Study of the Parallel Variable Distribution Algorithms for Solving Optimization Problems 

Author  XuFangFang 
Tutor  HeGuoPing 
School  Shandong University of Science and Technology 
Course  Applied Mathematics 
Keywords  PVD Algorithm "Forgetmenot" term SQP Type PVD Algorithm Maratos Effect Inexact PVD Algorithm Mixinteger Nonlinear Optimization Problem 
CLC  O224 
Type  Master's thesis 
Year  2010 
Downloads  46 
Quotes  0 
Parallel Variable Distribution algorithm(PVD algorithm) is a kind of parallel algorithm in the whole structure. The main difference from other algorithms is its "forgetmenot" term. Each processor has the primary responsibility for updating its block of variables while allowing the remaining "secondary" variables to change in a restricted fashion along some easily computable directions, which enhances robustness and flexibility of the algorithm. This thesis explains the important meaning of PVD algorithm by "forgetmenot" term.In order to get close to the reality, we need to improve the basic framework of PVD algorithm. The thesis gives the improvement direction of PVD algorithm, and puts forward two new PVD algorithms. Firstly, my thesis improves the existing SQP type PVD algorithm, and gives a new FSQP type PVD algorithm, whose search direction is the combination of descent direction, feasible direction and secondorder revised direction. This new algorithm is very effective in preventing the occurrence of maratos effect. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. Secondly, we give a new inexact PVD algorithm for general optimization problem and the justification of its global convergence. In the algorithm, we choose projected gradient residual function as PVD direction, and we replace the minimization problem with a kind of sufficient descent condition.This thesis makes use of PVD algorithm to solve mixinteger nonlinear optimization problem. Its constraints are divided into:separable constrains and global constraints, then we compromise the global constrains to target function using penalty function method. So the mixinteger nonlinear optimization problem becomes separable constrained optimization problem, which can be solved by PVD algorithm of separable constrained optimization problem.