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101.
B. S. Goh 《Journal of Optimization Theory and Applications》2009,142(2):275-289
We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest
descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately
by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt
like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula
is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version
of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define
here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage
requirements for the full Hessian matrix in problems with a large number of variables.
The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research
as well as the referees for helpful comments. 相似文献
102.
POPMUSIC for the point feature label placement problem 总被引:1,自引:0,他引:1
Point feature label placement is the problem of placing text labels adjacent to point features on a map so as to maximize legibility. The goal is to choose positions for the labels that do not give rise to label overlaps and that minimize obscuration of features. A practical goal is to minimize the number of overlaps while considering cartographic preferences. This article proposes a new heuristic for solving the point feature label placement problem based on the application of the POPMUSIC frame. Computational experiments show that the proposed heuristic outperformed other recent metaheuristics approaches in the literature. Experiments with problem instances involving up to 10 million points show that the computational time of the proposed heuristic increases almost linearly with the problem size. New problem instances based on real data with more than 13,000 labels are proposed. 相似文献
103.
In this article we propose to partially integrate the antenna positioning (APP) and frequency allocation problems (FAP). The traditional wireless network design process examines these two major issues sequentially in order to avoid the very high complexity associated with the simultaneous resolution of the two problems. The proposed integration involves the introduction of interference protection guarantees within the APP. It is customary to define such guarantees in an intermediate step and to use them as input to FAP, in order to protect against interference in critical areas. The proposed approach consists of selecting these protections while solving the APP, allowing the optimization procedure to exploit the degrees of freedom that this would offer. Results on two real-life problem instances indicate a significant improvement in interference levels and resource utilization. 相似文献
104.
The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting problem, which subsumes several previous ones, is expressed as a linear mixed 0–1 program. As it turns out to be too time-consuming for exact solution of instances of realistic size, a Variable Neighborhood Search (VNS) heuristic is proposed, and compared with Multi-Start (MS), a Genetic Search algorithm (GA) and a Memetic Search algorithm (MA). VNS provides optimal solutions for all instances solved to optimality in a previous paper of the first two authors and outperforms MS, MA and GA on large instances. 相似文献
105.
The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems. 相似文献
106.
107.
多车场有时间窗的多车型车辆调度及其禁忌算法研究 总被引:12,自引:0,他引:12
本文针对物流配送中的多车场车辆调度问题提出了两种多车场的处理方法,介绍了多车场车辆调度问题中容量、时间窗、多车型等多种约束的处理方法,并且根据具体约束情况设计了禁忌算法,对多车场有时间窗的多车型车辆调度问题加以实现,给出了一个具有代表性的算例试验结果和结果分析,通过试验表明了此方法对优化有时间窗的多车型车辆调度问题的有效性. 相似文献
108.
Nenad Mladenović Milan Dražić Vera Kovačevic-Vujčić Mirjana Čangalović 《European Journal of Operational Research》2008
We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results. 相似文献
109.
Ekaterina Alekseeva Yuri Kochetov Alexander Plyasunov 《European Journal of Operational Research》2008
We study the complexity of finding local minima for the p-median problem. The relationship between Swap local optima, 0–1 local saddle points, and classical Karush–Kuhn–Tucker conditions is presented. It is shown that the local search problems with some neighborhoods are tight PLS-complete. Moreover, the standard local descent algorithm takes exponential number of iterations in the worst case regardless of the tie-breaking and pivoting rules used. To illustrate this property, we present a family of instances where some local minima may be hard to find. Computational results with different pivoting rules for random and Euclidean test instances are discussed. These empirical results show that the standard local descent algorithm is polynomial in average for some pivoting rules. 相似文献
110.
In this paper we consider the Bounded Length Median Path Problem which can be defined as the problem of locating a path-shaped facility that departures from a given origin and arrives at a given destination in a network. The length of the path is assumed to be bounded by a given maximum length. At each vertex of the network (customer-point) the demand for the service is given and the cost to reach the closest service-point is computed. The objective is to minimize the sum of these costs over all the customer-points in the network. 相似文献