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Fredrik Bagge Carlson
SystemIdentification
Commits
0218aa77
Commit
0218aa77
authored
Sep 07, 2015
by
Fredrik Bagge Carlson
Browse files
added cuckoo_search
parent
e5371d18
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src/cuckooSearch.jl
0 → 100644
View file @
0218aa77
using
Devectorize
"""
`cuckoo_search(f,X0;Lb=convert(Float64,Inf),Ub=convert(Float64,Inf),n=25,pa=0.25, Tol=1.0e5, max_iter = 1e5, timeout = Inf)`
\n
`n` = Number of nests (or different solutions)
`pa=0.25` Discovery rate of alien eggs/solutions
Change this if you want to get better results
Based on implementation by
@inproceedings{yang2009cuckoo,
title={Cuckoo search via L{
\'
e}vy flights},
author={Yang, XinShe and Deb, Suash},
booktitle={Nature \& Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on},
pages={210214},
year={2009},
organization={IEEE}
}
http://www.mathworks.com/matlabcentral/fileexchange/29809cuckoosearchcsalgorithm
"""
function
cuckoo_search
(
f
,
X0
;
Lb
=
convert
(
Float64
,
Inf
),
Ub
=
convert
(
Float64
,
Inf
),
n
=
25
,
pa
=
0.25
,
Tol
=
1.0e5
,
max_iter
=
1e5
,
timeout
=
Inf
)
nd
=
size
(
X0
,
1
);
X0t
=
X0
'
Lb
=
Lb
'
Ub
=
Ub
'
if
!
all
(
isfinite
(
Lb
))
Lb
=
X0t

0.99999
*
abs
(
X0t
);
end
if
!
all
(
isfinite
(
Ub
))
Ub
=
X0t
+
0.99999
*
abs
(
X0t
);
end
# Random initial solutions
nest
=
zeros
(
n
,
nd
)
nest
[
1
,
:
]
=
X0
for
i
=
2
:
n
nest
[
i
,
:
]
=
Lb
+
(
Ub

Lb
)
.*
rand
(
size
(
Lb
));
end
# Get the current best
fitness
=
10
^
20
*
ones
(
n
,
1
);
fmin
,
bestnest
,
nest
,
fitness
=
get_best_nest
(
f
,
nest
,
nest
,
fitness
);
N_iter
=
0
;
t0
=
time
()
## Starting iterations
while
fmin
>
Tol
&&
N_iter
<
max_iter
# Generate new solutions (but keep the current best)
new_nest
=
get_cuckoos
(
nest
,
bestnest
,
Lb
,
Ub
);
fnew
,
best
,
nest
,
fitness
=
get_best_nest
(
f
,
nest
,
new_nest
,
fitness
);
# Update the counter
N_iter
+=
n
;
if
fnew
<
fmin
fmin
=
fnew
;
bestnest
=
best
;
end
if
time
()

t0
>
timeout
display
(
"Cuckoo search: timeout
$(timeout)
s reached (
$
(time()t0)s)"
)
break
end
# Discovery and randomization
new_nest
=
empty_nests
(
nest
,
Lb
,
Ub
,
pa
)
;
# Evaluate this set of solutions
fnew
,
best
,
nest
,
fitness
=
get_best_nest
(
f
,
nest
,
new_nest
,
fitness
);
# Update the counter again
N_iter
+=
n
;
# Find the best objective so far
if
fnew
<
fmin
fmin
=
fnew
;
bestnest
=
best
;
end
if
time
()

t0
>
timeout
display
(
"Cuckoo search: timeout
$(timeout)
s reached (
$
(time()t0)s)"
)
break
end
end
## End of iterations
## Postoptimization processing
## Display all the nests
println
(
"Total number of iterations="
,
N_iter
);
squeeze
(
bestnest
'
,
2
),
fmin
end
##  All subfunctions are list below 
## Get cuckoos by ramdom walk
function
get_cuckoos
(
nest
,
best
,
Lb
,
Ub
)
# Levy flights
n
=
size
(
nest
,
1
);
# Levy exponent and coefficient
# For details, see equation (2.21), Page 16 (chapter 2) of the book
# X. S. Yang, NatureInspired Metaheuristic Algorithms, 2nd Edition, Luniver Press, (2010).
beta
=
3
/
2
;
sigma
=
(
gamma
(
1
+
beta
)
*
sin
(
pi
*
beta
/
2
)
/
(
gamma
((
1
+
beta
)
/
2
)
*
beta
*
2
^
((
beta

1
)
/
2
)))
^
(
1
/
beta
);
for
j
=
1
:
n
s
=
nest
[
j
,
:
];
# This is a simple way of implementing Levy flights
# For standard random walks, use step=1;
## Levy flights by Mantegna’s algorithm
u
=
randn
(
size
(
s
))
*
sigma
;
v
=
randn
(
size
(
s
));
betai
=
1
/
beta
@devec
step
=
u
./
abs
(
v
)
.^
betai
;
# In the next equation, the difference factor (sbest) means that
# when the solution is the best solution, it remains unchanged.
stepsize
=
0.01
*
step
.*
(
s

best
);
# Here the factor 0.01 comes from the fact that L/100 should the typical
# step size of walks/flights where L is the typical lenghtscale;
# otherwise, Levy flights may become too aggresive/efficient,
# which makes new solutions (even) jump out side of the design domain
# (and thus wasting evaluations).
# Now the actual random walks or flights
s
=
s
+
stepsize
.*
randn
(
size
(
s
));
# Apply simple bounds/limits
nest
[
j
,
:
]
=
simplebounds
(
s
,
Lb
,
Ub
);
end
nest
end
## Find the current best nest
function
get_best_nest
(
f
,
nest
,
newnest
,
fitness
)
# Evaluating all new solutions
for
j
=
1
:
size
(
nest
,
1
)
fnew
=
f
(
squeeze
(
newnest
[
j
,
:
]
'
,
2
));
if
fnew
<=
fitness
[
j
]
fitness
[
j
]
=
fnew
;
nest
[
j
,
:
]
=
newnest
[
j
,
:
];
end
end
# Find the current best
(
fmin
,
K
)
=
findmin
(
fitness
)
;
best
=
nest
[
K
,
:
];
fmin
,
best
,
nest
,
fitness
end
## Replace some nests by constructing new solutions/nests
function
empty_nests
(
nest
,
Lb
,
Ub
,
pa
)
# A fraction of worse nests are discovered with a probability pa
n
=
size
(
nest
,
1
);
# Discovered or not  a status vector
K
=
rand
(
size
(
nest
))
.>
pa
;
# In the real world, if a cuckoo’s egg is very similar to a host’s eggs, then
# this cuckoo’s egg is less likely to be discovered, thus the fitness should
# be related to the difference in solutions. Therefore, it is a good idea
# to do a random walk in a biased way with some random step sizes.
## New solution by biased/selective random walks
stepsize
=
rand
()
*
(
nest
[
randperm
(
n
),
:
]

nest
[
randperm
(
n
),
:
]);
new_nest
=
nest
+
stepsize
.*
K
;
end
# Application of simple constraints
function
simplebounds
(
s
,
Lb
,
Ub
)
# Apply the lower bound
ns_tmp
=
s
;
I
=
ns_tmp
.<
Lb
;
ns_tmp
[
I
]
=
Lb
[
I
];
# Apply the upper bounds
J
=
ns_tmp
.>
Ub
;
ns_tmp
[
J
]
=
Ub
[
J
];
# Update this new move
s
=
ns_tmp
;
end
# # ## You can replace the following by your own functions
# # # A ddimensional objective function
# # function fobj(u)
# # ## ddimensional sphere function sum_j=1^d (u_j1)^2.
# # # with a minimum at (1,1, ...., 1);
# # z=sum((u1).^2);
# # end
# # dims = 10
# # cuckoo_search(fobj,zeros(dims),10*ones(dims),10*ones(dims))
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