Topology Optimization of Square Steel Tube Concrete Truss Structures Using Pseudo-Full Internal Force Genetic Algorithm

Literature Overview

The paper by Xie Jun, Guo Fei, Zhu Shouqin, Liang Jinxiao, Yan Jie, and Dong Jie, published in the Journal of University of Jinan (Natural Science Edition) in 2023 (Vol. 37, No. 2, pp. 247-252), presents a topology optimization method for square steel tube concrete (SCFST) truss structures based on a pseudo-full internal force genetic algorithm. The authors from Hebei Architectural Engineering Institute propose an integrated optimization approach that combines the pseudo-full internal force algorithm with genetic algorithms to solve discrete variable topology optimization problems. This research was supported by the National Natural Science Foundation of China, the Hebei Provincial Higher Education Science and Technology Research Program, and the Zhangjiakou Science and Technology Development Program.

Topology Optimization Problem Formulation

Topology optimization in structural engineering involves determining the optimal arrangement of structural members within a given design domain to achieve a specified performance objective, such as minimum cost, minimum weight, or maximum stiffness. For SCFST truss structures, the optimization variables include the cross-section type of each square steel tube, the topology variables indicating whether each potential member is present or absent, and the concrete strength grade assigned to each member. The optimization objective is typically the minimization of total structural cost, subject to constraints on displacement, stress, and stability.

The discrete nature of these optimization variables makes the problem fundamentally different from continuous topology optimization, where material density is varied continuously. Discrete topology optimization is a mixed-integer programming problem that is NP-hard in general, requiring heuristic or metaheuristic algorithms for practical solution.

Pseudo-Full Internal Force Genetic Algorithm

The proposed pseudo-full internal force genetic algorithm is a hybrid optimization method that combines the strengths of two distinct approaches. The pseudo-full internal force algorithm is an iterative method that optimizes truss topology by adjusting member cross-sections to achieve a state where all members carry approximately equal internal forces, thereby maximizing material efficiency. The genetic algorithm is a population-based metaheuristic that explores the design space through selection, crossover, and mutation operations, capable of finding global optima in complex, non-convex design spaces.

The integration of these two methods is achieved through a specific initialization and operation strategy. Part of the initial population in the genetic algorithm is seeded with solutions produced by the pseudo-full internal force algorithm, providing high-quality starting points that guide the evolutionary search toward promising regions of the design space. Additionally, the pseudo-full internal force algorithm is applied as an operator after the standard genetic operations (selection, crossover, mutation), further refining the population by improving the internal force distribution of each candidate solution.

Penalty Function Modification and Computational Efficiency

A key innovation of the proposed method is the modification of the penalty function used in the genetic algorithm. Traditional penalty functions penalize constraint violations by adding a large value to the objective function, but the choice of penalty coefficient is often problematic—too large a penalty may dominate the objective function and hinder exploration, while too small a penalty may allow excessive constraint violations. The modified penalty function addresses these issues by adaptively adjusting the penalty strength based on the degree of constraint violation and the current state of the optimization process.

This modification improves the computational efficiency of the genetic algorithm by ensuring that feasible solutions are properly rewarded while infeasible solutions are adequately penalized without completely suppressing their contribution to the evolutionary search. The result is a more balanced exploration-exploitation trade-off that leads to faster convergence and higher-quality optimal solutions.

Numerical Example and Optimization Results

The proposed method was applied to a 12-bar truss structure optimization problem, and the results were compared against those obtained using the pseudo-full internal force algorithm alone and the genetic algorithm alone. The comparison demonstrates that the hybrid method produces solutions with lower total cost than either standalone method, confirming the effectiveness of the integration strategy.

The optimized topology after applying the proposed method features fewer structural members than the pre-optimization model, with each remaining member operating at or near its full capacity. This indicates that the optimization has achieved a high degree of material efficiency, with no redundant members consuming structural capacity without contributing to the overall structural performance.

Engineering Implications for SCFST Truss Design

The topology optimization method presented in this paper has significant implications for the practical design of SCFST truss structures. By systematically identifying the optimal member arrangement and cross-section assignments, engineers can reduce material consumption while maintaining or improving structural performance. This is particularly important for large-scale truss structures such as roof systems, bridge trusses, and industrial buildings, where material costs constitute a significant portion of the total project cost.

From a fabrication and welding perspective, the optimized topology produced by this method typically results in simpler joint configurations with fewer members connecting at each node. This simplification reduces the complexity of weld detailing, fabrication time, and quality control requirements, all of which contribute to cost savings and improved constructability. The method also ensures that the concrete strength grade is assigned optimally to each member, avoiding the common practice of using unnecessarily high-strength concrete in members that do not require it.

Reflections on Optimization Methodology and Practice

This paper demonstrates the power of hybrid optimization algorithms in solving complex structural design problems. The integration of physics-based algorithms (pseudo-full internal force) with metaheuristic search methods (genetic algorithm) creates a synergistic effect that outperforms either approach used in isolation. This philosophy of combining domain-specific knowledge with general-purpose optimization techniques is applicable across many areas of structural engineering, including welding process optimization, fatigue life prediction, and damage tolerance design.

The application of topology optimization to SCFST truss structures represents an important advancement in the design methodology for composite structural systems. As the use of SCFST structures continues to grow in applications ranging from civil infrastructure to industrial construction, the availability of systematic optimization tools will enable engineers to produce more efficient, economical, and reliable structures. The methodology presented here provides a foundation for further development of optimization approaches that incorporate additional design considerations such as seismic performance, fabrication constraints, and long-term durability.