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.
Real-time optimization (RTO) has become a standard practice to improve production benefits during the past years. The efficiency of solving optimization problems is critical because a large computational delay leads to the possible loss of validity and availability of RTO. In this study, the Mnemonic Enhancement Optimization (MEO) strategy of initialization for RTO has been extended by taking advantage of optimal sensitivity. The approximation precision and the solution information database accumulation efficiency of the proposed sensitivity-based MEO are briefly analyzed. The numerical results tested with a high-pressure column of a cryogenic air separation unit were in agreement with the theoretical analysis.
The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.
The dynamic mechanism of plate tectonics remains a reasonable theory, but one with shortcomings such as insufficient bases for plate division, unclear plate boundaries, and unclear geological characteristics. This book proposes that the world's continents should not be divided by plates, and that their formation is not due to plate tectonics but rather due to global crustal uplift evolution and sea-land evolution. This proposal is based on the authors' broad theoretical foundation and comprehensive professional knowledge, built up over more than ten years of in-depth research by many scholars on the evolution of the Earth's continents.In this book, many case studies are better explained by global crustal uplift and sea-land evolution. Namely, that the entire continents of the world are indivisible, and the changes of each land block over geological periods resulted from the sea-land changes.The book further develops the original 'geomechanics theory' created by the famous geologist Li Siguang. As a vibrant and highly rigorous work, Prof Li's book offered important theoretical guidance that enriched the global geological community and led to a re-development within geological science. The strong response highlights the significance of geomechanics theory and our theories that build upon it in this book.
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