<p>Quasi-Newton algorithms, particularly the BFGS technique, are well-defined methods for solving unconstrained single-objective optimization problems that have recently been extended to multiobjective optimization. However, implementing these methods for large-scale problems proves challenging due to the need to store Hessian approximations. To address this challenge, we suggest a scaled memoryless BFGS quasi-Newton technique designed for large-scale multiobjective optimization problems (MOPs), which eliminates the requirement for matrix storage while preserving convergence properties. Our approach applies a novel scaling technique to enhance efficiency and approximates the Pareto front uniformly through an iterative, memory-efficient approach. To validate the procedure, we investigate numerical test problems using well-known performance metrics and compare the results with some existing algorithms. The findings show that the suggested approach attains superior computational efficiency and solution quality, specially in high-dimensional settings. This study bridges the deep gap in large-scale multiobjective optimization, by suggesting a scalable and practical alternative to standard quasi-Newton techniques while maintaining theoretical rigor.</p>

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A scaled memoryless BFGS quasi-Newton method and a new algorithm for constructing the Pareto front of multiobjective optimization

  • F. Akbari,
  • E. Khorram,
  • M. Ghaznavi

摘要

Quasi-Newton algorithms, particularly the BFGS technique, are well-defined methods for solving unconstrained single-objective optimization problems that have recently been extended to multiobjective optimization. However, implementing these methods for large-scale problems proves challenging due to the need to store Hessian approximations. To address this challenge, we suggest a scaled memoryless BFGS quasi-Newton technique designed for large-scale multiobjective optimization problems (MOPs), which eliminates the requirement for matrix storage while preserving convergence properties. Our approach applies a novel scaling technique to enhance efficiency and approximates the Pareto front uniformly through an iterative, memory-efficient approach. To validate the procedure, we investigate numerical test problems using well-known performance metrics and compare the results with some existing algorithms. The findings show that the suggested approach attains superior computational efficiency and solution quality, specially in high-dimensional settings. This study bridges the deep gap in large-scale multiobjective optimization, by suggesting a scalable and practical alternative to standard quasi-Newton techniques while maintaining theoretical rigor.