Heuristic-guided technique for hybrid laminate stacking sequence multi modal optimization using branch-bound and relaxation methods

This study tackles the challenge of multimodal optimization for hybrid laminate stacking sequences under generic load conditions, including membrane and/or moment loading. The objective is to determine the optimal lay-up sequence of plies made from different materials to minimize laminate cost, while satisfying structural, weight, and manufacturing constraints. A key contribution of this work is the development of a novel heuristic function, integrated into the proposed algorithm, which significantly improves efficiency and robustness in solving problems where multiple global optima may coexist for hybrid laminates. The methodology employs an implicit, incrementally constructed directed graph (digraph), guided by the heuristic function at each decision step. This informed search strategy (augmented with both branch-and-bound and relaxation techniques) reduces the effective branching factor and mitigates the exponential growth of the search tree. The algorithm was validated through a series of benchmark tests for which global optima were previously obtained via brute-force search. Its performance was thoroughly assessed in terms of its ability to identify all optimal solutions and the number of iterations required to reach each one. Finally, the algorithm was applied to the redesign of a wind turbine blade root (based on the IEA 15-Megawatt Offshore Reference NREL wind project), achieving a cost reduction of up to 35 % while maintaining stiffness and mass within acceptable limits (below 5 %).