Forest management planning involves deciding which silvicultural treatment should be applied to each stand and at what time to best meet the objectives established for the forest. For this, many mathematical formulations have been proposed, both within the linear and non-linear programming frameworks, in the latter case generally considering integer variables in a combinatorial manner. We present a novel approach for planning the management of forests comprising single-species, even-aged stands, using a continuous, multi-objective formulation (considering economic and even flow) which can be solved with gradient-type methods. The continuous formulation has proved robust in forest with different structures and different number of stands. The results obtained show a clear advantage of the gradient-type methods over heuristics to solve the problems, both in terms of computational time (efficiency) and in the solution obtained (effectiveness). Their improvement increases drastically with the dimension of the problem (number of stands). It is advisable to rigorously analyze the mathematical properties of the objective functions involved in forest management planning models. The continuous bi-objective model proposed in this paper works with smooth enough functions and can be efficiently solved by using gradient-type techniques. The advantages of the new methodology are summarized as: it does not require to set management prescriptions in advance, it avoids the division of the planning horizon into periods, and it provides better solutions than the traditional combinatorial formulations. Additionally, the graphical display of trade-off information allows an a posteriori articulation of preferences in an intuitive way, therefore being a very interesting tool for the decision-making process in forest planning.

中文翻译：

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森林规划中均匀流量和土地和木材价值的同时优化：连续方法

森林管理规划涉及决定应该对每个林分进行哪种造林处理以及在什么时间最好地实现为森林制定的目标。为此，已经在线性和非线性规划框架内提出了许多数学公式，在后一种情况下，通常以组合方式考虑整数变量。我们提出了一种新的方法来规划由单一物种、偶龄林分组成的森林管理，使用连续的、多目标的公式（考虑经济和均匀流量），可以用梯度方法解决。连续公式已在具有不同结构和不同林分数量的森林中证明是稳健的。获得的结果表明梯度型方法比启发式方法在解决问题方面具有明显的优势，在计算时间（效率）和获得的解决方案（有效性）方面。它们的改进随着问题的维度（站数）而急剧增加。建议严格分析森林经营规划模型中涉及的目标函数的数学特性。本文提出的连续双目标模型具有足够平滑的函数，并且可以通过使用梯度类型的技术有效地解决。新方法论的优点概括为：不需要预先设定管理处方，避免将规划范围划分为多个时期，提供比传统组合公式更好的解决方案。此外，