提出一种新的群智能算法,即多目标快速群搜索优化(MQGSO)算法,以双层球面网壳为研究对象,进行结构节点最大位移最小化和结构质量最轻化的多目标优化设计,网壳优化后的Pareto前沿分布均匀且范围较广,分别对多目标优化和单目标优化后的结构进行多维地震作用时程响应分析。结果表明:多目标优化得到的结构优于单目标的优化结果,所提出的多目标快速群搜索算法能很好地实现复杂空间结构的多目标优化设计。

The multi‐objective quick group search optimization (MQGSO) algorithm was applied to the optimal design of double‐layer spherical shells . The optimization objectives were the minimum value of the maximum displacement and the weight of the structure .Taking the double‐layer spherical shells as an object ,the Pareto frontier of the optimization example structure had the full and broader distribution .Corresponding to the multi‐objective optimization results and the single‐objective optimization results ,the time history response analysis of optimized structure under multi‐dimensional earthquake action was carried out . The results show that the multi‐objective optimization results are better than those of the single‐objective one . The dynamic characteristics of the double‐layer shell example prove that the M QGSO algorithm can effectively deal with the multi‐objective optimal design of complex spacial structures .

为综合衡量配矿效果，基于多目标优化理论，以磨浮入选原矿组分指标、入选原矿品质稳定及最大限度利用原矿为目标，构建磷矿堆场多目标优化配矿模型，并采用改进的多目标遗传算法求解该模型。经约束多目标优化算例测试结果表明：改进的多目标遗传算法可以找到多目标优化问题分布广泛、均匀的Pareto最优解集。并针对磷矿浮选堆场开展多目标优化配矿，现场测试结果显示，矿石混配后P20；含量23．052％，MgO含量4．195％，混配原矿30654t，比常规优化方案资源利用率提高0．31％。研究结果表明，该多目标优化配矿技术可实现稳定矿石品质的同时最大限度地利用原矿。

In order to evaluate the effect of mine ore blending comprehensively , a new ore blending model was proposed for phosphate rock stacking yard , based on the multi-objective optimization the-ory.The stability of ore quality and ore component indexes requirements for mineral processing and maximum utilization of ore were chosen as the objective function of the multi-objective mathematical model.Multi-objective genetic algorithm was improved to solve the ore blending model.It was tested by two constrained multi-objective optimization examples , and the results indicated that the improved genetic algorithm could find the Pareto optimal solutions set in a multi-objective optimization problem and the Pareto optimal solutions are scattered extensively and uniformly.This method was applied to ore blending for phosphate rock stacking yard.The field test results showed that compared with the normal method the utilization rate of raw ore was increased by 0.31%by the new method , and a to-tal of 3

为了提高多目标优化问题的求解效率,提出了一种新的处理约束多目标优化问题的基于Kriging的多目标遗传算法(MOKGA)。MOKGA采用物理规划法将多目标优化转化为单目标优化,然后构建目标函数的考虑约束的EI(Expected Improvement)模型,并采用遗传算法进行求解。六峰值驼背函数和一个导弹多目标多学科设计优化问题用于MOKGA算法性能的测试。结果表明,与理论解相比,MOKGA算法有很好的优化结果;与NSGA II相比,MOKGA有很快的收敛性。

In order to improve the efficiency for solving multiobjective optimization problem ,a new method dealing with constrained multiobjective optimization is proposed ,which is multiobjective kriging based ge-netic algorithm ( MOKGA) .Physical programming is used in MOKGA to convert the multiobjective to a single objective ,and then EI ( Expected Improvement ) is made for the single objective taking into consid-eration the various constraints .Genetic algorithm is used to optimize the EI .Six-hump camel back func-tion and a multiobjective multidisciplinary design optimization of missile are used to test the performance of MOKGA.The results show that MOKGA can find good results as compared to theory solution and has fast convergence as compared with NSGA II .

通过Matlab软件,用遗传算法对三叶孔板换热器进行了传热性能优化设计研究。基于单目标和多目标遗传算法,选取火积耗散数和总成本作为目标函数,然后编程运算。结果表明：通过优化设计,三叶孔板换热器的有效度增加,泵功减小,热容流量比减小;在相同有效度情况下,多目标函数优化后的泵功比单目标函数减小了近13.7%,说明多目标函数优化比单目标优化的结果更有优越性;多目标函数优化更具有灵活性,其得到的Pareto解可供多角度选择。

The heat transfer performance optimization of trefoil -baffle support heat exchanger was carried out,by using genetic algorithm which possess a strong global optimization ability .Based on the single ob-jective and multi -objective genetic algorithm,the five variables and the constraint conditions were deter -mined to compute the results of the objective functions ,entransy dissipation number and total costs ,by writing programs.The results show that the effective degree of heat exchanger was increased ,the pump power and the rate of heat capacity flow were reduced by optimization design .Pump power of multi -ob-jective optimization was reduced about 13.7% than that of single objective optimization .So multi -objec-tive function optimization has more advantages .Moreover,the Pareto solution has more flexibility than sin-gle objective function optimization,it can be chosen by designer.

为了提高武器的射击精度,以某型机枪枪管为研究对象,建立枪管的有限元分析模型和以刚度与重量为目标的枪管多目标优化模型.该模型基于对枪管结构优化的分析以及枪管设计时的多目标要求,采用多目标遗传算法与有限元计算相结合的优化算法对枪管进行多目标优化,获得了枪管结构优化方案.实验结果表明:优化后枪管的固有频率提高了12.9%,最大应变量则减小了19.59%,枪管的综合性能有所提高.

In order to improve the fire accuracy of machine gun, taking the certain type machine gun barrel as research objective, the finite element modeling of the barrel was established, at the same time the barrel multi-object optimization model was established which taking intensity and weight as optimum target. On the basis of structure optimization and multi-object design demand of the barrel, the multi-object optimization design on the barrel was done by the method combined with finite element and multi-object genetic algorithm, and the structural optimization design is achieved. The test results show that the inherent frequency of the barrel increased 12.9 percent and the most dependent variable was decreased 19.59 percent after optimization, the combination property of barrel is increased obviously.