A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York

Dynamic Heterogeneity in Fully Miscible Blends of Polystyrene with Oligostyrene

Binary blends of polystyrene with oligostyrene are perfectly miscible (χ=0) yet dynamically heterogeneous. This is evidenced by independent probing of the dipole relaxation perpendicular to the backbone by dielectric spectroscopy and molecular dynamics. The self-concentration model with a single intra-molecular length scale qualitatively describes the slower segmental dynamics. A quantitative comparison based on MD however, requires a composition-dependent length scale. The pertinent dynamic length scale that best describes the slow segmental dynamics in miscible blends relates to both intra- and inter-molecular contributions

Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2

<div><p>The global mixed-integer quadratic optimizer, GloMIQO, addresses mixed-integer quadratically constrained quadratic programs (MIQCQP) to ε-global optimality. This paper documents the branch-and-cut framework integrated into GloMIQO 2. Cutting planes are derived from reformulation–linearization technique equations, convex multivariable terms, αBB convexifications, and low- and high-dimensional edge-concave aggregations. Cuts are based on both individual equations and collections of nonlinear terms in MIQCQP. Novel contributions of this paper include: development of a corollary to Crama's [<i>Concave extensions for nonlinear 0-1 maximization problems</i>, Math. Program. 61 (1993), pp. 53–60] necessary and sufficient condition for the existence of a cut dominating the termwise relaxation of a bilinear expression; algorithmic descriptions for deriving each class of cut; presentation of a branch-and-cut framework integrating the cuts. Computational results are presented along with comparison of the GloMIQO 2 performance to several state-of-the-art solvers.</p></div

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

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

Designing Energy-Efficient Heat Recovery Networks using Mixed-Integer Nonlinear Optimisation

Many industrial processes involve heating and cooling liquids: a quarter of the EU 2012 energy consumption came from industry and industry uses 73% of this energy on heating and cooling. We discuss mixed-integer nonlinear optimisation and its applications to energy efficiency. Our particular emphasis is on algorithms and solution techniques enabling optimisation for large-scale industrial networks. As a first application, optimising heat exchangers networks may increase efficiency in industrial plants. We develop deterministic global optimisation algorithms for a mixed-integer nonlinear optimisation model that simultaneously incorporates utility cost, equipment area, and hot/cold stream matches. We automatically recognise and exploit special mathematical structures common in heat recovery. We also computationally demonstrate the impact on the global optimisation solver ANTIGONE and benchmark large-scale test cases against heuristic approaches. As a second application, we discuss special structure in nonconvex quadratically-constrained optimisation problems, particularly through the lens of stream mixing and intermediate blending on process systems engineering networks. We take a parametric approach to uncovering topological structure and sparsity of the standard pooling problem in its p-formulation. We show that the sparse patterns of active topological structure are associated with a piecewise objective function. Finally, the presentation explains the conditions under which sparsity vanishes and where the combinatorial complexity emerges to cross over the P/NP boundary. We formally present the results obtained and their derivations for various specialised instances

Fronthaul data compression for Uplink CoMP in cloud radio access network (C-RAN)

The design of efficient wireless fronthaul connections for future heterogeneous networks incorporating emerging paradigms such as cloud radio access network has become a challenging task that requires the most effective utilisation of fronthaul network resources. In this paper, we propose to use distributed compression to reduce the fronthaul traffic in uplink Coordinated Multi-Point for cloud radio access network. Unlike the conventional approach where each coordinating point quantises and forwards its own observation to the processing centre, these observations are compressed before forwarding. At the processing centre, the decompression of the observations and the decoding of the user message are conducted in a successive manner. The essence of this approach is the optimisation of the distributed compression using an iterative algorithm to achieve maximal user rate with a given fronthaul rate. In other words, for a target user rate the generated fronthaul traffic is minimised. Moreover, joint decompression and decoding is studied and an iterative optimisation algorithm is devised accordingly. Finally, the analysis is extended to multi-user case and our results reveal that, in both dense and ultra-dense urban deployment scenarios, the usage of distributed compression can efficiently reduce the required fronthaul rate and a further reduction is obtained with joint operation

Evolution of novel wood decay mechanisms in Agaricales revealed by the genome sequences of Fistulina hepatica and Cylindrobasidium torrendii

Wood decay mechanisms in Agaricomycotina have been traditionally separated in two categories termed white and brown rot. Recently the accuracy of such a dichotomy has been questioned. Here, we present the genome sequences of the white-rot fungus Cylindrobasidium torrendii and the brown-rot fungus Fistulina hepatica both members of Agaricales, combining comparative genomics and wood decay experiments. C torrendii is closely related to the white-rot root pathogen Armillaria mellea, while F. hepatica is related to Schizophyllum commune, which has been reported to cause white rot. Our results suggest that C torrendii and S. commune are intermediate between white-rot and brown-rot fungi, but at the same time they show characteristics of decay that resembles soft rot. Both species cause weak wood decay and degrade all wood components but leave the middle lamella intact. Their gene content related to lignin degradation is reduced, similar to brown-rot fungi, but both have maintained a rich array of genes related to carbohydrate degradation, similar to white-rot fungi. These characteristics appear to have evolved from white-rot ancestors with stronger ligninolytic ability. F. hepatica shows characteristics of brown rot both in terms of wood decay genes found in its genome and the decay that it causes. However, genes related to cellulose degradation are still present, which is a plesiomorphic characteristic shared with its white-rot ancestors. Four wood degradation-related genes, homologs of which are frequently lost in brown-rot fungi, show signs of pseudogenization in the genome of F. hepatica. These results suggest that transition toward a brown-rot lifestyle could be an ongoing process in F. hepatica. Our results reinforce the idea that wood decay mechanisms are more diverse than initially thought and that the dichotomous separation of wood decay mechanisms in Agaricomycotina into white rot and brown rot should be revisited. (C) 2015 Elsevier Inc. All rights reserved