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Table 4.5.
Selected Pareto solutions for two-objective optimization.
No.
C
Mn
Cr
Mo
Temp
TS
EBt
Cv
EBc
Cost$
1
0.341
0.800
0.806
0.225
602
819
22
92
28
66.4
2
0.347
0.887
1.350
0.144
651
809
37
97
28
85.5
3
0.344
0.841
0.558
0.308
592
803
28
90
29
59.5
4
0.375
0.839
1.119
0.011
640
794
56
289
28
67.8
5
0.298
0.985
1.202
0.252
655
817
57
117
30
86.7
method provides useful, practical composition and tempering temperature
levels, with acceptable mechanical property requirement, model reliability
and overall costs incurred. It indicates that the produced solutions are very
consistent and always converged to a specific area that minimized the above
objective functions.
4.7. Conclusions
A multi-objective alloy design approach was used to determine the optimal
heat treatment regime and the required weight percentages for the chemical
composites to obtain the desired mechanical properties of steel. Based on
data-driven neurofuzzy models, the tensile strength and Charpy impact
toughness can be predicted effectively and then used to facilitate optimal
alloy design. The alloy design experimental results have shown that the
optimization algorithm can locate the constrained minimum design with
very good convergence, and also provide a range of optional solutions
which fit the pre-defined property requirement while securing a reasonable
production cost. Simulations also indicate that the algorithm produced
very consistent solutions and can be effectively used in other industrial
optimization problems.
An adaptive evolutionary Particle Swarm Optimization approach was
described and successfully applied to this multi-objective optimal design of
heat-treated alloy steels. Using a new PSO algorithm, AEPSO, we overcame
problems commonly encountered in the standard PSO algorithm which
related to its shortcomings for effective local search in the early stages of
the run coupled with its shortcomings for effective global search during the
late stages of the run. The introduction of an adaptive inertia weight and a
special mutation operator improved the diversity of the Pareto solutions and
the exploratory capability while keeping the algorithm simple. Compared
with some recently developed algorithms, the proposed algorithm can
