Exact Methods for Computing All Lorenz Optimal Solutions to Biobjective Problems

LNCS n°9346This paper deals with biobjective combinatorial optimization problems where both objectives are required to be well-balanced. Lorenz dominance is a refinement of the Pareto dominance that has been proposed in economics to measure the inequalities in income distributions. We consider in this work the problem of computing the Lorenz optimal solutions to combinatorial optimization problems where solutions are evaluated by a two-component vector. This setting can encompass fair optimization or robust optimization. The computation of Lorenz optimal solutions in biobjective combinatorial optimization is however challenging (it has been shown intractable and NP-hard on certain problems). Nevertheless, to our knowledge, very few works address this problem. We propose thus in this work new methods to generate Lorenz optimal solutions. More precisely, we consider the adaptation of the well-known two-phase method proposed in biobjective optimization for computing Pareto optimal solutions to the direct computing of Lorenz optimal solutions. We show that some properties of the Lorenz dominance can provide a more efficient variant of the two-phase method. The results of the new method are compared to state-of-the-art methods on various biobjective combinatorial optimization problems and we show that the new method is more efficient in a majority of cases.nonouirechercheInternationa

The Effects of Lung Protective Ventilation or Hypercapnic Acidosis on Gas Exchange and Lung Injury in Surfactant Deficient Rabbits

<div><p>Background</p><p>Permissive hypercapnia has been shown to reduce lung injury in subjects with surfactant deficiency. Experimental studies suggest that hypercapnic acidosis by itself rather than decreased tidal volume may be a key protective factor.</p><p>Objectives</p><p>To study the differential effects of a lung protective ventilatory strategy or hypercapnic acidosis on gas exchange, hemodynamics and lung injury in an animal model of surfactant deficiency.</p><p>Methods</p><p>30 anesthetized, surfactant-depleted rabbits were mechanically ventilated (FiO₂ = 0.8, PEEP = 7cmH₂O) and randomized into three groups: Normoventilation-Normocapnia (NN)-group: tidal volume (Vt) = 7.5 ml/kg, target PaCO₂ = 40 mmHg; Normoventilation-Hypercapnia (NH)-group: Vt = 7.5 ml/kg, target PaCO₂ = 80 mmHg by increasing FiCO₂; and a Hypoventilation-Hypercapnia (HH)-group: Vt = 4.5 ml/kg, target PaCO₂ = 80 mmHg. Plasma lactate and interleukin (IL)-8 were measured every 2 h. Animals were sacrificed after 6 h to perform bronchoalveolar lavage (BAL), to measure lung wet-to-dry weight, lung tissue IL-8, and to obtain lung histology.</p><p>Results</p><p>PaO₂ was significantly higher in the HH-group compared to the NN-group (p<0.05), with values of the NH-group between the HH- and NN-groups. Other markers of lung injury (wet-dry-weight, BAL-Protein, histology-score, plasma-IL-8 and lung tissue IL-8) resulted in significantly lower values for the HH-group compared to the NN-group and trends for the NH-group towards lower values compared to the NN-group. Lactate was significantly lower in both hypercapnia groups compared to the NN-group.</p><p>Conclusion</p><p>Whereas hypercapnic acidosis may have some beneficial effects, a significant effect on lung injury and systemic inflammatory response is dependent upon a lower tidal volume rather than resultant arterial CO₂ tensions and pH alone.</p></div