A Multi-Objective Mixed-variable Co-evolutionary Genetic Programming approach for stiffened composite panel design

Stiffened composite panels are widely used due to their high strength-to-weight ratio and design flexibility. Their optimization often relies on computationally expensive heuristic methods, which can significantly constrain the scale of composite structures that can be feasibly optimized. To address this limitation, we introduce a novel multi-objective framework, the Multi-Objective Mixed-variable Co-evolutionary Genetic Programming (MOMCGP) approach, to optimize the stacking sequence of stiffened composite panels. Compared to conventional GA variants, MOMCGP adopts a cooperative co-evolution strategy with species-specific sub-populations representing the base plate and individual stiffeners, combined with Pareto-based ranking, elitism, and rank-weighted mating to efficiently explore mixed discrete–categorical design spaces. Benchmark studies show that MOMCGP achieves faster convergence, maintains solution diversity, and scales more favorably with increasing design dimensionality than GA and NSGA-II. The framework is coupled with a spectral element method based on Chebyshev polynomials and a NURBS-based coarse quadrilateral meshing technique, enabling high-accuracy structural analysis with reduced computational cost. Validation against numerical and experimental benchmarks confirms the robustness of the approach. Comprehensive single- and multi-objective case studies across varied geometries, stiffener configurations, and boundary conditions further demonstrate MOMCGP's effectiveness in maximizing fundamental frequency while minimizing weight, establishing it as a promising tool for scalable lightweight structure design.