Negative Cycle Canceling with Neighborhood Heuristics for the Wind Farm Cabling Problem

The Wind Farm Cabling Problem (WCP) aims at finding the cost-minimal inter-array cable routing, also known as internal cable layout, of a wind farm so that all turbine generation is transmitted to the substations. For each possible connection in the wind farm, one of several cable types can be selected. Each cable type comes with a thermal capacity and unit length costs. WCP can be modeled as a graph theoretic minimum-cost flow problem with a step-cost function on each edge. We extend a deterministic "hill-climbing" heuristic from the literature. This heuristic runs into local minima from which it is not able to recover. We embed this algorithm into a framework which involves strategies for escaping these minima. These escaping strategies allow the heuristic to descend into other, possibly better, minima. We design three such strategies and provide an extensive statistical evaluation comparing these strategies. The best combination of strategies is evaluated against Gurobi 9.0.0 on a Mixed-integer Linear Program formulation and a Simulated Annealing-based heuristic from the literature on publicly available synthetic benchmark sets. Our simulations show that our framework works exceptionally well on the largest benchmark instances where it provides better solution within 15 minutes than Gurobi within one day on 80 % of the input instances. The simulations on the benchmark sets are complemented by a case study on the world's soon-to-be largest offshore wind farm: Hornsea One.