The performances of heuristic algorithms are highly dependent on the parameters used, and usually difficult to determine subjectively. Thus, how to balance the relations between the qualities of the solutions and the values of the parameters has been a hot and lasting topic in the field of optimization research. This article presented a statistical method to estimate the efficient parameter values of three alternative neighborhood search techniques of simulated annealing when applied to forest spatial harvest scheduling problems, as an example. The neighborhood search techniques included: the conventional version of simulated annealing (Method1), and the swapping version (Method2) and the changing version (Method3) of 2-element optimization (2-opt) moves. Results indicated that the performances of different neighborhood search strategies highly depended on the problem size, in which the superiorities of Method2 increased from about 10% for smaller cases (400 units) to approximately 80% of larger cases (>3600 units) when compared the objective function values with Method1 and Method3. The efficient parameter values of the cooling rate (CR), the number of iterations per temperature (Ntem), and the number of iterations used for generating initial solution (Nsol) could be estimated using polynomial functions with the number of units, while the initial temperature (IT) should be estimated using exponential function, where the determination coefficient ( $R^{2}$ ) of the fitted functions were all larger than 0.60 [except for Nsol and CR of Mehod1 ( $R^{2}=0.32$ and 0.42), CR of Method2 ( $R^{2}=0.20$ )]. The number of satisfactory solutions all increased linearly ( $R^{2} > 0.85$ ) with the number of units, while the solution efficiency decreased linearly ( $R^{2} > 0.30$ ). The verifications of two extra grid datasets indicated that the parameter optimization methods were valid.

中文翻译：

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森林空间规划问题中模拟退火不同邻域搜索技术的有效参数值估计

启发式算法的性能高度依赖于所使用的参数，通常难以主观确定。因此，如何平衡解的质量与参数值之间的关系一直是优化研究领域的一个热门而持久的课题。作为一个例子，本文提出了一种统计方法来估计模拟退火的三种替代邻域搜索技术在应用于森林空间收获调度问题时的有效参数值。邻域搜索技术包括：模拟退火的常规版本（方法 1），以及 2 元素优化（2-opt）移动的交换版本（方法 2）和变化版本（方法 3）。结果表明，不同的邻域搜索策略的性能高度依赖于问题的大小，其中相比，方法 2 的优势从较小案例（400 个单位）的约 10% 增加到较大案例（>3600 个单位）的约 80%。使用方法 1 和方法 3 的目标函数值。冷却速率的有效参数值（CR)，每个温度的迭代次数 (网络)，以及用于生成初始解的迭代次数 (纳索尔) 可以使用具有单位数的多项式函数来估计，而初始温度 (它) 应该使用指数函数估计，其中决定系数 ( $R^{2}$ ) 的拟合函数都大于 0.60 [除了 纳索尔 和 CR 方法 1 ( $R^{2}=0.32$ 和 0.42), CR 方法 2 ( $R^{2}=0.20$ )]。满意解的数量都呈线性增加（ $R^{2} > 0.85$ ) 随着单元数的增加，而求解效率线性下降 ( $R^{2} > 0.30$ ）。两个额外网格数据集的验证表明参数优化方法是有效的。