number of generations)
PRECI=20; %變數的二進位位元(Precision of variables)
GGAP=0.9; %代溝(Generation gap)
trace=zeros(2, MAXGEN); %尋優結果的初始值
FieldD=[20;-1;2;1;0;1;1]; %地區描述器(Build field descriptor)
Chrom=crtbp(NIND, PRECI); %初始種群
gen=0; %代計數器
variable=bs2rv(Chrom, FieldD); %計算初始種群的十進位轉換
ObjV=variable.*sin(10*pi*variable)+2.0; %計算目標函數值
while gen<MAXGEN
FitnV=ranking(-ObjV); %分配適應度值(Assign fitness values)
SelCh=select('sus', Chrom, FitnV, GGAP); %選擇
SelCh=recombin('xovsp', SelCh, 0.7); %重組
SelCh=mut(SelCh); %變異
variable=bs2rv(SelCh, FieldD); %子代個體的十進位轉換
ObjVSel=variable.*sin(10*pi*variable)+2.0; %計運算元代的目標函數值
[Chrom ObjV]=reins(Chrom, SelCh, 1, 1, ObjV, ObjVSel); %重插入子代的新種群
variable=bs2rv(Chrom, FieldD);
gen=gen+1; %代計數器增加
%輸出最優解及其序號，並在目標函數映像中標出，Y為最優解,I為種群的序號
[Y, I]=max(ObjV);hold on;
plot(variable(I), Y, 'bo');
trace(1, gen)=max(ObjV); %遺傳演算法效能跟蹤
trace(2, gen)=sum(ObjV)/length(ObjV);
end
variable=bs2rv(Chrom, FieldD); %最優個體的十進位轉換
hold on grid;
plot(variable,ObjV,'b*');
figure(2);
plot(trace(1,:));
hold on;
plot(trace(2,:),'-.');grid
legend('解的變化','種群均值的變化')
CRTBP.m - Create an initial population
This function creates a binary population of given size and structure.
Syntax: [Chrom Lind BaseV] = crtbp(Nind, Lind, Base)
Input Parameters:
Nind - Either a scalar containing the number of individuals
in the new population or a row vector of length two
containing the number of individuals and their length.
Lind - A scalar containing the length of the individual
chromosomes.
Base - A scalar containing the base of the chromosome
elements or a row vector containing the base(s)
of the loci of the chromosomes.
Output Parameters:
Chrom - A matrix containing the random valued chromosomes
row wise.
Lind - A scalar containing the length of the chromosome.
BaseV - A row vector containing the base of the
chromosome loci.
Author: Andrew Chipperfield
Date: 19-Jan-94
Tested under MATLAB v6 by Alex Shenfield (20-Jan-03)
BS2RV.m - Binary string to real vector
This function decodes binary chromosomes into vectors of reals. The
chromosomes are seen as the concatenation of binary strings of given
length, and decoded into real numbers in a specified interval using
either standard binary or Gray decoding.
Syntax: Phen = bs2rv(Chrom,FieldD)
Input parameters:
Chrom - Matrix containing the chromosomes of the current
population. Each line corresponds to one
individual's concatenated binary string
representation. Leftmost bits are MSb and
rightmost are LSb.
FieldD - Matrix describing the length and how to decode
each substring in the chromosome. It has the
following structure:
[len; (num)
lb; (num)
ub; (num)
code; (0=binary | 1=gray)
scale; (0=arithmetic | 1=logarithmic)
lbin; (0=excluded | 1=included)
ubin]; (0=excluded | 1=included)
where
len - row vector containing the length of
each substring in Chrom. sum(len)
should equal the individual length.
lb,
ub - Lower and upper bounds for each
variable.
code - binary row vector indicating how each
substring is to be decoded.
scale - binary row vector indicating where to
use arithmetic and/or logarithmic
scaling.
lbin,
ubin - binary row vectors indicating whether
or not to include each bound in the
representation range
Output parameter:
Phen - Real matrix containing the population phenotypes.
Author: Carlos Fonseca, Updated: Andrew Chipperfield,
Date: 08/06/93, Date: 26-Jan-94,
Tested under MATLAB v6 by Alex Shenfield (17-Jan-03) RANKING.M (RANK-based fitness assignment)
This function performs ranking of individuals.
Syntax: FitnV = ranking(ObjV, RFun, SUBPOP)
This function ranks individuals represented by their associated
cost, to be *minimized*, and returns a column vector FitnV
containing the corresponding individual fitnesses. For multiple
subpopulations the ranking is performed separately for each
subpopulation.
Input parameters:
ObjV - Column vector containing the objective values of the
individuals in the current population (cost values).
RFun - (optional) If RFun is a scalar in [1, 2] linear ranking is
assumed and the scalar indicates the selective pressure.
If RFun is a 2 element vector:
RFun(1): SP - scalar indicating the selective pressure
RFun(2): RM - ranking method
RM = 0: linear ranking
RM = 1: non-linear ranking
If RFun is a vector with length(Rfun) > 2 it contains
the fitness to be assigned to each rank. It should have
the same length as ObjV. Usually RFun is monotonously
increasing.
If RFun is omitted or NaN, linear ranking
and a selective pressure of 2 are assumed.
SUBPOP - (optional) Number of subpopulations
if omitted or NaN, 1 subpopulation is assumed
Output parameters:
FitnV - Column vector containing the fitness values of the
individuals in the current population.
Author: Hartmut Pohlheim (Carlos Fonseca)
History: 01.03.94 non-linear ranking
10.03.94 multiple populations
21.01.03 updated for MATLAB v6 by Alex Shenfield SELECT.M (universal SELECTion)
This function performs universal selection. The function handles
multiple populations and calls the low level selection function
for the actual selection process.
Syntax: SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP)
Input parameters:
SEL_F - Name of the selection function
Chrom - Matrix containing the individuals (parents) of the current
population. Each row corresponds to one individual.
FitnV - Column vector containing the fitness values of the
individuals in the population.
GGAP - (optional) Rate of individuals to be selected
if omitted 1.0 is assumed
SUBPOP - (optional) Number of subpopulations
if omitted 1 subpopulation is assumed
Output parameters:
SelCh - Matrix containing the selected individuals.
Author: Hartmut Pohlheim
History: 10.03.94 file created
22.01.03 tested under MATLAB v6 by Alex Shenfield RECOMBIN.M (RECOMBINation high-level function)
This function performs recombination between pairs of individuals
and returns the new individuals after mating. The function handles
multiple populations and calls the low-level recombination function
for the actual recombination process.
Syntax: NewChrom = recombin(REC_F, OldChrom, RecOpt, SUBPOP)
Input parameters:
REC_F - String containing the name of the recombination or
crossover function
Chrom - Matrix containing the chromosomes of the old
population. Each line corresponds to one individual
RecOpt - (optional) Scalar containing the probability of
recombination/crossover occurring between pairs
of individuals.
if omitted or NaN, 1 is assumed
SUBPOP - (optional) Number of subpopulations
if omitted or NaN, 1 subpopulation is assumed
Output parameter:
NewChrom - Matrix containing the chromosomes of the population
after recombination in the same format as OldChrom.
Author: Hartmut Pohlheim
History: 18.03.94 file created
22.01.03 tested under MATLAB v6 by Alex Shenfield
(NOTE : doesn't work with low level recmut.m) MUT.m
This function takes the representation of the current population,
mutates each element with given probability and returns the resulting
population.
Syntax: NewChrom = mut(OldChrom,Pm,BaseV)
Input parameters:
OldChrom - A matrix containing the chromosomes of the
current population. Each row corresponds to
an individuals string representation.
Pm - Mutation probability (scalar). Default value
of Pm = 0.7/Lind, where Lind is the chromosome
length is assumed if omitted.
BaseV - Optional row vector of the same length as the
chromosome structure defining the base of the
individual elements of the chromosome. Binary
representation is assumed if omitted.
Output parameter:
NewChrom - A Matrix containing a mutated version of
OldChrom.
Author: Andrew Chipperfield
Date: 25-Jan-94
Tested under MATLAB v6 by Alex Shenfield (21-Jan-03) REINS.M (RE-INSertion of offspring in population replacing parents)
This function reinserts offspring in the population.
Syntax: [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel)
Input parameters:
Chrom - Matrix containing the individuals (parents) of the current
population. Each row corresponds to one individual.
SelCh - Matrix containing the offspring of the current
population. Each row corresponds to one individual.
SUBPOP - (optional) Number of subpopulations
if omitted or NaN, 1 subpopulation is assumed
InsOpt - (optional) Vector containing the insertion method parameters
ExOpt(1): Select - number indicating kind of insertion
0 - uniform insertion
1 - fitness-based insertion
if omitted or NaN, 0 is assumed
ExOpt(2): INSR - Rate of offspring to be inserted per
subpopulation (% of subpopulation)
if omitted or NaN, 1.0 (100%) is assumed
ObjVCh - (optional) Column vector containing the objective values
of the individuals (parents - Chrom) in the current
population, needed for fitness-based insertion
saves recalculation of objective values for population
ObjVSel - (optional) Column vector containing the objective values
of the offspring (SelCh) in the current population, needed for
partial insertion of offspring,
saves recalculation of objective values for population
Output parameters:
Chrom - Matrix containing the individuals of the current
population after reinsertion.
ObjVCh - if ObjVCh and ObjVSel are input parameters, then column
vector containing the objective values of the individuals
of the current generation after reinsertion.
Author: Hartmut Pohlheim
History: 10.03.94 file created
19.03.94 parameter checking improved
26.01.03 tested under MATLAB v6 by Alex Shenfield
