In a wind farm turbines convert wind energy into electrical energy. The generation of each turbine is transmitted, possibly via other turbines, to a substation that is connected to the power grid. On every possible interconnection there can be at most one of various different cable types. Each type comes with a cost per unit length and with a capacity. Designing a cost-minimal cable layout for a wind farm to feed all turbine production into the power grid is called the Wind Farm Cabling Problem (WCP). We consider a formulation of WCP as a flow problem on a graph where the cost of a flow on an edge is modeled by a step function originating from the cable types. Recently, we presented a proof-of-concept for a negative cycle canceling-based algorithm for WCP [14]. We extend key steps of that heuristic and build a theoretical foundation that explains how this heuristic tackles the problems arising from the special structure of WCP. A thorough experimental evaluation identifies the best setup of the algorithm and compares it to existing methods from the literature such as Mixed-integer Linear Programming (MILP) and Simulated Annealing (SA). The heuristic runs in a range of half a millisecond to approximately one and a half minutes on instances with up to 500 turbines. It provides solutions of similar quality compared to both competitors with running times of one hour and one day. When comparing the solution quality after a running time of two seconds, our algorithm outperforms the MILP- and SA-approaches, which allows it to be applied in interactive wind farm planning.

翻译：在风电场中，风力涡轮机将风能转化为电能。每台涡轮机的发电量通过可能经由其他涡轮机的路径传输至与电网相连的变电站。每条潜在互联线上最多可铺设一种不同类型的电缆，每种电缆类型具有单位长度成本和容量。为风电场设计成本最优的电缆布局以将所有涡轮机发电量馈入电网的问题被称为风电场电缆布局问题（WCP）。我们将WCP建模为图上的流问题，其中边上流的成本由电缆类型产生的阶跃函数描述。我们近期提出了基于负环取消法求解WCP的概念验证算法[14]。本文扩展了该启发式算法的关键步骤，并建立了理论框架，阐明该算法如何应对WCP特殊结构带来的挑战。通过详尽的实验评估，我们确定了算法的最优配置，并将其与文献中现有的混合整数线性规划（MILP）和模拟退火（SA）方法进行对比。该启发式算法在包含多达500台风力涡轮机的实例上运行时间介于半毫秒至约一分半钟之间。与运行时间为一小时和一天的两种竞品算法相比，本算法可提供质量相近的解。在运行两秒后的解质量比较中，本算法优于MILP和SA方法，使其可应用于交互式风电场规划场景。