We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than its travel speed, so relocation times are negligible with respect to construction times. It is required to find a construction schedule that minimizes a non-decreasing function of the times when various connections of interest become operational. Most problems of this class are strongly NP-hard on general networks, but are often tree-efficient, that is, polynomially solvable on trees. We develop a generic local search heuristic approach and two metaheuristics (Iterated Local Search and Tabu Search) for solving tree-efficient network construction problems on general networks, and explore them computationally. Results of computational experiments indicate that the methods have excellent performance.

中文翻译：

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网络构建问题中基于树优化的启发式和元启发式

我们考虑最近引入的一类网络构建问题，其中交通网络的边缘需要由服务器（施工人员）构建。服务器的构建速度恒定，远低于其行进速度，因此迁移时间相对于构建时间可以忽略不计。需要找到一个施工进度表，以最小化各种感兴趣的连接开始运行的时间的非递减函数。此类的大多数问题在一般网络上都是强 NP-hard 问题，但通常是树有效的，即在树上可多项式求解。我们开发了一种通用的局部搜索启发式方法和两种元启发式（迭代局部搜索和禁忌搜索）来解决一般网络上的树高效网络构建问题，并在计算上探索它们。