The Study Of Improved Model And Accelerated Gradient Algorithm About The Pooling Problem

The pooling problem is a fundamental problem in petroleum industry,which is a class of nonconvex optimization problems.In 1978,Haverly proposed the pooling problem at the first time.Since then many scholars chose to study the properties of the pooling problem and design related algorithms.Because the feeds in production may have different attribute qualities,the pooling problem has been proved to be NP-hard.Besides,Dai has also proved that the pooling problem is still strongly NPhard even with only one quality.Hence,how to solve the nonconvex optimization problems is important recently.On the other hand,with the development of the industry,it is more significant to solve large-scale pooling problems.In this thesis,we firstly introduce the related concepts and analyse the structure of P-formulation about the pooling problem.Then we improve the problem to obtain an equivalent transformation in terms of auxiliary variables.Since it is difficult to solve the pooling problem with the existence of the nonconvex constraints,we covert the original pooling problem into a non-convex and non-smooth composite problem,where the objective function is constructed by a nonconvex but smooth item and a nonsmooth but convex item.Considering practical issues,we solve the improved P-formulation by using the improved accelerated gradient algorithm furthermore.Finally,we choose 7 classical examples of the pooling problem.The results of the numerical experiments show the advantages of the model and the algorithm.