多目标最优控制问题的优化及其在水平井设计中的应用

Optimization of multi-objective optimal control problems and its application in designing of horizontal wells

为求得一类多目标系统在有效解集上均匀分布的多个具有代表性的满意解,提出一种改进的GA算法.该算法由多个适应值函数引导搜索,其中每个适应值函数都等于两个性能指标标准化以后的加权和且其权值由均匀设计产生;为保持群体的多样性和加速算法收敛还构造一个新的选择算子,该算子在选取下一代种群时按均匀设计选取多个搜索方向引导搜索.将该算法用于辽河油田多口水平井的优化设计,数值结果表明该算法的有效性.

An improved GA was presented for finding several representative and satisfactory solutions of a category of multi-objective systems uniformly distributed on the set of non-trivial solutions. In this algorithm the searching was guided by multiple fitness functions, each of which was equal to the weighted sum of two standardized performance indexes, and its weighting magnitude was generated by the uniform design. In order to keep the diversity of group and quicken the convergency of algorithm, a new selection op- erator was constituted as well. The operator selects several search directions to direct search by uniform design when generating the new population. This algorithm was used for the optimization design of several horizontal wells of Liaohe oil field, and it was shown by the numeric computation that the algorithm was valid.