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Modeling and combined application of MOEA/D and TOPSIS to optimize WEDM performances of A286 superalloy


Superalloys are categorized as difficult to process materials with a broad spectrum of applications in industries. Process modeling and optimization of WEDM performances on nickel- and titanium-based superalloys are widely investigated. However, such investigations on iron-based superalloy are still lacking and hence probed in the present article. Thus, the paper targets modeling the correlation between the performance parameters and the control parameters with two popular techniques: response surface methodology (RSM) and artificial neural network (ANN) for WEDM of a typical iron-based superalloy, i.e., A286 superalloy. A comparison between the model estimates and the experimental values is made to check ANN and RSM's prediction accuracy. The estimates by the ANN model are exact and consistent with the experimental results. An analysis of variance (ANOVA) test is performed to perceive the degree of statistical significance of parameters. Moreover, a novel two-stage procedure, i.e., MOEA/D in collaboration with TOPSIS method, is implemented to search the optimal condition for process performances. The quality of Pareto-optimal solutions acquired using MOEA/D is compared to that of Pareto-optimal solutions obtained using NSGA II, PESA II, and MMOPSO through the use of a hypervolume (HV) parameter. Wilcoxon’s test is performed to identify the statistical difference between MOEA/D and competing algorithms. The optimal parametric combination recommended by the proposed optimization approach is Ton = 130 µs, Toff = 52 µs, Ipeak = 12 A, Wf = 5 m/min and SV = 30 V. The proposed optimization technique can also be exploited in other manufacturing processes.

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Wire electric discharge machining


Material removal rate

SR :

Surface roughness

T on :

Pulse-on time

T off :

Pulse-off time

I peak :

Peak current

W f :

Wire feed rate


Servo voltage


Cutting speed

L :

Plate thickness

\(\lambda_{c}\) :

Cutoff length


Multi-objective evolutionary algorithm


Multi-objective evolutionary algorithm based on decomposition


Multi-objective optimization problem


Non-dominated sorting genetic algorithm II


Pareto-envelope-based selection algorithm II


Multi-objective particle swarm optimization




Technique for order preference by similarity to ideal solution (TOPSIS)

\(S^{ + }\) :

Positive ideal solution

\(S^{ - }\) :

Negative ideal solution

\(E_{i}^{ + }\) :

Separation from the positive ideal solution

\(E_{i}^{ - }\) :

Separation from the negative ideal solution

\(CC_{i}\) :

Relative closeness coefficient


Multiple-criteria decision-making


Response surface methodology


Artificial neural network


Multilayer perceptron

\(d_{\max }\) :

The maximum value of the response parameter

\(d_{\min }\) :

The minimum value of the response parameter

\(d_{i}\) :

The nominal value of the response parameter


Levenberg–Marquardt algorithm


Gradient descent learning function


Preference-based multi-objective optimization


Teaching–learning-based optimization


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Correspondence to Saikat Ranjan Maity.

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See Table 8.

Table 8 Allocation of ranks to non-dominated optimal solutions exploiting TOPSIS method

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Saha, S., Maity, S.R., Dey, S. et al. Modeling and combined application of MOEA/D and TOPSIS to optimize WEDM performances of A286 superalloy. Soft Comput 25, 14697–14713 (2021).

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  • Wire electric discharge machining
  • Modeling
  • Optimization
  • MOEA/D