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<p>Kidney Paired Donation (KPD), also referred to as kidney exchange, seeks to enhance transplant opportunities for patients with end-stage renal disease by pairing incompatible patient-donor pairs (PDPs) with others facing similar challenges. Several combinatorial optimization problems have been proposed in the literature to optimize the exchange and address different aspects of KPD. This paper introduces a novel variant, named <i>Cardinality Constrained Cycles and Chains Problem with Desensitization, Orphan Recipients, and Prioritization</i> (4CDOP), which accounts for several overlooked aspects in previous works. To address the 4CDOP, we provide a first mathematical model and three heuristics: a Carousel Greedy (CG) algorithm, a tailored Kernel Search (KS) procedure, and a hybrid Kernousel (KO) algorithm combining CG and KS. This study is primarily computational: we evaluate the proposed algorithms across a new set of extensive benchmark instances. The results show that KO achieves the best solutions when computation time is not constrained, making it particularly suitable from the classical analysis perspective for optimization problems. However, in scenarios needing repeated execution under time constraints, such as simulations, KS offers the best trade-off between solution quality and runtime efficiency, showcasing its versatility for real-world KPD studies.</p>

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Kidney Exchanges with Desensitization and Orphans: A Matheuristic Approach

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Domenico Serra,
  • Carmine Sorgente,
  • Monica Gentili,
  • Raffaele Cerulli

摘要

Kidney Paired Donation (KPD), also referred to as kidney exchange, seeks to enhance transplant opportunities for patients with end-stage renal disease by pairing incompatible patient-donor pairs (PDPs) with others facing similar challenges. Several combinatorial optimization problems have been proposed in the literature to optimize the exchange and address different aspects of KPD. This paper introduces a novel variant, named Cardinality Constrained Cycles and Chains Problem with Desensitization, Orphan Recipients, and Prioritization (4CDOP), which accounts for several overlooked aspects in previous works. To address the 4CDOP, we provide a first mathematical model and three heuristics: a Carousel Greedy (CG) algorithm, a tailored Kernel Search (KS) procedure, and a hybrid Kernousel (KO) algorithm combining CG and KS. This study is primarily computational: we evaluate the proposed algorithms across a new set of extensive benchmark instances. The results show that KO achieves the best solutions when computation time is not constrained, making it particularly suitable from the classical analysis perspective for optimization problems. However, in scenarios needing repeated execution under time constraints, such as simulations, KS offers the best trade-off between solution quality and runtime efficiency, showcasing its versatility for real-world KPD studies.