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多目标过程综合可归结为1个多目标混合整数非线性规划(MOMINLP),主要有2大类求解技术:多目标数学规划法和以多目标遗传算法(MOGA)为代表的进化算法。MOGA能并行处理多个目标,鲁棒性强,近年来得到长足发展。但由于无法从理论上保证得到问题的真正非劣解,应用受到了一定限制。本文应用多目标遗传算法NSGA-Ⅱ对废料最少问题进行求解,得到近似非劣解集。提出1个逐步插值算法,对近似解集中的点依次进行筛选,给出了所选点的搜索目标函数的构造方法,并应用SQP法对其寻优,得到真正的非劣解。将精确解与近似解进行比较表明,NSGA-Ⅱ的求解精度较高,绝大部分近似解的最大可能误差不超过3%,可为实际工程中的初步决策提供依据。
Multi-objective process synthesis can be attributed to a multi-objective mixed integer non-linear programming (MOMINLP), there are two major types of solving techniques: multi-objective mathematical programming and evolutionary algorithm represented by multi-objective genetic algorithm (MOGA). MOGA can handle multiple targets in parallel, strong robustness, in recent years has been rapid development. However, due to the inability to obtain the true non-inferiority of the problem theoretically, the application is subject to certain restrictions. In this paper, we use the multi-objective genetic algorithm NSGA-Ⅱ to solve the least scrap problem and get approximate non-inferior solution set. A stepwise interpolation algorithm is proposed to filter the points of the approximate solutions sequentially. The construction method of the search objective function for the selected point is given. The SQP method is used to optimize it to obtain a true non-inferior solution. The comparison between the exact solution and the approximate solution shows that NSGA-Ⅱ has higher solution accuracy, and the maximum possible error of most approximate solutions does not exceed 3%, which may provide the basis for the preliminary decision-making in practical engineering.