دانلود رایگان مقاله کارایی پارتو جامع در بهینه سازی همتای قوی

Abstract

In this paper, an innovative concept named Comprehensive Pareto Efficiency is introduced in the context of robust counterpart optimization, which consists of three sub-concepts: Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). Different algorithms are developed for computing robust solutions with respect to these three sub-concepts. As all sub-concepts are based on the Probability of Constraint Violation (PCV), formulations of PCV under different probability distributions are derived and an alternative way to calculate PCV is also presented. Numerical studies are drawn from two applications (production planning problem and orienteering problem), to demonstrate the Comprehensive Pareto Efficiency. The numerical results show that the Comprehensive Pareto Efficiency has important significance for practical applications in terms of the evaluation of the quality of robust solutions and the analysis of the difference between different robust counterparts, which provides a new perspective for robust counterpart optimization.

6. Conclusion

In this paper, we introduced the concept of Comprehensive Pareto Efficiency in robust counterpart optimization which includes Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). We theoretically proved that RC2 under Normal distribution and RC∞ under Cauchy distribution achieve the best performance, with all PRO solutions generated are GPRO and EPRO. The numerical results of two applications show that PRO solutions can improve the performance compare with non-PRO solutions. By considering GPRO and EPRO solutions, we can have a deep understanding of the quality of the robust solutions and the difference between different robust counterparts. In general, the Comprehensive Pareto Efficiency provides a new perspective for robust counterpart optimization and has important significance in practice which can help us to find high quality solutions and make better decisions. We only consider single uncertain constraint in this paper, it is interesting to consider multiple uncertain constraints in robust counterpart optimization, many researchers have worked on this which is known as joint chance constraint. Future work will be conducted to extend the current concept to the multiple uncertain constraints case.