Multi-objective discrete optimization of laminated structures

Abstract The paper is dedicated to the multi-objective optimal design of laminated composite structures. In order to provide sound-engineering designs, a few alternative and/or conflicting objectives must be taken into account. It is reasonable to consider the multi-objective optimization as a sensible enrichment with respect to single objective optimization, since the solutions are enforced to result optimal at the same time with respect to different objectives. Multi-objective optimization methods gained in the last years a growing interest in engineering, due to the possibility to determine a design possessing at the same time optimality with respect to different conflicting requirements. This problem is approached and suitably solved by Evolution Strategies, a computational algorithm based on Darwinian theories, that allow to solve optimization problems without using gradient-based information on the objective functions and the constraints. The presence of multiple objectives has been taken into account coupling the algorithm with a cooperative game theoretic approach and, for sake of comparison, with other methods, such as weighted objectives or Trade-off. With the game theoretic approach, all objective functions have the same importance, and the optimal solution is found using a bargaining function. The ply orientations in the stacking sequence of the laminate are the assumed design variables, of discrete type, a common situation in engineering practice. The results obtained for two different typical laminate designs show the effectiveness of the proposed method.