Название: Integer Optimization and its Computation in Emergency Management
Автор: Zhengtian Wu
Издательство: Academic Press/Elsevier
Год: 2023
Страниц: 298
Язык: английский
Формат: pdf
Размер: 10.8 MB

Studies on integer optimization in emergency management have attracted engineers and scientists from various disciplines such as management, mathematics, computer science, and other fields. Although there are a large number of literature reports on integer planning and emergency events, few books systematically explain the combination of the two. Researchers need a clear and thorough presentation of the theory and application of integer programming methods for emergency management.

Integer Optimization and its Computation in Emergency Management investigates the computation theory of integer optimization, developing integer programming methods for emergency management and explores related practical applications. Pursuing a holistic approach, this book establishes a fundamental framework for this topic, intended for graduate students who are interested in operations research and optimization, researchers investigating emergency management, and algorithm design engineers working on integer programming or other optimization applications.

The simple distributed model has been used in our implementation. There are one master computer and a certain number of slave computers in this distributed computing system. The master computer takes charge of computing the solution space of the polytope, dividing the solution space to segments, sending the segments to the slave computers, receiving the computation result from the slave computers, and exporting the computation result. Each slave computer receives the segment, judges whether there exists an integer point in its segment using Dang and Ye's fixed-point iterative method, and sends its result to the master.

All the programs are coded in C++ and run on Microsoft Windows platform. Two algorithms have been considered for the bounding linear program in Dang's iterative method. One is the simplex algorithm, the most popular algorithm for linear programming. We can call the API function in CPLEX Concert Technology to carry out this method. The other algorithm is the self-dual embedding technique presented in Todd, Shinji Mizuno "Mathematics of Operations Research". This algorithm detects LP infeasibility based on a proved criterion, and to our knowledge, it is the best method to solve linear programming problems by Dang and Ye's algorithm.

The main contribution of this study is developing a deterministic annealing neural network method that aims to obtain an approximated solution of graph partitioning. This deterministic annealing neural network (DANN) algorithm is a continuation method that attempts to identify a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. The proof of the global convergence of the iterative procedure is also given in this study. Numerical results show effectiveness of the proposed method.