Main menu >> Chemical Engineering >> Optimization and Process Systems Engineering
Chemical Engineering
Optimization and Process Systems Engineering
- A Lagrangian Approach to the Pooling Problem
- BARON: An All-Purpose Global Optimization Package
- Branch-and-Reduce Algorithms for Global Optimization
- Bridging the Gap between Heuristics and Optimization in Process Synthesis and Operations
- Combinatorial Problems in Computational Chemistry
- Modeling and Optimization Techniques for Scheduling Continuous Chemical Processes
- Planning in the Process Industry under Uncertainty
^ A Lagrangian Approach to the Pooling Problem
N. V. Sahinidis,* N. Adhya, M. Tawarmalani
National Science Foundation, DMI 95-02722; Mobil Technology Center
Pooling and blending occur frequently in the petrochemical industry where crude oils, procured from various sources, are mixed together to manufacture several end-products. Finding optimal solutions to pooling problems requires the solution of nonlinear optimization problems with multiple local minima. This project introduces a new Lagrangian relaxation approach for developing lower bounds for the pooling problem. This research team proved that, for the multiple quality case, the Lagrangian approach provides tighter lower bounds than the standard linear programming relaxations used in global optimization algorithms.
^ BARON: An All-Purpose Global Optimization Package
N. V. Sahinidis,* M. Tawarmalani
National Science Foundation, DMI 94-14615, DMI 95-02722
The area of global optimization software is so important and yet so underdeveloped. This projects aims to develop BARON: an all-purpose, high-performance global optimization methodology to support engineering design and manufacturing. BARON (Branch-And-Reduce-Optimization-Navigator) executes a global optimization strategy by navigating its way through user-provided subroutines. Its optimization strategy integrates conventional branch-and-bound with a wide variety of range-reduction tests and branching schemes. Specialized modules have been developed for special problem classes, including concave minimization over polyhedra, polynomial programs, mixed integer and quadratic programs, and factorable programs.
^ Branch-and-Reduce Algorithms for Global Optimization
N. V. Sahinidis,* M. Tawarmalani
National Science Foundation, DMI 94-14615, DMI 95-02722
Realistic treatments of physical and engineering systems frequently involve nonlinear models in which optimization requires escaping from local minima traps. This project develops global optimization methodologies. The algorithms solve sequences of convex underestimating subproblems obtained by evolutionary subdivision of the search region. Novel features include optimally based and feasibility based range reduction, new branching rules, new bounding schemes, and efficient heuristics to accelerate convergence. The project addresses applications in engineering design, molecular structure determination, and economics. Special classes of problems are also considered, including minimization of concave functions over convex sets, minimization of products of convex functions, bilinear programs, integer programs, and factorable programs.
^ Bridging the Gap between Heuristics and Optimization in Process Synthesis and Operations
N. V. Sahinidis,* K. Furman, S. Ahmed
National Science Foundation, CTS 97-04643
Heuristics in process synthesis and operations offer fast solutions but no guarantee of optimality. Optimization approaches, on the other hand, offer rigor but suffer combinatorial explosion of computational requirements. This research team pursues analytical investigations to characterize the behavior of heuristics and optimization algorithms and produces a framework that combines the strengths of the two approaches while eliminating their weaknesses. This research proved that process planning is NP-hard and that synthesis of heat exchanger networks is NP-hard in the strong sense. As the relaxation gap of integer programming formulations for these problems asymptotically diminishes, relaxation-based heuristics that are optimal in expectation are developed.
^ Combinatorial Problems in Computational Chemistry
N. V. Sahinidis,* A. Vaia, G. Nanda, M. Tawarmalani
University of Illinois; National Science Foundation, BES 98-73586
The enumeration of large, combinatorial search spaces presents a central conceptual difficulty in many problems in combinatorial chemistry, chemometrics, and molecular design. This research develops novel mathematical models and algorithms to address such combinatorial challenges. In one application area, the team is developing models and algorithms for interpreting FTIR spectra. In another application area, they are developing a systematic methodology for the design of environmentally benign alternative refrigerants. This has led to the identification of several novel potential alternatives. The team is developing molecular design techniques with an emphasis on minimizing the environmental impact over the entire life cycle of the new compounds.
^ Modeling and Optimization Techniques for Scheduling Continuous Chemical Processes
N. V. Sahinidis,* E. Kourpas
Technical Association of the Pulp and Paper Industry Foundation; National Science Foundation, DMI 95-02722
The goal of this project is to develop novel modeling and optimization techniques for improving energy efficiency and productivity in the process industry. Production of paper, dyes, and polymers are some examples. In particular, this research addresses the development of novel formulations for short-term, reactive scheduling of continuous production facilities with resource constraints and sequence-dependent changeovers, the development of efficient optimization algorithms for solving these scheduling formulations, and the potential of the developed techniques to reduce waste and minimize costs.
^ Planning in the Process Industry under Uncertainty
N. V. Sahinidis,* S. Ahmed
National Science Foundation, DMI 94-14615, DMI 95-02722
As the chemical industry is becoming increasingly competitive, tools to hedge against uncertainty become increasingly important. The project develops a two-stage stochastic optimization approach to the problem of planning in the process industries. Both discrete and continuous random parameters are considered. In one research direction, the team introduced the upper partial mean as a new measure of robustness and developed robust process planning algorithms under uncertainty. In another research direction, the team developed approximation algorithms for two-stage stochastic integer programs. The research group provides proofs that these schemes are optimal in expectation as the problem size increases.
