Optimization of composite structures by estimation of distribution algorithms.

摘要

The design of high performance composite laminates, such as those used in aerospace structures, leads to complex combinatorial optimization problems that cannot be addressed by conventional methods. These problems are typically solved by stochastic algorithms, such as evolutionary algorithms.; This dissertation proposes a new evolutionary algorithm for composite laminate optimization, named Double-Distribution Optimization Algorithm (DDOA). DDOA belongs to the family of estimation of distributions algorithms (EDA) that build a statistical model of promising regions of the design space based on sets of good points, and use it to guide the search. A generic framework for introducing statistical variable dependencies by making use of the physics of the problem is proposed. The algorithm uses two distributions simultaneously: the marginal distributions of the design variables, complemented by the distribution of auxiliary variables. The combination of the two generates complex distributions at a low computational cost.; The dissertation demonstrates the efficiency of DDOA for several laminate optimization problems where the design variables are the fiber angles and the auxiliary variables are the lamination parameters. The results show that its reliability in finding the optima is greater than that of a simple EDA and of a standard genetic algorithm, and that its advantage increases with the problem dimension. A continuous version of the algorithm is presented and applied to a constrained quadratic problem. Finally, a modification of the algorithm incorporating probabilistic and directional search mechanisms is proposed. The algorithm exhibits a faster convergence to the optimum and opens the way for a unified framework for stochastic and directional optimization.