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

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201

Phase Diagram of Tapered Copolymers Based on Isoprene and Styrene

Although several phase diagrams of block copolymers prepared by sequential monomer addition are known today, the phase diagrams of the corresponding tapered copolymers have not been reported in detail and this despite the industrial importance of the latter. A phase diagram based on a series of tapered diblock copolymers is reported, generated by the sec-butyllithium initiated statistical anionic copolymerization of styrene and isoprene in cyclohexane. This affords copolymers with polyisoprene volume fractions, f, in the range of 0.43 < f < 0.82 and total molar mass in the range of 46–160 kg mol–1. The phase diagram consists of lamellae, hexagonally packed cylinders, weakly ordered hexagonally packed cylinders (CYL), and perforated (PL) as well as irregular bicontinuous morphologies. The phase state in the tapered copolymers bears some similarities and several distinct differences in comparison to the respective copolymers prepared by conventional sequential monomer addition. It is shown that the weakly ordered CYL/PL morphologies comprise a large part of the phase diagram that is significantly extended in comparison to diblock copolymers prepared sequentially. On the other hand, the composition range for the bicontinuous morphologies is similar in the two systems (0.64 < fPI < 0.68)

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids

The recently discovered scaling law for the relaxation times, tau=f(T,V^g), where T is temperature and V the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [I. Avramov, J. Non-Cryst. Solids 262, 258 (2000).]. In this modification the entropy is calculated by an alternative route, while retaining the approximation that the heat capacity is constant with T and P. The resulting expression for the variation of the relaxation time with T and V is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy. we find that the scaling exponent g can be identified with the Gruneisen constant.Comment: 24 pages, 7 figure

Heat integration of an Olefins Plant: Pinch Analysis and mathematical optimization working together

This work explores a two-step, complexity reducing methodology, to analyze heat integration opportunities of an existing Olefins Plant, identify and quantify reduction of energy consumption, and propose changes of the existing heat exchanger network to achieve these goals. Besides the analysis of plant design conditions, multiple operational scenarios were considered to propose modifications for handling real plant operation (flexibility). On the strength of plant complexity and large dimension, work methodology was split into two parts: initially, the whole plant was evaluated with traditional Pinch Analysis tools. Several opportunities were identified and modifications proposed. Modifications were segregated to represent small and independent portions of the original process. One of them was selected to be re-analyzed, considering two scenarios. Reduction of problem dimension allowed mathematical methodologies (formulation with decomposition, applying LP, MILP and NLP optimization methods) to synthesize flexible networks to be applied, generating a feasible modification capable of fulfilling the proposed operational scenarios

Stationary probability density of stochastic search processes in global optimization

A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability contain the global optima can be readily defined. The density estimation procedure involves a controlled number of linear operations, with a computational cost per iteration that grows linearly with problem size

Constant-time solution to the Global Optimization Problem using Bruschweiler's ensemble search algorithm

A constant-time solution of the continuous Global Optimization Problem (GOP) is obtained by using an ensemble algorithm. We show that under certain assumptions, the solution can be guaranteed by mapping the GOP onto a discrete unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is applied. For adequate sensitivities of the measurement technique, the query complexity of the ensemble search algorithm depends linearly on the size of the function's domain. Advantages and limitations of an eventual NMR implementation are discussed.Comment: 14 pages, 0 figure

Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows

Athermal plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated from simulations at different densities include the distributions of energy drops, stress drops, and strain intervals between the flow events. By reference to hidden scale invariance we show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allows one to predict the plastic flow-event properties at other densities. We furthermore demonstrate quasiuniversality of the flow-event statistics

Genome sequence of the button mushroom Agaricus bisporus reveals mechanisms governing adaptation to a humic-rich ecological niche

Agaricus bisporus is the model fungus for the adaptation, persistence, and growth in the humic-rich leaf-litter environment. Aside from its ecological role, A. bisporus has been an important component of the human diet for over 200 y and worldwide cultivation of the "button mushroom" forms a multibillion dollar industry. We present two A. bisporus genomes, their gene repertoires and transcript profiles on compost andduringmushroomformation.The genomes encode a full repertoire of polysaccharide-degrading enzymes similar to that of wood-decayers. Comparative transcriptomics of mycelium grown on defined medium, casing-soil, and compost revealed genes encoding enzymes involved in xylan, cellulose, pectin, and protein degradation aremore highly expressed in compost. The striking expansion of heme-thiolate peroxidases and β-etherases is distinctive from Agaricomycotina wood-decayers and suggests a broad attack on decaying lignin and related metabolites found in humic acid-rich environment. Similarly, up-regulation of these genes together with a lignolytic manganese peroxidase, multiple copper radical oxidases, and cytochrome P450s is consistent with challenges posed by complex humic-rich substrates. The gene repertoire and expression of hydrolytic enzymes in A. bisporus is substantially different from the taxonomically related ectomycorrhizal symbiont Laccaria bicolor. A common promoter motif was also identified in genes very highly expressed in humic-rich substrates. These observations reveal genetic and enzymatic mechanisms governing adaptation to the humic-rich ecological niche formed during plant degradation, further defining the critical role such fungi contribute to soil structure and carbon sequestration in terrestrial ecosystems. Genome sequence will expedite mushroom breeding for improved agronomic characteristics