Abstract The present contribution derives a theoretical framework for constructing novel geometrical constraints in the context of density-based topology optimization. Principally, predefined dimensionality is enforced locally on components optimized structures. These are defined using principal values (singular values) from singular value decomposition points clouds represented by elemental ce...

In this paper, we present a survey of various existing algorithms for computing the matrix geometric mean and derive new second-order optimization algorithms to compute the Karcher mean. These new algorithms are constructed using the standard definition of the Riemannian Hessian. The survey includes the ALM-list of desired properties for a geometric mean, the analytical expression for the mean ...

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using classical optimization methods, this paper presents a Multi-Objective Bees Algorithm (MOBA) for solving the multi-objective optimal of mechanical engineering problems design. In the pre...

Geometric uncertainty refers to the deviation of the geometric boundary from its ideal position, which may have a non-trivial impact on design performance. Since geometric uncertainty is embedded in the boundary which is dynamic and changes continuously in the optimization process, topology optimization under geometric uncertainty (TOGU) poses extreme difficulty to the already challenging topol...

This paper presents a multi objective geometric programming model which determines the product`s selling price in two markets. We assume demand is a function of price and marketing expenditure in two markets. The cost of production is also assumed to be a function of demands in both markets. Our model is a posynomial function which is solved using Geometric Programming (GP). In our GP implement...