Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
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DOI：
10.1162/evco.1994.2.3.221
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发表时间：
1994-01-01
影响因子：
6.8
通讯作者：
Deb, Kalyanmoy
中科院分区：
文献类型：
--
作者：
Srinivas, N.;Deb, Kalyanmoy
在尝试解决多目标优化问题时，许多传统方法会将目标向量标量化为单一目标。在这种情况下，所得到的解决方案对标量化过程中使用的权重向量非常敏感，要求用户对基本问题有所了解。此外，在解决多目标问题时，设计者可能会对一组帕累托最优点而非单点感兴趣。由于遗传算法（GA）的工作对象是点群，因此在多目标优化问题中使用遗传算法来同时捕捉多个解决方案似乎很自然。尽管 Schaffer 已经实现了矢量评估遗传算法（VEGA），并尝试解决一些多目标问题，但该算法似乎偏向于某些区域。在本文中，我们研究了戈德伯格（Goldberg）在遗传算法中的非支配排序概念，以及一种同时找到多个帕累托最优点的利基和分化方法。在 Schaffer 等人使用的三个问题上获得的原理证明结果表明，所提出的方法可以扩展到更高维度和更困难的多目标问题上。此外，还讨论了一些关于扩展和应用该算法的建议。
In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.