A speciation-based bilevel niching method for multimodal truss design problems

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.

     

目前有效需求不足的实证分析

我国经济运行目前已进入通货紧缩阶段，主要表现为社会总需求小于社会总供给，即有效需求不足。有效需求不足的根本原因是居民收入偏低、农村城镇化进程缓慢、投资主体单一及投资结构不合理，财政政策空间未被充分利用，对外贸易额下降。