👂🎴 🕸️
The
term
„
heuristics
“
comes
from
the
Greek
word
„
heuriskein
''
“
which
means
„
to
find
“
or
„
to
discover
.
“
This
term
reflects
the
idea
of
finding
or
discovering
solutions
through
intuitive
or
trial
-
and
-
error
methods
.
<
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>
Mathematico
-
logical
heuristics
involve
using
structured
mathematical
or
logical
methods
to
solve
problems
.
They
include
techniques
like
calculus
for
optimizing
functions
''
linear
programming
for
maximizing
or
minimizing
linear
objectives
under
constraints
''
and
3
-
SAT
for
solving
complex
logical
puzzles
.
These
heuristics
apply
rigorous
mathematical
rules
and
logic
to
break
down
and
solve
problems
step
-
by
-
step
.
They
are
especially
useful
for
structured
problems
where
precise
''
logical
solutions
are
needed
''
like
in
operations
research
''
computer
science
''
and
engineering
.<
br
>
div
>
<
div
>
Calculus
-
based
heuristics
''
like
Newton
'
s
method
or
gradient
descent
''
use
principles
of
calculus
to
find
solutions
to
complex
problems
.
They
involve
calculating
slopes
or
gradients
to
understand
how
a
function
changes
.
For
instance
''
gradient
descent
moves
towards
the
lowest
point
of
a
function
''
similar
to
finding
the
bottom
of
a
valley
-
this
point
is
often
the
best
solution
.
These
methods
are
powerful
for
optimizing
problems
''
like
in
machine
learning
or
economics
''
where
finding
the
most
efficient
point
is
crucial
.<
br
>
div
>
The
3
-
SAT
(
3
-
Satisfiability
)
problem
is
a
classic
question
in
computer
science
and
mathematical
logic
.
It
'
s
a
specific
type
of
Boolean
satisfiability
problem
.
In
3
-
SAT
''
you
'
re
given
a
formula
composed
of
several
clauses
''
where
each
clause
is
a
disjunction
(
an
„
OR
“
operation
)
of
exactly
three
literals
(
variables
or
their
negations
).
The
challenge
is
to
determine
if
there
exists
an
assignment
of
truth
values
(
true
or
false
)
to
the
variables
that
makes
the
entire
formula
true
.
This
problem
is
known
for
being
<
strong
>
NP
-
complete
''
meaning
it
'
s
easy
to
check
a
solution
but
potentially
very
hard
to
find
one
strong
>''
especially
as
the
number
of
variables
increases
.
This
characteristic
makes
3
-
SAT
important
in
theoretical
computer
science
''
particularly
in
studies
related
to
computational
complexity
.
Nature
-
inspired
heuristics
are
problem
-
solving
methods
modeled
after
natural
processes
.
Like
how
birds
flock
or
bees
forage
''
these
algorithms
mimic
nature
to
tackle
complex
problems
.
They
use
strategies
like
evolution
''
ant
colony
behavior
''
or
bird
flocking
to
find
good
solutions
''
blending
randomness
with
specific
rules
from
nature
.
These
methods
are
useful
for
tough
problems
where
traditional
approaches
might
fail
''
creatively
applying
nature
'
s
wisdom
to
areas
like
computer
science
''
engineering
''
and
logistics
to
find
efficient
''
often
surprising
''
solutions
.
<
div
>
Simulated
Annealing
is
a
technique
for
finding
good
solutions
to
tough
problems
.
It
'
s
like
trying
different
temperatures
to
shape
a
metal
perfectly
.
At
first
''
it
allows
big
changes
(
high
temperature
)''
even
if
they
seem
wrong
''
to
explore
different
options
.
Gradually
''
it
cools
down
(
lowers
the
temperature
)''
making
smaller
''
more
careful
adjustments
.
This
process
helps
avoid
getting
stuck
with
a
not
-
so
-
great
solution
(
local
optimum
)
and
aims
for
a
better
one
''
although
it
might
not
always
be
the
best
possible
(
global
optimum
).<
br
>
div
>
<
div
>
Ant
Colony
Optimization
is
inspired
by
how
real
ants
find
the
shortest
paths
to
food
.
In
this
method
''
virtual
ants
roam
through
possible
solutions
''
leaving
pheromone
trails
.
Stronger
trails
attract
more
ants
''
suggesting
better
solutions
.
Over
time
''
the
best
paths
have
more
pheromones
''
guiding
ants
towards
them
.
It
'
s
great
for
complex
problems
like
routing
or
scheduling
''
where
finding
the
best
route
matters
.
It
'
s
like
following
a
trail
to
the
best
answer
based
on
the
collective
wisdom
of
many
trials
.<
br
>
div
>
Evolutionary
Optimization
mimics
natural
selection
''
like
how
animals
evolve
.
Imagine
a
population
of
potential
solutions
.
Those
fitting
the
problem
best
(
like
the
fittest
animals
)
are
chosen
to
'
reproduce
.'
They
mix
and
mutate
to
create
new
solutions
or
'
offspring
.'
Over
generations
''
this
process
'
evolves
'
better
solutions
''
as
unfit
ones
are
discarded
.
It
'
s
a
trial
-
and
-
error
method
using
principles
of
evolution
''
effectively
finding
good
solutions
for
complex
problems
by
simulating
survival
of
the
fittest
in
a
virtual
environment
.
Caching
is
a
technique
used
in
computing
to
store
frequently
accessed
data
in
a
readily
available
location
for
quick
retrieval
.
It
'
s
like
having
a
small
''
fast
memory
space
for
storing
the
most
commonly
used
information
''
reducing
the
need
to
repeatedly
access
slower
storage
areas
.
In
problem
-
solving
''
caching
is
crucial
for
enhancing
performance
and
efficiency
.
By
remembering
previously
computed
results
''
systems
can
avoid
redoing
complex
calculations
''
significantly
speeding
up
the
process
of
solving
repetitive
or
similar
problems
.
This
approach
is
widely
used
in
software
development
''
web
browsing
''
and
data
processing
.
Human
heuristics
are
simple
''
intuitive
rules
we
use
to
make
quick
decisions
''
like
„
avoid
dark
alleys
at
night
.
“
They
are
based
on
our
experiences
and
common
sense
''
helping
us
navigate
everyday
choices
efficiently
without
much
thought
.
Useful
in
fast
-
paced
or
uncertain
situations
''
these
shortcuts
can
lead
to
good
enough
decisions
.
However
''
they
'
re
not
always
reliable
for
complex
''
critical
decisions
or
in
unfamiliar
contexts
''
as
they
can
oversimplify
situations
and
be
influenced
by
biases
''
potentially
leading
to
poor
choices
.
Trial
and
Error
Repetition
Game
&
Playfulness
Curiosity
Intuition
<
br
>
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