## Abstracts

### Prof Mathias Stolpe (Technical University of Denmark, Denmark)

**Talk title:**Truss Topology Optimization with Discrete Design Variables -- Recent Developments and Future Challenges

**Abstract:**Truss topology optimization with discrete design variables is important from an engineering perspective due to the numerous relevant applications. Designs found by truss optimization can provide ideas for innovative structures in the conceptual design phase. These designs can in turn be used as good starting points for the preliminary and detailed design phases. It is also important from a mathematical perspective due to the theoretical and numerical challenges associated with modelling and solving the associated optimization problems. Optimization methods which have been developed for truss topology design can potentially be generalized to solve optimal design problems for other classes of structural optimization problems.

Truss topology optimization has been an active research area since the 1960s and is still very active today. The presentation gives an overview of developed models, theory, and numerical methods and heuristics for optimization of truss structures with discrete design variables. Although some important historical achievements are presented the main focus is placed on recent developments, in particular on models and methods for global optimization in truss topology design. The overview is followed by a presentation of future modelling and numerical challenges in the field. The emphasis is placed on matters which should be resolved to increase the engineering applicability and increase the capabilities to solve sufficiently large-scale problems.

### Prof Matthew Gilbert (University of Sheffield, UK)

**Talk title:**Application of Layout Optimization to Engineering Analysis and Design Problems

**Abstract:**To verify the safety of solids and structures against collapse engineers have traditionally had to rely either on simplistic hand type calculations, or on significantly more complex computational tools which identify the collapse state in an indirect, iterative, manner (which can be costly in terms of computer and/or operator time). Additionally, in many engineering disciplines the initial design stage is carried out in an ad-hoc manner, with engineering intuition often used to identify structurally efficient designs. Layout optimization methods can potentially address both these problems, and similarities between analysis and design formulations can also potentially be exploited. In the presentation the corresponding layout optimization formulations will be briefly described and then applied to truss design problems and to the problem of identifying the critical layout of discontinuities in a solid body at the point of collapse. In each case mathematical programming techniques are used to obtain solutions. Future directions in the field of layout optimization will then be briefly considered.

### Dr Paul Shepherd (University of Bath, UK)

**Talk title:**Truss Optimisation in Practice

**Abstract:**This presentation will outline the context in which structural optimisation takes place in practice. Aimed primarily at non-engineers and those without direct experience of how buildings are designed and built in practice, and using real case studies from industry, it will give an overview of the building design process and focus in particular on practicing engineers' approach to structural optimisation.

Current design involves many assumptions, and design decisions are made for a variety of reasons, some of which can be counter-intuitive, if not counter-factual. Whilst we all want to develop innovative solutions to exciting research problems, we must at the same time ensure that our results are of interest to those we hope will use them in the field. Sometimes this will involve working hard to open practitioners' eyes to new ways of working, but it will also inevitably involve adapting our research to accept some of the harder-to-quantify multiple-objectives that appear in the real world. This shouldn't be seen as a chore, but instead a real challenge, and something that will benefit all of our research in the long run.

### Dr Tomasz Sokol (Warsaw University of Technology, Poland)

**Talk title:**On topological optimization of trusses using adaptive ground structure methods

**Abstract:**Each optimization problem can be formulated in various ways that are formally equivalent, in the sense that all they lead to the same optimal solution. Different formulations may require, however, different optimization methods, and generally lead to numerical tasks of different complexity and execution time. The aim of this lecture is to present a new ground structure method for truss topology optimization problems. The ground structure methods became popular and important tools due to their robustness and reliability. Here, contrary to other methods, the positions of nodes are frozen. To obtain a good approximation of the optimal layout a relatively dense set of nodes with a huge number of possible connections, i.e. potential bars, is required. This inevitably leads to large-scale optimization problems which are hard to solve in a direct way. This drawback can be overcome by iterative approach with selective subsets of active bars and nodes. Here one big task is replaced by a series of much smaller subtasks. The main advantage of the ground structure methods results from the fact that the topology optimization problem can be formulated and solved in the framework of linear programming. This enables finding globally optimal layouts strictly corresponding to exact Michell structures. The proposed method enabled to obtain new important solutions which extend the class of known Michell trusses to 3D space and multiple load conditions. The new results clearly indicate that the optimal 3D trusses form shell-like structures composed of lattice surfaces.

### Helen Fairclough (University of Sheffield, UK)

**Talk title:**The use of Mixed Integer-Linear Programming to impose buildability constraints on optimization of pin jointed trusses

**Abstract:**The discrete nature of the solutions from ground structure based optimization methods makes them well suited for use in building and structural engineering applications. However, solutions identified by these methods, as with similar results found from analytic methods of optimisation, are generally far too complex for economic construction using traditional methods.

In conjunction with engineering practitioners, a number of quantifiable measures have been identified as practical limitations for real-world construction. These have then been formulated using additional constraints and integer variables, and added to the classical plastic, stress based form.

However, the computational demands of this formulation are very high when applied to topology optimisation problems at a practical scale, necessitating the use of lower resolution ground structures. To improve the results, a second stage of continuous, non-linear optimisation is used to refine the structures. We will assess how effective this is at approximating globally optimal results, and discuss some possibilities for improving the computational efficiency of the method.

### Dr Alemseged Weldeyesus (University of Edinburgh, UK)

**Talk title:**Truss topology optimization by LP and SDP

**Abstract:**In this presentation, we focus on two classes of truss topology optimization. The classical least-weight truss topology optimization in plastic design formulated as Linear Programming (LP) and an extended version of it formulated as SemiDefinite Programming (SDP), where stability constrains are taken into account. In both cases, the problems are known to be large-scale demanding special purpose optimization methods.

We demonstrate how these problems can be efficiently solved by primal-dual interior point methods. We discuss several techniques that can be employed to the methods and improve their performance. These include column generation to approximate the original large-scale problems by a sequence of smaller sub problems, exploiting algebraic structures to reduce the size of linear systems originating in the algorithm, warm-start strategy to compute initial points for the algorithm and improve convergence, and the use of iterative methods to solve the linear.

Joint work with Jacek Gondzio.