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151.
Yigui Ou 《Applied Numerical Mathematics》2011,61(7):900-909
This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step. Further, when the trial step is not accepted, the method performs an inexact line search along it instead of resolving a new linear system. Under reasonable assumptions, the algorithm is proven to be globally and superlinearly convergent. Numerical results are also reported that show the efficiency of this proposed method. 相似文献
152.
This paper addresses a special kind of container loading problem with shipment priority. We present a tree search method, which is based on a greedy heuristic. In the greedy heuristic, blocks made up of identical items with the same orientation are selected for packing into a container. Five evaluation functions are proposed for block selection, and the different blocks selected by each evaluation function constitute the branches of the search tree. A method of space splitting and merging is also embedded in the algorithm to facilitate efficient use of the container space. In addition, the proposed algorithm covers an important constraint called shipment priority to solve practical problems. The validity of the proposed algorithm is examined by comparing the present results with those of published algorithms using the same data. 相似文献
153.
The Barzilai–Borwein (BB) gradient method has received many studies due to its simplicity and numerical efficiency. By incorporating a nonmonotone line search, Raydan (SIAM J Optim. 1997;7:26–33) has successfully extended the BB gradient method for solving general unconstrained optimization problems so that it is competitive with conjugate gradient methods. However, the numerical results reported by Raydan are poor for very ill-conditioned problems because the effect of the degree of nonmonotonicity may be noticeable. In this paper, we focus more on the nonmonotone line search technique used in the global Barzilai–Borwein (GBB) gradient method. We improve the performance of the GBB gradient method by proposing an adaptive nonmonotone line search based on the morphology of the objective function. We also prove the global convergence and the R-linear convergence rate of the proposed method under reasonable assumptions. Finally, we give some numerical experiments made on a set of unconstrained optimization test problems of the CUTEr collection. The results show the efficiency of the proposed method in the sense of the performance profile introduced (Math Program. 2002;91:201–213) by Dolan and Moré. 相似文献
154.
A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems. 相似文献
155.
156.
157.
In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis
of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets
of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness
of these algorithms are given. 相似文献
158.
159.
Let , be independent and identically distributed random variables with values in . We transform (‘prune’) the sequence , of discrete random samples into a sequence , of contiguous random sets by replacing with if . We consider the asymptotic behaviour of as . Applications include path growth in digital search trees and the number of tables in Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value. 相似文献
160.
An inverse problem is solved for estimating fuel cell operating parameters such as current density, pressure and fuel flow rate (FFR) separately and then simultaneously two parameters in an internal reforming solid oxide fuel cell (IRSOFC). Initially, a mathematical model for the forward problem is developed to simulate the IRSOFC steady state operation and its performance in terms of power output and then an inverse problem is solved for recovering the above parameters using a simplex search minimization algorithm. The objective function (IRSOFC power) and the estimation accuracy are studied for the effects of initial guess values of the operating parameters and the number of iterations required for retrieval of these parameters. The objective function is represented by the sum of square of the error between a given IRSOFC power and the power evaluated based on some arbitrary guessed values of the unknowns which is then regularized in an iterative manner for solution of the inverse fuel cell problem. The study reveals that a multiple combinations of parameters (current density, operating pressure and FFR) exist which provides guidelines for selecting feasible combinations of these parameters required for meeting a given power requirement. The results show relatively good agreement between the inverse and exact solutions. 相似文献