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Designing low-cost network layouts is an essential step in planning linked infrastructure. For the case of capacitated trees, such as oil or gas pipeline networks, the cost is usually a function of both pipeline diameter (i.e. ability to carry flow or transferred capacity) and pipeline length. Even for the case of incompressible, steady flow, minimizing cost becomes particularly difficult as network topology itself dictates local flow material balances, rendering the optimization space non-linear. The combinatorial nature of potential trees requires the use of graph optimization heuristics to achieve good solutions in reasonable time. In this work we perform a comparison of known literature network optimization heuristics and metaheuristics for finding minimum-cost capacitated trees without Steiner nodes, and propose novel algorithms, including a metaheuristic based on transferring edges of high valency nodes. Our metaheuristic achieves performance above similar algorithms studied, especially for larger graphs, usually producing a significantly higher proportion of optimal solutions, while remaining in line with time-complexity of algorithms found in the literature. Data points for graph node positions and capacities are first randomly generated, and secondly obtained from the German emissions trading CO 2  source registry. As political will for applications and storage for hard-to-abate industry CO 2  emissions is growing, efficient network design methods become relevant for new large-scale CO 2  pipeline networks.

Heuristic Methods for Minimum-Cost Pipeline Network Design – a Node Valency Transfer Metaheuristic