论文标题
关于合并问题的顺序线性编程的有效性
On the Effectiveness of Sequential Linear Programming for the Pooling Problem
论文作者
论文摘要
本文的目的是比较局部解决方案技术的性能(即采用随机起点的顺序线性编程(SLP))与最新的全球求解器(例如男爵和更复杂的本地求解器)(例如顺序二次编程和集合问题的内部点)。这些问题可能具有许多本地Optima,我们提供了一个小例子,说明了如何发生这种情况。 我们证明,自从快速可靠的QP求解器,内部点方法和复杂的全球求解器的到来以来,SLP通常被认为是过时的 - 当标准是在给定可接受的可接受时间预算中找到解决方案的质量时,对于重要的合并问题而言,仍然是重要的选择方法。 此外,我们引入了一种新的公式,对于固定需求的情况,QQ构造专门使用比例变量。我们比较了SLP和全球求解器男爵在QQ形成和其他常见配方方面的性能。与其他测试的其他配方相比,带有QQ成型的男爵会产生较弱的界限,但对于SLP和Baron,QQ构造都在给定时间预算中找到了最佳解决方案。可以通过类似PQ样切割来增强QQ构造,在这种情况下,获得与PQ构型相同的边界。但是,由于其他约束,相关的时间罚款导致时间预算内的解决方案质量较差。
The aim of this paper is to compare the performance of a local solution technique -- namely Sequential Linear Programming (SLP) employing random starting points -- with state-of-the-art global solvers such as Baron and more sophisticated local solvers such as Sequential Quadratic Programming and Interior Point for the pooling problem. These problems can have many local optima, and we present a small example that illustrates how this can occur. We demonstrate that SLP -- usually deemed obsolete since the arrival of fast reliable QP solvers, Interior Point Methods and sophisticated global solvers -- is still the method of choice for an important class of pooling problem when the criterion is the quality of the solution found within a given acceptable time budget. In addition we introduce a new formulation, the qq-formulation, for the case of fixed demands, that exclusively uses proportional variables. We compare the performance of SLP and the global solver Baron on the qq-formulation and other common formulations. While Baron with the qq-formulation generates weaker bounds than with the other formulations tested, for both SLP and Baron the qq-formulation finds the best solutions within a given time budget. The qq-formulation can be strengthened by pq-like cuts in which case the same bounds as for the pq-formulation are obtained. However the associated time penalty due to the additional constraints results in poorer solution quality within the time budget.