• Since the 1970s that the idea of a general algorithmic framework, which
can be applied with relatively few modifications to different optimization
problems, emerged.
• Metaheuristics: methods that combine rules and randomness while
imitating natural phenomena.
• These methods are from now on regularly employed in all the sectors of
business, industry, engineering.
• Besides all of the interest necessary to application of metaheuristics,
occasionally a new metaheuristic algorithm is introduced that uses a
novel metaphor as guide for solving optimization problems.
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• particle swarm optimization algorithm (PSO): models the flocking
behavior of birds;
• harmony search (HS): models the musical process of searching for a
perfect state of harmony;
• bacterial foraging optimization algorithm (BFOA): models foraging
as an optimization process where an animal seeks to maximize
energy per unit time spent for foraging;
• artificial bee colony (ABC): models the intelligent behavior of
honey bee swarms;
• League Championship algorithm (LCA): tries to mimic a
championship environment wherein artificial teams play in an
artificial league for several weeks
• fire fly algorithm (FA): performs based on the idealization of the
flashing characteristics of fireflies.
• Optics Inspired Optimization (OIO): performs based on the
rationale of optical characteristics of concave and convex mirrors.
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Analyze
step
Exploit
step
Find
step
F3EA
metaheuristic
Finish
Step
Fix
step
 In 2014 General S.A. McChrystal wrote about the “F3EA” targeting cycle which had
been, used in the Afghanistan and Iraq wars.
 Find: the process through which targets (i.e., person or location) are identified.
 Fix: the process that allows the prepared targets to be monitored in preparation for
action.
 Finish: the process by which targets are actioned, killed or destroyed.
 Exploit: the process by which opportunities presented by the target effect are

identified (target site exploitation, gathering information from the target area, battle
damage assessment)
Analyze: is an assessment phase that pertains to the results of attacks on targets.
 The F3EA metaheuristic algorithm specifically mimics the
targeting process
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The F3EA metaheuristic algorithm is composed of five steps.
 The Find step imitates the target selection process.
 This step is a new selection mechanism to evolutionary computations.
 Here we imitate the detection process followed by military radar devices.
 The Fix step mimics the aiming process toward the target to monitor it
 It is a local search step,
 This step is modeled as a single variable optimization problem to scan the
function surface on a given path to determine the location of a local
optimum via line search techniques.
 The Finish step develops an adaptive mutation stage. Here we use the
projectile motion equations to develop a mathematical model for
generation of new solutions.
 In the Exploit step, we seek for opportunities presented in mating the
solutions by crossover operation.
 The Analyze step is a replacement step by which whenever a new solution
generated during the Fix or Exploit step provided a better function value, it
enters into population or updates the global best solution found so far.
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Echo
signals
These objects are
detectable with respect to
their size and distance
from radar
Transmitt
ed energy
R max  4  pGA (4 ) 2 S min
The most important use of the radar range equation is the determination of the maximum
range at which a target has a high probability of being detected by the radar.
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 To imitate the radar process of detecting military objects to attain
an individual selection mechanism for evolutionary computation
 Each individual is treated as an enemy’s military facility.
 To generate a new solution from the i-th individual parent solution
- assume that the parent solution Pi t temporarily makes role as an
artificial radar device
- all other individuals Pjt are assumed to be enemy’s military
facilities that may or may not be detected by the artificial radar
R
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t
max ij
 (f (Pi )  f
t
t
min
 f  f (P ) 
) 4  t
e
t
 f max  f min



t
max
t
j
t
 f ( P jt )  f min
a 
t
 f ( Pit )  f min





,i  j
Among all detectable individuals by Pi t , one can be selected based on any logic to
generate a new solution in the so-called Finish step of the F3EA algorithm .
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 During this step, an artificial rocket is launched from Pi t towards Pjt
and the explosion position E ijt which is determined via the projectile
motion equations, forms a new solution in the domain.
 To develop the model of the Finish step, we need to assume that:
- The artificial rocket is a time bomb which will be exploded a
certain duration after its launch.
- Neglecting the air or wind drag, the explosion time is equal to the
theoretic rocket’s time of fight.
- When the rocket is launched, it is subjected to an air drag force.
Wind also blows which produces a force.
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11
x (T )  w ij T  m (v
t
ij
t
x
t
ij
t
ij
z (T )  w ij T  m w
t
ij
t
z
t
ij
E it  Pi t  x (T ijt )
t
ij
t
z
t
0 ij
ij
cos  w
(1  e
(Pjt  Pi t )
Pjt  Pi t
t
ij
T ijt m ijt
 z (T ijtk )
t
x
ij
)(1  e
T ijt m ijt
)
)
( Z ijt  )
Z ijt 
x (T ijt ) is the explosion position on the line connecting Pi t and Pjt (x-axis)
z (T ijt ) is the explosion position on the so called z-axis
• E it is a the position of new solution generated in the Finish step.
• Its extraction is completely matched with theoretical Physics and
can be obtained by simulation of the projectile motion.
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13
 The Fix step which is a local search step mimics the aiming process
toward the target to monitor it.
 From figure, to hit the military tank target, the angle by which the
rocket is launched should be acute enough that the rocket traverses
the highest peak.
 We implement such an idea as a single-variable optimization
problem in the Fix step of F3EA metaheuristic to obtain locally
improved solutions.
f (G0t  S t )
G 0t   *S t
G 0t
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Gdt  Gdt 1  sdt ed
min f (Gdt 1  s dt ed )
s. t.  dt (x min,d  g dt 1,d )  s dt   dt (x max,d  g dt 1,d )
min f (G 0t  S t )
s. t. min    max

 min  ( x
d 1,..., n
t
t
(
x

g
)
s
 min,d 0d d 
d 1,..., n
 g 0t d ) s dt 
min  max
max
15
max,d


t
t
,
(
x

g
)
s
max,d
0d
d 
s t 0 
s dt  0
t
t
,
(
x

g
)
s

min,d
0d
d 
0
s dt  0
d
s dt
• The Exploit step of F3EA metaheuristic algorithm tries to
exploit the outcome of the Finish step via crossover operations.
t
• The feasible solution E it differs from Pi in all dimensions.
• Due to the early convergence of the algorithm to local optima,
it may not be a good choice to make changes in all dimensions
• To simulate the number of changes, we use a truncated
geometric distribution.
t n

 t
ln(1

(1

(1

q
t
i ) ) rand(0,1))
ci  
 , c i  {1, 2,..., n }
t
ln(1  q i )


16
q it  1, q it  0
• The Analyze step, is a replacement step.
• New solutions which are generated during the Fix or Exploit
steps may enter to population or update the global best
solution.
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

f ( x )   100 ( x  x )  (1  x )

f ( x )   ( x  10 cos(2x )  10 )

f1 ( x ) 
n
xi2
i 1
n 1
2
2
i
i 1
n
3
i 1
2
2
i 1
2
i
xi  [5.12,5.12]
i

x  
i 1



exp( 1 .
n
n
i 1
n
2
i
x i  [32 , 32]
cos(2xi ))  20  e
f 5 (x )   i 1 x i sin( x i )
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xi  [2.048 ,2.048 ]
i


f 4 ( x )  20 exp   0.2 1 .
n

n
xi  [100 ,100 ]
xi  [512 .03,511 .97 ]
 The number of variables is considered as 30.
 The termination criteria is either counting 1E+05 function
evaluations or reaching the global minimum within the gap of 1E-3.
 As the only input parameter, The population size of F3EA algorithm
is set to 50.
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