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<p>Multi-objective optimization is essential in addressing problems characterized by multiple, often conflicting objectives. Instead of seeking the Pareto-front, lexicographic multi-objective optimization (LMOO) aims to find a solution respecting a hierarchical prioritization of objectives. This type of problem typically arises from real-world applications with an explicit expression of preferences or when dealing with engineered cost functions, such as when modeling soft constraints. This paper introduces a non-preemptive method for solving LMOO problems, by transforming them into single-objective approximations through a robust and efficient calculation of objective weights. The authors present an algorithm to calculate the weights starting from an upper and lower bound of each objective. The weights can be manipulated to control the approximation of the solution with respect to the exact LMOO solution. The proposed method can be applied to linear and non-linear problems with continuous or discrete domains.</p>

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Weighting method for non-preemptive multi-objective mathematical programming

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Leonardo Ferro,
  • Gianluca Filaci,
  • Andrea Manzini,
  • Antonio Ornatelli

摘要

Multi-objective optimization is essential in addressing problems characterized by multiple, often conflicting objectives. Instead of seeking the Pareto-front, lexicographic multi-objective optimization (LMOO) aims to find a solution respecting a hierarchical prioritization of objectives. This type of problem typically arises from real-world applications with an explicit expression of preferences or when dealing with engineered cost functions, such as when modeling soft constraints. This paper introduces a non-preemptive method for solving LMOO problems, by transforming them into single-objective approximations through a robust and efficient calculation of objective weights. The authors present an algorithm to calculate the weights starting from an upper and lower bound of each objective. The weights can be manipulated to control the approximation of the solution with respect to the exact LMOO solution. The proposed method can be applied to linear and non-linear problems with continuous or discrete domains.