A Bi-directional Evolutionary Structural Optimisation algorithm with an added connectivity constraint

This paper proposes the introduction of a connectivity constraint in the Bi-directional Evolutionary Structural Optimisation (BESO) method, which avoids the possibility of arriving at highly non-optimal local optima. By developing a constraint that looks at the usefulness of complete members, rather than just elements, local optima are shown to be avoided. This problem, which affects both evolutionary and discrete optimisation techniques, has divided the optimisation community and resulted in significant discussion. This discussion has led to the development of what is now known in the literature as the Zhou-Rozvany (Z-R) problem. After analysing previous attempts at solving this problem, an updated formulation for the convergence criteria of the proposed BESO algorithm is presented. The convergence of the sequence is calculated by the structure's ability to safely carry the applied loads without breaking the constraints. The Z-R problem is solved for both stress minimisation and minimum compliance, further highlighting the flexibility of the proposed formulation. Finally, this paper aims to give some new insights into the uniqueness of the Z-R problem and to discuss the reasons for which discrete methods struggle to find suitable global optima.