Truss geometry and topology optimization with global stability constraints

In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the cross-sectional areas of the bars and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal-dual interior point implementation. During the solution process, both the cross-sectional areas of the bars and the coordinates of the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and to improve the quality of the optimal designs

Multi-objective heat transfer search algorithm for truss optimization

© 2019, Springer-Verlag London Ltd., part of Springer Nature. Abstract: In the real world, we often come across conditions like optimization of more than one objective functions concurrently which are of conflicting nature and that makes the prospect of the problem more intricate. To overpower this contrasting state, an efficient meta-heuristic (MH) is required, which provides a balanced trade-off between diverging objective functions and gives an optimum set of solutions. In this article, a recently proposed MH called Heat Transfer Search (HTS) algorithm is enforced to elucidate the structural optimization problems with Multi-objective functions (described as MOHTS). MOHTS is an efficient MH which works on the principle of heat transfer and thermodynamics, where search agents are molecules which interact with other molecules and with surrounding through conduction, convection, and radiation modes of heat transfer. Five challenging benchmark problems of truss optimization have been taken into consideration here to examine the effectiveness of MOHTS. Procure results through the proposed method show the predominance over considered MHs. These benchmark problems are considered for discrete design variables for the structural optimization problem with two objectives, namely minimization of truss weight and maximization of nodal displacement. Here, the Pareto-optimal front achieved through computational experiments, in the process of optimization, is evaluated by three distinct performance quality indicators namely the Hypervolume, the Front spacing metric, and Inverted Generational Distance. Also, the obtained results after a number of runs are compared with other existing optimizers in the literature like multi-objective ant system, multi-objective ant colony system, and multi-objective symbiotic organism search, which manifest the superiority in the performance of the proposed algorithm over others. The statistical analysis of the experimental work has been carried out by conducting Friedman’s rank test and Post-Hoc Holm–Sidak test. Graphic abstract: [Figure not available: see fulltext.]

Structural optimization using multi-objective modified adaptive symbiotic organisms search

© 2019 Elsevier Ltd Multiple objective structural optimization is a challenging problem in which suitable optimization methods are needed to find optimal solutions. Therefore, to answer such problems effectively, a multi-objective modified adaptive symbiotic organisms search (MOMASOS) with two modified phases is planned along with a normal line method as an archiving technique for designing of structures. The proposed algorithm consists of two separate improved phases including adaptive mutualism and modified parasitism phases. The probabilistic nature of mutualism phase of MOSOS lets design variables to have higher exploration and higher exploitation simultaneously. As search advances, a stability between the global search and a local search has a significant effect on the solutions. Therefore, an adaptive mutualism phase is added to the offer MOASOS. Also, the parasitism phase of MOSOS offers over exploration which is a major issue of this phase. The over exploration results in higher computational cost since the majority of the new solutions gets rejected due to inferior objective functional values. In consideration of this issue, the parasitism phase is upgraded to a modified parasitism phase to increase the possibility of getting improved solutions. In addition, the proposed changes are comparatively simple and do not need an extra parameter setting for MOSOS. For the truss problems, mass minimization and maximization of nodal deflection are considered as objective functions, elemental stresses are considered as behavior constraints and (discrete) elemental sections are considered as side constraints. Five truss optimization problems validate the applicability of the considered meta-heuristics to solve complex engineering. Also, four constrained benchmark engineering design problems are solved to demonstrate the effectiveness of MOMASOS. The results confirmed that the proposed adaptive mutualism phase and modified parasitism phase with a normal line method as an archiving technique provide superior and competitive results than the former obtained results