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<p>In this study, we present a mathematical model for solving the multi-objective nonlinear fractional programming problems (MONFPP) with deterministic constraints, focusing on three primary goals: maximizing profit through efficient resource utilization, minimizing emissions generated in production, and reducing energy consumption per unit produced. We first determine individual upper and lower bounds for each goal to achieve these objectives using the sequential least squares programming (SLSQP) method. The SLSQP technique provides an iterative optimization framework adept at handling complex constrained nonlinear fractional programming problems, effectively managing equality and inequality constraints. We then apply a novel neutrosophic goal programming approach within the mathematical model of MONFPP to identify a balanced compromise solution. A numerical example demonstrates the practicality and effectiveness of this approach, with the compromise optimal solution obtained using CPLEX 22.1.1 optimization software. This study highlights the robustness and applicability of the MONFPP model in achieving multi-objective optimization across diverse metrics.</p>

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A mathematical programming approach to solve the multi-objective nonlinear fractional programming problem

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Wajahat Ali,
  • Mohammad Sheihan Javaid,
  • Mohammad Nabeel,
  • Shakeel Javaid

摘要

In this study, we present a mathematical model for solving the multi-objective nonlinear fractional programming problems (MONFPP) with deterministic constraints, focusing on three primary goals: maximizing profit through efficient resource utilization, minimizing emissions generated in production, and reducing energy consumption per unit produced. We first determine individual upper and lower bounds for each goal to achieve these objectives using the sequential least squares programming (SLSQP) method. The SLSQP technique provides an iterative optimization framework adept at handling complex constrained nonlinear fractional programming problems, effectively managing equality and inequality constraints. We then apply a novel neutrosophic goal programming approach within the mathematical model of MONFPP to identify a balanced compromise solution. A numerical example demonstrates the practicality and effectiveness of this approach, with the compromise optimal solution obtained using CPLEX 22.1.1 optimization software. This study highlights the robustness and applicability of the MONFPP model in achieving multi-objective optimization across diverse metrics.