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Game-theoretic differential evolution for multiobjective optimization of green sand mould system

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Abstract

Many large-scale engineering problems often take a multiobjective form. Thus, several solution options to the MO problem are usually ascertained by the engineer. Then the most desirable options with respect to the industrial circumstances and online operating conditions are selected. In this work, the trade-off solutions are obtained using the weighted-sum approach. In addition the standard metaheuristic, differential evolution is improved using concepts from evolutionary game theory. These techniques are then applied to solve the industrial green sand mould development problem. The solutions are then examined and discussed from various standpoints.

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Abbreviations

\(N\) :

Length of individual string

\(P\) :

Population size

\(I\) :

Individuals (vectors) in the population

\(x^{p}_{i}\) :

Principal parent

\(x^{a}_{i}\) :

Auxiliary parent

\(V_{i}\) :

Mutated vector

\(F\) :

Mutation amplification factor

CR:

The probability of the crossover

\(x^{G}_{i}\) :

Population of vectors

\(x^{\mathrm{child}}_{i}\) :

Child trial vector

gen:

Current generation

Max:

Maximum number of generations

\(w_{j}\) :

Scalar weights

\(j\) :

The individual objective functions

\(M\) :

Maximum number of objective functions

DE:

Differential evolution

GTDE-1:

Game-theoretic differential evolution (strategy 1)

GTDE-2:

Game-theoretic differential evolution (strategy 2)

EGT:

Evolutionary game theory

MO:

Multiobjective

PSO:

Particle swarm optimization

GA:

Genetic algorithm

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Correspondence to P. Vasant.

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Communicated by V. Loia.

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Ganesan, T., Vasant, P., Elamvazuthi, I. et al. Game-theoretic differential evolution for multiobjective optimization of green sand mould system. Soft Comput 20, 3189–3200 (2016). https://doi.org/10.1007/s00500-015-1694-5

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