An exact dynamic programming algorithm for large-scale unconstrained two-dimensional guillotine cutting problems

In this paper, the two-dimensional cutting problem with defects is discussed. The objective is to cut some rectangles in a given shape and direction without overlapping the defects from the rectangular plate and maximize some profit associated. An Improved Heuristic-Dynamic Program (IHDP) is presented to solve the problem. In this algorithm, the discrete set contains not only the solution of one-dimensional knapsack problem with small rectangular block width and height, but also the cutting positions of one unit outside four boundaries of each defect. In addition, the denormalization recursive method is used to further decompose the sub problem with defects. The algorithm computes thousands of typical instances. The computational experimental results show that IHDP obtains most of the optimal solution of these instances, and its computation time is less than that of the latest literature algorithms.

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On the 2-MRS Problem in a Tree with Unreliable Edges

Journal of Applied Mathematics ◽

10.1155/2013/743908 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Wei Ding ◽

Yu Zhou ◽

Guangting Chen ◽

Hongfa Wang ◽

Guangming Wang

Keyword(s):

Dynamic Programming ◽

Communication Networks ◽

Large Scale ◽

Dynamic Programming Algorithm ◽

Programming Algorithm ◽

Probability Models ◽

Expected Number ◽

Node Pair ◽

Reliable Source ◽

General Graphs

This paper extends the well-known most reliable source (1-MRS) problem in unreliable graphs to the 2-most reliable source (2-MRS) problem. Two kinds of reachable probability models of node pair in unreliable graphs are considered, that is, the superior probability and united probability. The 2-MRS problem aims to find a node pair in the graph from which the expected number of reachable nodes or the minimum reachability is maximized. It has many important applications in large-scale unreliable computer or communication networks. The #P-hardness of the 2-MRS problem in general graphs follows directly from that of the 1-MRS problem. This paper deals with four models of the 2-MRS problem in unreliable trees where every edge has an independent working probability and devises a cubic-time and quadratic-space dynamic programming algorithm, respectively, for each model.

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A Modified on-Line Rolling Generation Dispatch Model for Accommodating Large-Scale Wind Power

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.325-326.569 ◽

2013 ◽

Vol 325-326 ◽

pp. 569-572

Author(s):

Yin Cheng ◽

Hai Xin Li ◽

Jing Wei Liu ◽

Yan Zhe Xu ◽

Guo Qiang Sun ◽

...

Keyword(s):

Dynamic Programming ◽

Wind Power ◽

Large Scale ◽

Dynamic Programming Algorithm ◽

Numerical Results ◽

Programming Algorithm ◽

Primal Problem ◽

On Line ◽

Dual Relaxation ◽

Generation Dispatch

This paper proposes an improved strategy for on-line rolling generation dispatch. Based on the framework of Lagrange dual relaxation, the problem is transformed and decomposed into primal-problem and N subproblems multipliers and system constrains are satisfied iteratively. The sub-problems are solved by an efficient dynamic programming algorithm without changing the condition of convergence of the framework. Numerical results indicate that the proposed method is fast and efficient in dealing with numerous system constrains.

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Performance Of Two Heuristics For Solving Large Scale Two-Dimensional Guillotine Cutting Problems

INFOR Information Systems and Operational Research ◽

10.1080/03155986.1995.11732276 ◽

1995 ◽

Vol 33 (2) ◽

pp. 145-155

Author(s):

Reinaldo Morabito ◽

Marcos N. Arenales

Keyword(s):

Large Scale ◽

Two Dimensional ◽

Cutting Problems ◽

Guillotine Cutting

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