摘要：A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multiobjective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid’s area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Paretooptimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effec tively deal with multi-objective optimizations with black-box functions.

摘要：Purpose–The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation(IG-FRBFNN)and their optimization realized by means of the multiobjective particle swarm optimization(MOPSO).Design/methodology/approach–In fuzzy modeling,complexity,interpretability(or simplicity)as well as accuracy of the obtained model are essential design *** the performance of the IG-RBFNN model is directly affected by some parameters,such as the fuzzification coefficient used in the FCM,the number of rules and the orders of the polynomials in the consequent parts of the rules,the authors carry out both structural as well as parametric optimization of the network.A multi-objective particle swarm optimization using Crowding Distance(MOPSO-CD)as well as O/WLS learning-based optimization are exploited to carry out the structural and parametric optimization of the model,respectively,while the optimization is of multiobjective character as it is aimed at the simultaneous minimization of complexity and maximization of ***–The performance of the proposed model is illustrated with the aid of three *** proposed optimization method leads to an accurate and highly interpretable fuzzy ***/value–A MOPSO-CD as well as O/WLS learning-based optimization are exploited,respectively,to carry out the structural and parametric optimization of the *** a result,the proposed methodology is interesting for designing an accurate and highly interpretable fuzzy model.

摘要：To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.

摘要：In the lattice design of a diffraction-limited storage ring（DLSR） consisting of compact multi-bend achromats（MBAs）, it is challenging to simultaneously achieve an ultralow emittance and a satisfactory nonlinear performance, due to extremely large nonlinearities and limited tuning ranges of the element parameters. Nevertheless, in this paper we show that the potential of a DLSR design can be explored with a successive and iterative implementation of the multi-objective particle swarm optimization（MOPSO） and multi-objective genetic algorithm（MOGA）. For the High Energy Photon Source, a planned kilometer-scale DLSR, optimizations indicate that it is feasible to attain a natural emittance of about 50 pm·rad, and simultaneously realize a sufficient ring acceptance for on-axis longitudinal injection, by using a hybrid MBA lattice. In particular, this study demonstrates that a rational combination of the MOPSO and MOGA is more effective than either of them alone, in approaching the true global optima of an explorative multi-objective problem with many optimizing variables and local optima.

摘要：The pylon structure of an airplane is very complex, and its high-fidelity analysis is quite time-consuming. If posterior preference optimization algorithm is used to solve this problem, the huge time consumption will be unacceptable in engineering practice due to the large amount of evaluation needed for the algorithm. So, a new interactive optimization algorithm-interactive multi-objective particle swarm optimization （IMOPSO） is presented. IMOPSO is efficient, simple and operable. The decision-maker can expediently determine the accurate preference in IMOPSO. IMOPSO is used to perform the pylon structure optimization design of an airplane, and a satisfactory design is achieved after only 12 generations of IMOPSO evolutions. Compared with original design, the maximum displacement of the satisfactory design is reduced, and the mass of the satisfactory design is decreased for 22%.