... Nick Sahinidis, Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA. Computer-Aided Molecular Design (CAMD) is a powerful technique to identify compounds ... The property method used for these stages is the GC+ method... more
... Nick Sahinidis, Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA. Computer-Aided Molecular Design (CAMD) is a powerful technique to identify compounds ... The property method used for these stages is the GC+ method developed by Gani and coworkers [ ...
The arithmetic solution of partial differential equations (PDE) is a computationally demanding problem that appears in many scientific disciplines. Although until recently direct methods were preferred for the solution of such systems... more
The arithmetic solution of partial differential equations (PDE) is a computationally demanding problem that appears in many scientific disciplines. Although until recently direct methods were preferred for the solution of such systems because of their robustness and predictable behavior, recent development in iterative solvers have shifted the focus towards their direction [1]. The main driving force behind the use of iterative solvers is their computational efficiency for solving very large linear systems on high-performance computers, and in this work we present the use of Graphics Processing Units (GPUs) for the efficient solution of PDEs by various iterative methods. The nine test problems studied arise from computational fluid dynamics, heat transfer and structural mechanics applications and are commonly used in a wide variety of industrial and engineering problems. In [2] it is shown that for these problems the most robust and efficient iterative algorithm on a 16-node Linux c...
Sequestration of CO2 in existing and abandoned oil reservoirs, deep saline aquifers, and coal seams are currently among techniques intensely studied by the international research community for their potential to reduce greenhouse gases.... more
Sequestration of CO2 in existing and abandoned oil reservoirs, deep saline aquifers, and coal seams are currently among techniques intensely studied by the international research community for their potential to reduce greenhouse gases. In the case of sequestration to abandoned oil reservoirs, CO2 is pressurized and stored in these reservoirs, and a cement plug is placed at the bottom of the injection well. This cement plug, combined with an impermeable layer of caprock, creates a seal for the storage system, thus preventing CO2 from escaping. A main concern for any sequestration system is whether it may leak CO2 over a long-term time horizon consisting of up to many thousand years. The outcome depends on the competition between CO2 sequestration and leakage processes. Leakages after sequestration in an abandoned reservoir may occur from failure of the manmade cement seal, or through naturally existing fractures in the caprock. Additionally, the CO2 source pool may be dissolved into...
Air Liquide operates a number of industrial gas pipeline networks around the world. Each of them connects several air separation plants and a number of customers. In each of the plants, there can be one or more air separation units (ASU),... more
Air Liquide operates a number of industrial gas pipeline networks around the world. Each of them connects several air separation plants and a number of customers. In each of the plants, there can be one or more air separation units (ASU), which separates air into pure oxygen, nitrogen and argon in either gas or liquid phase. Usually, the gaseous oxygen and nitrogen supply different pipeline sections at different pressure levels after being pressurized either in the ASU or by compressors downstream of the ASU. The operation of such a network of plants, pipelines and customers is complicated due to the rapidly fluctuating electricity prices and customer demands. To efficiently operate this network under these conditions, real-time optimization techniques are necessary. The real-time optimization model was developed by Air Liquide to describe both plant and pipeline operations through mass balance, energy balance and regression on historical data. Nonconvex functional forms are necessa...
Research Interests:
NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming Theory, Algorithms, Software, and Applications MohitTawarmalani and Nikolaos V. Sahinidis ic... more
NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming Theory, Algorithms, Software, and Applications MohitTawarmalani and Nikolaos V. Sahinidis ic Publishers
Research Interests:
... For certain nonlinear functions, we develop convexification techniques Mohit Tawarmalani: Krannert School of Management, Purdue University. e-mail: mtawarma@mgmt.purdue.edu. ... Wenow derive a few properties of the convex envelope as... more
... For certain nonlinear functions, we develop convexification techniques Mohit Tawarmalani: Krannert School of Management, Purdue University. e-mail: mtawarma@mgmt.purdue.edu. ... Wenow derive a few properties of the convex envelope as a corollary of the above result. ...
Research Interests:
ABSTRACT
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT
ABSTRACT
ABSTRACT
NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming Theory, Algorithms, Software, and Applications MohitTawarmalani and Nikolaos V. Sahinidis ic... more
NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming Theory, Algorithms, Software, and Applications MohitTawarmalani and Nikolaos V. Sahinidis ic Publishers
Research Interests:
Research Interests: Engineering, Physics, Chemistry, Computational Biology, Biology, and 14 moreMedicine, Multidisciplinary, Optimization Problem, Software, Protein structure, Proteins, PLoS one, Protein Function, Amino Acids, Line Search Derivative Free Optimization, Source Code, Amino Acid Profile, Protein Conformation, and Internet
Research Interests:
Research Interests: Cognitive Science, Distributed Computing, Parallel Computing, Iterative Methods, Heat Transfer, and 10 moreDistributed Shared Memory System, Scientific Computing, Computation Fluid Dynamics, PARTIAL DIFFERENTIAL EQUATION, Linux Cluster, Linear System, Linear Systems, Differential equation, Conjugate Gradient, and graphic processing unit (GPU)
ABSTRACT
Research Interests:
Research Interests:
ABSTRACT We consider the problem of constructing the convex envelope of a lower semi-continuous function defined over a compact convex set. We formulate the envelope representation problem as a convex optimization problem for functions... more
ABSTRACT We consider the problem of constructing the convex envelope of a lower semi-continuous function defined over a compact convex set. We formulate the envelope representation problem as a convex optimization problem for functions whose generating sets consist of finitely many compact convex sets. In particular, we consider nonnegative functions that are products of convex and component-wise concave functions and derive closed-form expressions for the convex envelopes of a wide class of such functions. Several examples demonstrate that these envelopes reduce significantly the relaxation gaps of widely used factorable relaxation techniques.
Research Interests:
... global concave minimization. In IE Grossmann, editor, Global Optimization inEngineering Design, Kluwer Academic Publishers, Boston, MA. 5. BA Murtagh and MA Saunders (1995), MD/OS 5.4 User's Guide. Technical... more
... global concave minimization. In IE Grossmann, editor, Global Optimization inEngineering Design, Kluwer Academic Publishers, Boston, MA. 5. BA Murtagh and MA Saunders (1995), MD/OS 5.4 User's Guide. Technical Report ...
Research Interests:
In the tradition of modeling languages for optimization, a single model is passed to a solver for solution. In this paper, we extend BARON’s modeling language in order to facilitate the communication of problem-specific relaxation... more
In the tradition of modeling languages for optimization, a single model is passed to a solver for solution. In this paper, we extend BARON’s modeling language in order to facilitate the communication of problem-specific relaxation information from the modeler to the branch-and-bound solver. This effectively results into two models being passed from the modeling language to the solver. Three important
Research Interests:
Research Interests:
ABSTRACT In the simplex method for linear optimisation, two linear systems involving a square non-singular basis matrix B and its transpose are solved at each iteration. A column of B is then replaced, and the solution of these two linear... more
ABSTRACT In the simplex method for linear optimisation, two linear systems involving a square non-singular basis matrix B and its transpose are solved at each iteration. A column of B is then replaced, and the solution of these two linear systems is required again. For the past four decades, researchers have made considerable advancements in updating the sparse LU factors of the basis matrix in this algorithm. This paper reviews the state-of-the-art in LU update procedures, while analysing each procedure to gain a full understanding of the progress made in this area.
Research Interests:
ABSTRACT This paper reviews the computational aspects of the LU factorisation of large-scale linear optimisation bases. In the simplex algorithm, the solution of two linear systems, involving a square basis matrix and its transpose,... more
ABSTRACT This paper reviews the computational aspects of the LU factorisation of large-scale linear optimisation bases. In the simplex algorithm, the solution of two linear systems, involving a square basis matrix and its transpose, accounts for a large portion of the computation time. The most widely used solution technique is LU factorisation and accompanying update routines. The utilisation of a column replacement update procedure means that a given factorisation may be kept over a large number of simplex iterations. Therefore, a significant emphasis is placed on the sparsity of the LU factors. This emphasis means that a suitable factorisation routine must be chosen with care. A review of LU factorisation is offered, including stability monitoring and analysis, sparsity analysis, error analysis, algorithmic aspects, and state-of-the-art LU factorisation routines.
Research Interests:
ABSTRACT High levels of emissions of ozone-depleting substances and greenhouse gases from supermarkets around the world can be attributed to the leakage of hydrofluorocarbons (HFCs) and the generation of electric power required for retail... more
ABSTRACT High levels of emissions of ozone-depleting substances and greenhouse gases from supermarkets around the world can be attributed to the leakage of hydrofluorocarbons (HFCs) and the generation of electric power required for retail food refrigeration. Indirect refrigeration loops are ideally suited for reductions mandated by regulation standards because they reduce leakage and can lead to significantly lower total energy consumption. Hence, the design and identification of fluids that boost refrigeration performance while meeting safety and environmental guidelines is of considerable interest. Using a recently developed molecular design methodology (Samudra and Sahinidis, AIChE J., published online Apr 25, 2013, 10.1002/aic.14112) as our starting point, in this work, we developed a model and search technique for identifying ideal secondary refrigerants. Accurate property models that predict characteristic refrigerant properties guided the search for molecules. We also included environmental and safety metrics [biodegradability and lethal concentration (LC50)], along with performance criteria for heat-transfer efficiency, to analyze the candidate molecules. We identified a number of novel molecules as well as known compounds that have not been used as secondary refrigerants.
Research Interests:
ABSTRACT
Research Interests:
Research Interests:
ABSTRACT In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as... more
ABSTRACT In this paper, surrogate models are built iteratively using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the values of the uncertain parameters into the closed-form polynomial functions. On the basis of the results of MC simulation, the uncertainties of injecting CO2 underground are quantified for a saline aquifer. Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO2 injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.
Research Interests:
Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity... more
Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning. The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The
Research Interests:
The package planning (chip layout and compaction) problem can be stated in terms of an optimization problem. The goal is to find the relative placement and shapes of the chips in a way that minimizes the total chip area subject to linear... more
The package planning (chip layout and compaction) problem can be stated in terms of an optimization problem. The goal is to find the relative placement and shapes of the chips in a way that minimizes the total chip area subject to linear and nonlinear constraints. The constraints arise from geometric design rules, distance and connectivity requirements between various components, area and communication costs and other designer-specified requirements. The problem has been addressed in various settings. It is of unusual computational difficulty due to the nonconvexities- involved. This paper presents a new mixed-integer nonlinear programming formulation for simultaneous chip layout and two-dimensional compaction. Global optimization algorithms are developed for this model as well as for an existing formulation for the chip compaction problem. These algorithms are implemented with the global optimization software BARON and illustrated by solving several example problems.
Research Interests:
... 21. NV Sahinidis, IE Grossmann, R. Fornari and M. Chathrathi, Long range planning model for the chemical process industries. Computers Chem. Engng 13, 10491063 (1989). 22. ... 25. LA Wolsey, Strong formulations for mixed integer... more
... 21. NV Sahinidis, IE Grossmann, R. Fornari and M. Chathrathi, Long range planning model for the chemical process industries. Computers Chem. Engng 13, 10491063 (1989). 22. ... 25. LA Wolsey, Strong formulations for mixed integer programming: a survey. Math. Progr. ...