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The present paper studies the integrated size and topology optimization of skeletal structures under natural frequency constraints. It is found that, unlike the conventional compliance-oriented topology optimization problems, the considered problem may be strongly singular in the sense that the corresponding feasible domain may be disconnected and the global optimal solutions are often located at the tips of some separated low dimensional sub-domains when the cross-sectional areas of the structural components are used as design variables. As in the case of stress-constrained topology optimization, this unpleasant behavior may prevent the gradient-based numerical optimization algorithms from finding the true optimal topologies. To overcome the difficulties posed by the strongly singular optima, some particular forms of area/moment of inertia-density interpolation schemes, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A new local search algorithm for multiobjective optimization problems is proposed to find the global optima accurately and diversely. This paper models the cooperatively local search as a potential field, which is called neighborhood field model (NFM). Using NFM, a new Multiobjective Neighborhood Field Optimization (MONFO) algorithm is proposed. In MONFO, the neighborhood field can drive each individual moving towards the superior neighbor and away from the inferior neighbor. MONFO is compared with other popular multiobjective algorithms under twelve test functions. Intensive simulations show that MONFO is able to deliver promising results in the respects of accuracy and diversity, especially for multimodal problems. [ABSTRACT FROM AUTHOR]

Abstract  Instead of the past mathematical analyses, an intuitive geometric analysis of the collaborative optimization (CO) algorithm is presented in this paper, which reveals some geometric properties of CO and gives a direct geometric interpretation of the reason for the reported computational difficulties in CO. The analysis shows that if the system-level optimum point at one iteration is outside the feasible region of the original optimization problem, at the next iteration, the system-level optimization problem may be infeasible due to the system-level consistency equality constraints. One way to solve the problem of the infeasibility is to relax the system-level consistency equality constraints using inequality constraints. However it is a delicate job to determine a rational relaxed tolerance because feasibility and consistency have conflicting requirements for the tolerance, that is, the more relaxed the better for feasibility while the stricter the better for consistency. Based on the geometric analysis, a method of variable relaxed tolerance is put forward to solve this problem. In this method, an adaptive adjustment of the tolerance is made at each iteration according to the quantified inconsistency between two subsystems. In the last section, the capabilities and limitations of the proposed method are illustrated by three examples. [ABSTRACT FROM AUTHOR]