Pooling problem: Alternate formulations and solution methods

Copyright @ 2004 INFORMSThe pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion. of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.This project was funded by Ultramar Canada and Luc Massé. The work of C. Audet was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 and by CRPC (Center for Research on Parallel Computation). The work of J. Brimberg was supported by NSERC grant #OGP205041. The work of P. Hansen was supported by FCAR(Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95ER1048, and NSERC grant #GP0105574

Tight-and-Cheap Conic Relaxation for the AC Optimal Power Flow Problem

The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks

Process Simulation and Control Optimization of a Blast Furnace Using Classical Thermodynamics Combined to a Direct Search Algorithm

Several numerical approaches have been proposed in the literature to simulate the behavior of modern blast furnaces: finite volume methods, data-mining models, heat and mass balance models, and classical thermodynamic simulations. Despite this, there is actually no efficient method for evaluating quickly optimal operating parameters of a blast furnace as a function of the iron ore composition, which takes into account all potential chemical reactions that could occur in the system. In the current study, we propose a global simulation strategy of a blast furnace, the 5-unit process simulation. It is based on classical thermodynamic calculations coupled to a direct search algorithm to optimize process parameters. These parameters include the minimum required metallurgical coke consumption as well as the optimal blast chemical composition and the total charge that simultaneously satisfy the overall heat and mass balances of the system. Moreover, a Gibbs free energy function for metallurgical coke is parameterized in the current study and used to fine-tune the simulation of the blast furnace. Optimal operating conditions and predicted output stream properties calculated by the proposed thermodynamic simulation strategy are compared with reference data found in the literature and have proven the validity and high precision of this simulation

Environmental Constraints Guide Migration of Malaria Parasites during Transmission

Migrating cells are guided in complex environments mainly by chemotaxis or structural cues presented by the surrounding tissue. During transmission of malaria, parasite motility in the skin is important for Plasmodium sporozoites to reach the blood circulation. Here we show that sporozoite migration varies in different skin environments the parasite encounters at the arbitrary sites of the mosquito bite. In order to systematically examine how sporozoite migration depends on the structure of the environment, we studied it in micro-fabricated obstacle arrays. The trajectories observed in vivo and in vitro closely resemble each other suggesting that structural constraints can be sufficient to guide Plasmodium sporozoites in complex environments. Sporozoite speed in different environments is optimized for migration and correlates with persistence length and dispersal. However, this correlation breaks down in mutant sporozoites that show adhesion impairment due to the lack of TRAP-like protein (TLP) on their surfaces. This may explain their delay in infecting the host. The flexibility of sporozoite adaption to different environments and a favorable speed for optimal dispersal ensures efficient host switching during malaria transmission

CONICOPF: conic relaxations for AC optimal power flow computations

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite relaxations for large-scale meshed networks in terms of optimality gap and computation time: the tight-and-cheap relaxation (TCR) and the quadratic convex relaxation (QCR). We compare these relaxations on 60 PGLib-OPF test cases with up to 1,354 buses under three operating conditions and show that TCR dominates QCR on all 20 typical (TYP) test cases, on 18 out of 20 active power increase (API), and 12 out of 20 small angle difference (SAD). Selected state-of-the-art conic relaxations are implemented in the new MATLAB-based package CONICOPF available on GitHub