· 2010
A comprehensive treatment of nonlinear programming concepts and algorithms, especially as they apply to challenging applications in chemical process engineering.
This study aims at improving the solution efficiency of Mixed Integer Nonlinear Programming (MINLP) through parallelism. Unlike most conventional parallel implementations of MINLP solvers, which utilize multi-threads to share the burden in the serial mode, the proposed method combines hybrid algorithms running on different threads. Two types of algorithms are designed in a parallel structure. One is the Quesada and Grossman's LP/NLP based branch and bound algorithm (QG); the other is Tabu Search (TS). The proposed method attempts to minimize the search space through continuous communication and exchange of intermediate results from each thread. Three kinds of information are exchanged between the two threads. First, the best solution in TS, if feasible, serves as a valid upper bound for QG. Second, new approximations which can further tighten the lower bound of QG can be generated at nodes provided by the TS. Third, strong branching in QG may fix some integer variables, which can help reduce the search space of TS. Both threads can thus benefit from the exchanged information in the hybrid method. Numerical results show that solution time can be greatly reduced for the tested MINLP. In addition, complexity analysis of the parallel approach suggests that the proposed method has the potential for superlinear speedup.
Over the last 20 years, fundamental design concepts and advanced computer modeling have revolutionized process design for chemical engineering. Team work and creative problem solving are still the building blocks of successful design, but new design concepts and novel mathematical programming models based on computer-based tools have taken out much of the guess-work. This book presents the new revolutionary knowledge, taking a systematic approach to design at all levels.
Topics of the conference focused on the integration of process design across subsystems, downstream concerns such as operability, safety and the environment, and the opportunities and challenges in design posed by continuous advances in computer hardware and software environments.
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· 1995
Abstract: "Previous experience with predictive control algorithms has shown that the way the optimization problems are formulated and solved has a big impact in the success of the control strategy. Here a multiple shooting formulation is proposed, where a process model is integrated separately inside each sampling interval, and the corresponding equality constraints are added directly to the optimization problem. It is shown that the resulting formulation provides a more reliable framework for the solution of predictive control problems, both in the linear and nonlinear cases. This strategy is compared with the original nonlinear Newton-type (state space) algorithm, on a number of process models with challenging features, including the reactor model from the Tennessee Eastman problem."
This IMA Volume in Mathematics and its Applications LARGE-SCALE OPTIMIZATION WITH APPLICATIONS, PART II: OPTIMAL DESIGN AND CONTROL is one of the three volumes based on the proceedings of the 1995 IMA three week Summer Program on "Large-Scale Optimization with Applications to Inverse Problems, Optimal Control and Design, and Molecular and Struc tural Optimization." The other two related proceedings appeared as Vol ume 92: Large-Scale Optirpization with Applications, Part I: Optimization in Inverse Problems and Design and Volume 94: Large-Scale Optimization with Applications, Part III: Molecular Structure and Optimization. We would like to thank Lorenz T. Biegler, Thomas F. Coleman, An drew R. Conn, and Fadil N. Santosa for their excellent work as organizers of the meetings and for editing the proceedings. We also take this opportunity to thank the National Science Founda tion (NSF), the Department of Energy (DOE), and the Alfred P. Sloan support made the workshops possible.
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