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This study introduces a novel genetic algorithm technique for solving complex multi-objective probabilistic fractional programming problems with discrete random variables, offering a direct path to Pareto optimal solutions.

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Area of Science:

  • Operations Research
  • Optimization Techniques
  • Probabilistic Programming

Background:

  • Multi-objective optimization problems with fractional objectives are common in real-world scenarios.
  • Incorporating probabilistic elements and discrete random variables adds significant complexity.
  • Existing methods may require deterministic transformations, which can be computationally intensive.

Purpose of the Study:

  • To develop a direct method for solving multiple-objective probabilistic fractional programming problems.
  • To handle discrete random variables with Pascal and Hypergeometric distributions.
  • To find Pareto optimal solutions without converting to a deterministic model.

Main Methods:

  • Construction of a multiple-objective probabilistic mathematical model with fractional objectives.
  • Modeling coefficients and right-hand side parameters as discrete random variables.
  • Utilizing stochastic simulation to check probabilistic constraint feasibility.
  • Application of a genetic algorithm approach to find Pareto optimal solutions.

Main Results:

  • The genetic algorithm successfully obtains Pareto optimal solutions for the proposed probabilistic model.
  • The study demonstrates conflicting objective function values, typical in multi-objective optimization.
  • The method was validated with numerical and supply chain management examples.

Conclusions:

  • The proposed genetic algorithm technique is effective for solving multi-objective probabilistic fractional programming problems.
  • This approach avoids the need for deterministic model conversion, simplifying the solution process.
  • The method provides valuable insights for applications like supply chain management optimization.