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The purpose of this study is to enable the planning of construction projects with simultaneous consideration of time, cost and safety risks. It also aims to improve the decision-making process by evaluating the effectiveness of the Rao-2 algorithm in solving multi-objective time-cost-safety risk problems. In the end, this model is designed to support project managers in enhancing management approaches by addressing project challenges and constraints more efficiently.

In this study, the Rao-2 algorithm, along with Grey Wolf Optimization (GWO) and Whale Optimization algorithm (WOA), were improved using the crowding distance-based non-dominated sorting method. Rao-2 was first compared to GWO and WOA. Subsequently, it was compared with well-established algorithms in the literature, including genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE). The C-metric, hypervolume and spread metrics were employed for performance measurement. The performance of the algorithms was evaluated on four case studies consisting of 11, 13, 18 and 25 activities.

The results revealed that Rao-2 performs better than other algorithms as the number of activities increases, when compared using the Hypervolume, Spread and C-metric measures. In terms of performance measures, the GWO algorithm outperformed Rao-2 in some evaluation metrics for the instance involving 11 activities. However, as the number of activities grew, the Rao-2 method consistently generated higher-quality Pareto fronts and outperformed GWO and WOA in all evaluation metrics. The solutions generated by Rao-2 were also superior to those obtained from GA, PSO and DE in all case studies, further demonstrating the capability of our framework to produce a wide range of optimal solutions with high diversity across different case studies.

This research demonstrates that Rao-2 not only improves solution quality when generating Pareto fronts but also achieves better results with fewer function evaluations compared to GA, PSO and DE. The algorithm's efficiency makes it particularly well-suited for optimizing time, cost and safety risks in large-scale construction projects, which in turn positions Rao-2 as a better choice for such projects by producing superior results compared to other algorithms. By providing high-quality solutions with reduced computational demands, Rao-2 offers a faster and more resource-efficient tool for decision-making, contributing to advancements in both the theory and practice of construction project management.