A multistart variable neighborhood descent metaheuristic for the board packing problem

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Sergio Pérez-Peló, Anna Martínez-Gavara, Jesús Sánchez-Oro, Ana D. López-Sánchez
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Abstract

The Board Packing Problem (BoPP) considers a rectangular board divided in cells with m rows and n columns. In this problem, a subset from a set of rectangles with different costs may be allocated on the cells, and in turns, each cell has an associated revenue obtained if a rectangle is placed on it. The objective of the BoPP is to allocate rectangles on the board, covering cells in order to maximize the total profit, measured as the revenues of the selected cells where the rectangle is placed minus the cost of purchasing such rectangles. The revenue of a cell is collected only once, and only if a rectangle is covering the cell. We propose a Variable Neighborhood Descent (VND) approach for solving the BoPP. Two constructive procedures are proposed for generating the initial solution for the VND: a totally greedy approach and a greedy randomized method to favor diversity. The experimental comparison analyses the contribution of each component of the final algorithm and then performs a competitive testing to evaluate the performance of the algorithm when comparing it with the best method found in the state of the art. The superiority of the proposal is supported by non-parametric statistical tests.

Abstract Image

Abstract Image

棋盘布局问题的多起始变量邻域下降元启发式算法
板布局问题(BoPP)考虑一个矩形板,它被分成m行n列的单元格。在这个问题中,可以将一组具有不同成本的矩形的子集分配到单元格上,并且反过来,如果将矩形放置在每个单元格上,则每个单元格都有相应的收益。BoPP的目标是在电路板上分配矩形,覆盖单元,以最大化总利润,以矩形放置的选定单元的收入减去购买这些矩形的成本来衡量。一个单元的收入只被收集一次,并且只有当一个矩形覆盖该单元时才会被收集。我们提出了一种可变邻域下降(VND)方法来求解BoPP。对于VND的初始解,提出了两种建设性的生成方法:完全贪婪法和偏向多样性的贪婪随机化法。实验比较分析了最终算法的每个组成部分的贡献,然后进行竞争性测试,以评估算法的性能,并将其与现有的最佳方法进行比较。非参数统计检验支持了该建议的优越性。
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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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