Truss design is a well-known structural optimization problem that has important practical applications in various fields. Truss design problems are typically multimodal by nature, meaning that it offers multiple optimal solutions concerning the topology (combinatorial optimization problem) and/or sizes (continuous optimization problem) of the members, but they are evaluated to have similar or equally good objective function values. From a practical standpoint, it is desirable to find as many alternative designs as possible, rather than finding a single design, as often practiced. Several techniques based on classical and metaheuristic optimization methods have been developed for simultaneous optimization of topology and size of a truss. However, all these methods unable to find multiple topologies and their corresponding size solutions in a single run. A few metaheuristics incorporating niching techniques have been developed for finding multiple topologies for the truss design problem, but these studies ignored the fact that for each known topology, multiple design solutions in terms of size can be found. To address this issue, this paper proposes a bi-level truss formulation and subsequently a speciation-based bilevel niching method (BiL-NM) using such a formulation. The BiL-NM consists of a modified SPSO niching method which is robust to find multiple topologies and a canonical PSO for their corresponding size solutions. Extensive empirical studies are carried out to analyze the accuracy, robustness, and efficiency of the BiL-NM. The results confirm that the proposed BiL-NM is superior in all these three aspects over the state-of-the-art methods on several low to high-dimensional truss design problems.

桁架设计是众所周知的结构优化问题，在各个领域都有重要的实际应用。桁架设计问题本质上通常是多模态的，这意味着它提供了关于构件的拓扑（组合优化问题）和/或尺寸（连续优化问题）的多个最优解，但它们被评估为具有相似或同样好的目标函数值. 从实用的角度来看，希望找到尽可能多的替代设计，而不是像经常实践的那样找到单一的设计。已经开发了几种基于经典和元启发式优化方法的技术，用于同时优化桁架的拓扑和尺寸。然而，所有这些方法都无法在一次运行中找到多个拓扑及其相应大小的解决方案。已经开发了一些结合了生态位技术的元启发式方法来寻找桁架设计问题的多种拓扑，但这些研究忽略了这样一个事实，即对于每个已知的拓扑，可以找到多种尺寸的设计解决方案。为了解决这个问题，本文提出了一种双层桁架公式，随后提出了一种使用这种公式的基于物种形成的双层生态位方法 (BiL-NM)。BiL-NM 由改进的 SPSO 壁龛方法组成，该方法可以稳健地找到多种拓扑结构，并为其相应大小的解决方案提供规范的 PSO。进行了广泛的实证研究来分析 BiL-NM 的准确性、鲁棒性和效率。