Structural optimization using evolutionary multimodal and bilevel optimization techniques

Abstract

This research aims to investigate the multimodal properties of structural optimization using techniques from the field of evolutionary computation, specifically niching and bilevel techniques. Truss design is a well-known structural optimization problem which has important practical applications in many fields. Truss design problems are typically multimodal by nature, meaning that it offers multiple equally good design solutions with respect to the topology and/or sizes 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. Niching is an intuitive way of finding multiple optimal solutions in a single optimization run. Literature shows that existing niching methods are largely designed for handling continuous optimization problems. There does not exist a well-studied niching method for constrained discrete optimization problems like truss design problems. In addition, there are no well-defined multimodal discrete benchmark problems that can be used to evaluate the reliability and robustness of such a niching method. This thesis fills the identified research gaps by means of five major contributions. In the first contribution, we design a test suite for producing a diverse set of challenging multimodal discrete benchmark problems, which can be used for evaluating the discrete niching methods. In the second contribution, we develop a binary speciation-based PSO (B-SPSO) niching method using the concept of speciation in nature along with the binary PSO (BPSO). The results show that the proposed multimodal discrete benchmark problems are useful for the evaluation of the discrete niching methods like B-SPSO. In light of this study, a time-varying transfer function based binary PSO (TVT-BPSO) is developed for the B-SPSO which is the third contribution of this thesis. We propose this TVT-BPSO for maintaining a better balance between exploration/exploitation during the search process of the BPSO. The results show that the TVT-BPSO outperforms the state-of-the-art discrete optimization methods on the large-scale 0-1 knapsack problems. The fourth contribution is to consider and formulate the truss design problem as a bilevel optimization problem. With this new formulation, truss topology can be optimized in the upper level, at the same time the size of that truss topology can be optimized in the lower level. The proposed bilevel formulation is a precursor to the development of a bilevel niching method (Bi-NM) which constitutes the fifth contribution of this thesis. The proposed Bi-NM method performs niching at the upper level and a local search at the lower level to further refine the solutions. Extensive empirical studies are carried out to examine the accuracy, robustness, and efficiency of the proposed bilevel niching method in finding multiple topologies and their size solutions. Our results confirm that the proposed bilevel niching method is superior in all these three aspects over the state-of-the-art methods on several low to high-dimensional truss design problems