Information Technology Reference
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4 Experiments
In this section, some comparative experiments are arranged to examine the per-
formance of the proposed EINET-TSP algorithm, where some TSP benchmark
instances from TSPLIB [16], a standard library of sample instances for the TSP
(and related problems) from various sources and of various types, are chosen.
Firstly, a diversity analysis of EINET is discussed.
4.1 Diversity Analysis
Population diversity is an important evaluation parameter for evolution algo-
rithms. The study of Ref. introduced Phenotypical Diversity (PDM) and Geno-
typical Diversity (GDM) evaluation parameters of the population in the search
process [17, 18]. PDM and GDM are defined as:
PDM
=
aff
avg
aff
max
(11)
E
min
=
diff
avg
−
diff
min
E
min
E
max
−
E
−
GDM
=
(12)
diff
max
−
diff
min
where
aff
avg
and
aff
max
represent the average and maximum fitness values
of the population in the current generation, respectively. is the average Eu-
clidean distance between all individuals and the best individuals of the pop-
ulation in the current generation, which defined by the average antibody dif-
ference;
E
max
and
E
min
represent the maximum and minimum difference of
the antibody, respectively. Both PDM and GDM belong to the interval [0,1].
Usually, if
PDM >
0
.
9and
GDM <
0
.
1, the algorithm tends to converge. If
0
<PDM
≤
0
.
9and
GDM
≥
0
.
1, then the algorithm is in the normal search
process.
To analyze the diversity of EINET, here, EINEI-TSP was applied to the two
benchmark instances from TSPLIB, eil51and kroA100. From Fig.4 and Fig.5,
the PDM curve before the enzymatic reaction operator and the PDM curve af-
ter the enzymatic reaction operator, we can see that EINET can better keep
diversity in the search process and converge to the optimal point in a stable
manner. Note that, before enzymatic reaction operator, there is a good diver-
sity with the PDM below 0.6, which avoid the algorithm running into the local
optimization solution. This verifies that hormonal regulation operator can re-
cruit new antibodies to keep high population diversity during the run. While,
after enzymatic reaction, each antibody was one local optimal solution, the
PDM is always below 0.9. More analytically, the optimal solution curves of
each generation show that when the algorithm is close to the local optimiza-
tion solution, the diversity can help it jump out local optimization and tend to
converge.
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