Overview of Multiobjective Optimization - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 26

START

Get the nondominated
solutions and update
the Pareto-optimal
solutions set if necessary

Set the required
parameters

Randomly generate the
initial routes of ants
and set g = 0

Update the
trail level by (2.13)

Get the new ant colony
using (2.12) based on
the attractiveness and
trail level

Yes

g = MAXIMUM
ITERATION?

No

g = g + 1

Objective value
evaluation

Output Pareto-optimal
solutions

Rank assignment
based on
Pareto dominance

END

Figure 2.12
Flowchart.of.ACO.

and. p i k .is.given.by

α β

τ + η

τ

ij ij

if( ) ij ∉ tabu

∑

k

α β

( + η )

k

p = . (2.12)

is is

ij

s tabu

∉

k

0 otherwise

.

where. tabu k . is. the. unreachable. move. of. agent. k . from. state. i ;. α. and. β. rep-
resent. the. impacts. of. η ij . and. τ ij ,. respectively,. which. are. user-deined;. and.
0 < α, β < 1.
When.all.the.ants.finish.their.moves,.the.trails'.levels.are.updated.by

τ ( ) g = ρτ ( g − 1) + ∆τ . (2.13)

ij ij ij

.

where.0 < ρ < 1.is.the.evaporation.coeficient.determined.by.the.programmer,.
∆τ ij . is. the. sum. of. the. contributions. of. all. ants. that. have. been. moved. from.
state. i .to. j ,.which.is.computed.by

N

∑

k

∆τ = ∆τ . (2.14)

ij ij

.

k = 1