利用加权切贝雪夫方法，将多目标优化问题化简为单目标优化问题。
The problem of multiobjective optimization is simplified to that of scalar objective optimization by weighted Tchebycheff procedure.
同时为了将不等式约束优化问题转化为单目标优化问题，对惩罚函数法进行了改进。
At the mean time, the penalty function was improved by transmuting the inequality constrained optimization problem into single target optimization one.
基于双群体搜索机制分别对约束多目标优化问题和约束单目标优化问题进行了研究。
Hence, constrained multiobjective and constrained numerical optimization problems are done in this thesis based on double populations.
最后，着重研究应急资源调度的单目标优化问题，并指出了单目标优化模型的局限性。
Finally, the article mainly researches the problems of single-objective optimization in scheduling contingency resources, and points out the limitations of single-objective optimized model.
然后，利用线性加权法和主要目标法将多目标优化问题转化为单目标优化问题，采用精确算法思想进行模型求解。
Then it USES linear weighting method and main target method to convert the problem of multi-objective optimization into a mono-objective one and works out its solution via exact algorithm.
研究人员在对型线类型设计和优化的研究中，缺乏简洁有效的模式，往往简化为单目标优化问题，而且采用传统的方法与手段。
Many researchers usually simplify it as a single optimization problem using traditional methods for lack of the concise and effective mode.
通过把单目标最优解模糊化，将双目标模糊优化问题转化为单目标极小化极大问题求解；
The problem of fuzzy optimization of two objectives is transformed into single objective problem by means of the fuzziness of optimum solutions of single objective.
随着工程问题日益的复杂化，传统的、单目标、确定性优化设计方法已不能满足设计要求。
Along with the complication of project, the methods of traditional, simple objective and definite optimization have not been able to satisfy the design request.
单级斜齿圆柱齿轮减速器的优化设计，是一个多目标优化问题。
The single stage skewed tooth cylindrical gears reduction gear optimized design, is a multi-objective optimization question.
采用最大模糊满意度法将多目标优化问题转化为单目标非线性规划问题；
Secondly, multi-objective optimization problem is reformulated into a nonlinear single-objective programming problem by means of fuzzy satisfaction-maximizing method.
利用线性加权和法，建立了评价函数，将多目标优化问题转化为单目标非线性规划问题。
By linear weighing-sum method, the multi-objective optimization was converted into a linear programming problem with the evaluation equation. Process parameters were optimized with SQP algorithm.
利用线性加权和法，建立了评价函数，将多目标优化问题转化为单目标非线性规划问题。
By linear weighing-sum method, the multi-objective optimization was converted into a linear programming problem with the evaluation equation. Process parameters were optimized with SQP algorithm.
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