多目标优化问题的研究

针对传统方法求解多目标优化问题的局限性,应用一种新的算法求解。遗传算法从问题解的串集开始搜索,覆盖面大,可以同时处理群体中的多个个体,利于全局择优,减少陷入局部最优的风险,而最小生成树具有过程简单清晰、适用性广泛的特点,结合两者的优点,构造了基于生成树的遗传算法。首先通过加权目标规划法求出最优解,然后通过遗传算法和基于生成树的遗传算法求解,结果表明,对于小规模的多目标优化问题,两种算法都可以求出最优解,在求解时间方面,基于生成树的遗传算法比遗传算法更优越。

Research on Multiobjective Optimization Problem

Aiming at the limitation of the traditional methods to solve the multi-objective optimization problem , this paper applies a new kind of algorithm to it .Genetic Algorithm （ GA） starts to search from the set of solution with its big coverage able to handle more than one individual at the same time , beneficial to global optimization , reducing the risk of fall into local optimum , while the minimum spanning tree has the characteristics of simple process and wide applicability .Combined with the advantages of the both algorithms , genetic algorithm is constructed on the basis of spanning tree .By finding the optimal solution by weighted goal programming method , and then solving the problem by the genetic algorithm and genetic algorithm based on spanning tree , the result shows that for small-scale multi-objective optimization problem , two algorithms can find out the optimal solution , and in terms of sol-ving time, genetic algorithm based on spanning tree is superior to genetic algorithm .