In this paper, we demonstrate the combination of machine learning and three dimensional numerical simulations for multi-objective optimization of low pressure die casting. The cooling of molten metal inside the mold is achieved typically by passing water through the cooling lines in the die. Depending on the cooling line location, coolant flow rate and die geometry, nonuniform temperatures are imposed on the molten metal at the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. A finite volume based numerical solver is used to determine the temperature-time history and correlate the inputs to outputs. The objective of this research is to develop and demonstrate a procedure to obtain the initial and wall temperatures so as to optimize the product quality. The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization in this work. The number of function evaluations required for NSGA-II can be of the order of millions and hence, the finite volume solver cannot be used directly for optimization. Therefore, a multilayer perceptron feed-forward neural network is first trained using the results from the numerical solution of the fluid flow and energy equations and is subsequently used as a surrogate model. As an assessment, simplified versions of the actual problem are designed to first verify results of the genetic algorithm. An innovative local sensitivity based approach is then used to rank the final Pareto optimal solutions and select a single best design.

Original languageEnglish (US)
Pages (from-to)130-141
Number of pages12
JournalJournal of Manufacturing Processes
StatePublished - Mar 2020


  • Deep neural networks
  • Die casting
  • Multi-objective optimization

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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