Multiobjective pilgrimage walk optimization to enhance finite element analysis of double-layer barrel vaults and grid roofs
This study introduces a novel Multi-Objective Pilgrimage Walk Optimization (MOPWO) algorithm designed to address complex, conflicting design challenges in structural engineering. Inspired by the collective behaviors of devotees accompanying Matsu's palanquin, the algorithm extends the single-objective framework to effectively discover Pareto-optimal solutions. To validate its efficiency, the researchers integrate MOPWO with finite element analysis to optimize double-layer barrel vaults and grid roofs. The empirical results demonstrate that the algorithm successfully balances minimizing structural weight and reducing nodal displacement, outperforming established metaheuristic benchmarks in optimization accuracy, convergence speed, and structural diversity.
Fig. 1. Matsu pilgrimage procession.
Technology Overview
The MOPWO technology models collective searching behaviors through advanced population management, fast non-dominated sorting, and a time-governing mechanism. By embedding an external archive to preserve diverse Pareto-optimal solutions, the algorithm prevents premature convergence. Methodologically, it synchronizes with finite element analysis software to dynamically evaluate and refine structural parameters of complex truss roofs.
Applications & Benefits
This algorithm is applicable to spatial structural engineering, large-span roof design, and computational optimization in civil architecture. It offers significant benefits by providing engineers with a diverse set of trade-off design alternatives instead of a single solution. Ultimately, it minimizes material consumption, guarantees structural safety, and drastically reduces computational time for complex engineering simulations.
Abstract：
This study introduces a novel Multi-Objective Pilgrimage Walk Optimization (MOPWO) algorithm designed to address complex engineering optimization problems involving multiple conflicting objectives. Inspired by the devout followers who accompany Matsu's palanquin, the algorithm emulates their collective search behavior. MOPWO integrates advanced population management, fast non-dominated sorting, and an enhanced time-governing mechanism to extend the single-objective pilgrimage walk optimization (PWO) framework and effectively identify Pareto-optimal solutions in multi-objective search spaces. The performance of MOPWO is evaluated against nine established multi-objective metaheuristic algorithms—MOALO, MODA, MOEA/D, MOFPA, MOGOA, MOGWO, MOHHO, MOPSO, and MOWCA—across 21 standard multi-objective benchmark functions. Results demonstrate that MOPWO achieves more precise approximations of Pareto-optimal fronts. Its superiority is further confirmed by the Wilcoxon rank-sum test using three widely used performance indicators: hypervolume (HV), generational distance (GD), and spacing (SP). The applicability of MOPWO is validated through five large-scale structural engineering design problems: a 384-bar double-layer barrel vault, a 672-bar double-layer grid roof, a 768-bar double-layer barrel vault, a 1520-bar double-layer grid roof, and a 1536-bar double-layer barrel vault. Comparative analysis with previously published results confirms the algorithm's effectiveness in identifying high-quality Pareto solutions. These findings establish MOPWO as a robust and efficient computational approach for solving multi-objective optimization problems.
Multiobjective pilgrimage walk optimization to enhance finite element analysis of double-layer barrel vaults and grid roofs
Author：Chou Jui-Sheng, Liu Chi-Yun, Truong Dinh-Nhat
Year：2026
Source publication： Journal of Building Engineering, Volume 120, February 2026, 115190
Subfield Highest percentage： 99% Architecture #2/210