The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.
A new method for solving the multidisciplinary design optimization problems with a minimal computational effort is presented. The proposed methodology is based on the combination of artificial neural network model and Improved Multi-Objective Collaborative Optimization. In the artificial neural network–Improved Multi-Objective Collaborative Optimization scheme, the back-propagation algorithm is used for training the artificial neural network metamodel and the Non-dominated Sorting Genetic Algorithm-II is used to search a Pareto optimality set for the objective functions of stiffened panels. The artificial neural network–Improved Multi-Objective Collaborative Optimization algorithm aims firstly to decompose the global optimization problem hierarchically into optimization design problem at system level and several sub-problems at sub-system level and secondly to replace each optimization problem at the system and subsystem levels by artificial neural network model to limit the computational cost. To highlight the efficiency and effectiveness of the proposed artificial neural network–Improved Multi-Objective Collaborative Optimization method, mathematical and engineering examples are presented. Results obtained from the application of the artificial neural network–Improved Multi-Objective Collaborative Optimization approach to an optimization problem of a stiffened panel are compared with those obtained by traditional optimization without using prediction tools. The new method (artificial neural network–Improved Multi-Objective Collaborative Optimization) was proven to be superior to traditional optimization. These results have confirmed the efficiency and effectiveness of the artificial neural network–Improved Multi-Objective Collaborative Optimization method. In addition, it converges at faster rate than traditional optimization. The traditional optimization method converges within 7918 s, while artificial neural network–Improved Multi-Objective Collaborative Optimization requires only 42 s, clearly, the artificial neural network–Improved Multi-Objective Collaborative Optimization method is much more efficient.
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