Multimodal truss structure design using bilevel and niching based evolutionary algorithms

Finding an optimal design for a truss structure involves optimizing its topology, size, and shape. A truss design problem is usually multimodal, meaning that the problem offers multiple optimal designs in terms of topology and/or size 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. A few metaheuristics based methods with niching techniques have been used for finding multiple topologies for the truss design problem, but these studies have ignored any emphasis in finding multiple solutions in terms of size. To overcome this issue, this paper proposes to formulate the truss problem as a bilevel optimization problem, where stable topologies can be found in the upper level and the optimized sizes of the members of these topologies can be found in the lower level. As a result, a new bilevel niching method is proposed to find multiple optimal solutions for topology level as well as for the size level simultaneously. The proposed method is shown to be superior over the state-of-the-art methods on several benchmark truss-structure design problems.