Evaluation matrix.

The selection of construction plans for adverse geological conditions frequently encountered during the construction of bridge pile foundations will have a significant impact on the project’s progress, quality, and cost. There is a need for the optimization of multi-attribute decision-making methods, considering the subjectivity in in weight allocation and the practical implementation obstacles. In this study, an evaluation framework for pile foundation construction schemes in karst areas was established. The directed graph and Bellman-Ford algorithm are employed to improve the Analytic Network Process (ANP) in the systematic structure, thereby calculating the subjective weights of various indicators. Simultaneously, based on the concept of dynamic weighting, a multiple linear regression is introduced for analyzing the weights of similar projects, resulting in the derivation of universal weights for the primary indicators within the evaluation system. The combination weights are subsequently determined through the weighted average of the two types of weights. Finally, the comprehensive scores of alternative schemes are computed using the grey-fuzzy evaluation method to enable decision-making in scheme selection. Cloud model, ELECTRE-II, and VIKOR methodologies were utilized for the comparison of results. Combining with a case study of a bridge project in karst development area in southern China, the findings indicate that the improved ANP method possesses practical applicability and yields effective computational results. The introduction of universal weights serves to ameliorate the inherent subjectivity in weight allocation. The pile foundation quality achieved using the optimal construction plan is classified as Class I, which prove the feasibility of the model.