A hybrid algorithm coupling genetic programming and Nelder–Mead for topology and size optimization of trusses with static and dynamic constraints

Abstract

Truss optimization aims to provide the lightest truss to gain the maximum benefit out of available resources. Truss optimization may subject to static and dynamic constraints. Static constraints include structural kinematic stability, maximum allowable stress in truss members, maximum allowable deflection in the truss nodes and critical buckling load. However, dynamic constraints impose limits on the natural frequency of the desired truss to avoid the destructive resonance phenomenon. Taking both static and dynamic constraints into account may lead to growth in the search space but dwindling its feasible region; the search space becomes very non-convex and may subterfuge the solver to trap in a local optimum. Another design consideration may include fabricational constraints to present design variables from a set of available cross-sections to satisfy the design codes. This paper proposes a hybrid genetic programming algorithm to deal with the barriers of this complex problem. It looks for the optimum connectivity table (among the truss nodes) and optimal cross-sectional areas for its members subject to design constraints. It also benefits from a Nelder–Mead local search operator to improve the competence and true convergence of the algorithm. Our algorithm has been applied to some numerical examples considering both types of continuous and discrete design variables; It proved its efficiency to find better solutions (lighter trusses) in comparison with other methods in the literature for most of the cases.