The combat of retrofitting urban drainage networks with nature-based solutions: a benchmark comparison

Retrofitting urban drainage networks (UDNs) with nature-based solutions (NBS) to improve integrated system performance is a complex multi-objective problem, requiring a trade-off between capital costs, hydraulic constraints, social and environmental co-benefits. Although optimisation-based approaches are increasingly used, the lack of benchmark case studies limits comparison between implementation strategies. To address this gap, the "Combat of Retrofitting Urban Drainage Networks with NBS" was organised to compare NBS placement workflows under a common evaluation framework. A calibrated combined sewer network, including seven predefined NBS types, was provided to six participating teams. The teams applied diverse methods, including evolutionary, heuristic and rule-based sequential optimisation algorithms, and linear programming. The submitted solutions were evaluated using seven performance indicators reflecting hydraulic and environmental objectives. Most teams adopted multi-stage workflows that combined algorithmic optimisation with domain knowledge to reduce search space or guide allocation. Within this benchmark, the highest-ranked solution integrated expert knowledge throughout the workflow and achieved balanced performance across all indicators; however, its transferability to other case studies may be limited due to reliance on expert knowledge. Several more automated approaches relied on representative rainfall events and Pareto-optimal solutions. Based on the results, a practical framework is proposed for selecting methodologies according to the application purpose, available computational resources, problem structure, and required temporal representation. Future research should improve representative-event selection, systematically embed domain knowledge, develop computationally efficient hybrid approaches, and incorporate multicriteria analysis directly into optimisation. The case study and results are provided as a benchmark to support more reproducible and comparable methodological development.