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In-Depth Information
Fitness Function.
The
cost
and
profit
function can be directly used as fitness
functions for each objectives for MOEAs:
cost
should be minimised while
profit
should be maximised.
Algorithm.
The case study compares three different evolutionary algorithms
to random search: NSGA-II, Pareto-GA and a single-objective GA. Pareto-GA
is a variation of a generic single-objective GA that uses Pareto-optimality only
for the selection process. The single-objective GA is used to deal with the multi-
objective formulation of NRP by adopting different sets of weights with the
weighted-sum approach. When using weighted-sum approach for two objective
functions,
f
1
and
f
2
, the overall fitness
F
of a candidate solution
x
is calculated
as follows:
f
2
(
x
)
Depending on the value of the weight,
w
, the optimisation will target different
regions on the Pareto front. The case study considered 9 different weight values
ranging from 0.1 to 0.9 with step size of 0.1 to achieve wider Pareto fronts.
F
(
x
)=
w
·
f
1
(
x
)+(1
−
w
)
·
Results.
Figure 14 shows results for an artificial instance of NRP with 40 re-
quirements and 15 customers. Random search produces normally distributed
solutions, whereas the weighted-sum, single-objective GA tends to produce so-
lutions at the extremes of the Pareto front. Pareto-GA does produce some so-
lutions that dominate most of the randomly generated solutions, but it is clear
0
NSGA−II
Pareto GA
Random search
Single−Objective GA
−20
−40
−60
−80
−100
−120
−140
−160
−180
0
2000
4000
6000
8000
10000
12000
14000
Score
(
a
) 15 customers; 40 requirements
Fig. 14.
Plot of results for NRP from different algorithms taken from Zhang and
Harman [113]
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