Algorithms for the circular two‐dimensional open dimension problem

Akeb, Hakim; Hifi, Mhand

doi:10.1111/j.1475-3995.2008.00655.x

Cited by 24 publications

(37 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first set of 6 instances named SY1-SY6 are taken from Stoyan and Yaskov (1998), and the second set of 12 instances identified as SY12, SY13, SY14, SY23, SY24, SY34, SY56, SY123, SY124, SY134, SY234, SY1234 are taken from Akeb and Hifi (2008). Note that the second set of instances are obtained by concatenating the six original instances of the first set, e.g., SY12 is obtained by concatenating SY1 and SY2, and SY1234 is obtained by concatenating SY1, SY2, SY3, SY4, etc.…”

Section: Results and Analysismentioning

confidence: 99%

“…Kallrath (2009) also applied several heuristics, including a branch and reduce optimization navigator, a column enumeration approach and a symmetry constraints breaking strategy. Akeb and Hifi (2008) proposed an open strip generation solution, an exchangeorder strategy to augment the first heuristic and a hybrid heuristic that combines beam search with a series of predetermined interval search. For further improvements, Akeb et al (2011) proposed an augmented algorithm which incorporates a beam search, a binary search, a multi-start strategy and a separate-beams strategy.…”

Section: Related Literaturementioning

confidence: 99%

See 1 more Smart Citation

Iterated tabu search for the circular open dimension problem

Huang

2013

European Journal of Operational Research

View full text Add to dashboard Cite

This paper mainly investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. An iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. This process is repeated until a feasible solution has been found or the allowed computation time has been elapsed. Computational experiments based on well-known benchmark instances show that ITS produces quite competitive results with respect to the best known results. For 18 representative CODP instances taken from the literature, ITS succeeds in improving 13 best known results within reasonable time. In addition, for another challenging related variant: the problem of packing arbitrary sized circles into a circular container, ITS also succeeds in improving many best known results. Supplementary experiments are also provided to analyze the influence of the perturbation operator, as well as the acceptance criterion.

show abstract

Section: Results and Analysismentioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Iterated tabu search for the circular open dimension problem

Huang

2013

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…CODP is also known as the strip cutting/packing problem (cf. Akeb and Hifi [4] and Huang et al [5]). …”

Section: Introductionmentioning

confidence: 92%

“…Section 3 summarizes the principle of the minimum local-distance position procedure (MLDP). Section 4 describes the BSBIS (Beam Search BinaryInterval Search) algorithm already considered in Akeb and Hifi [4]. Section 5 details the proposed constructive algorithm which combines beam search (using separate beams), multi-start, and look-ahead strategies.…”

Section: Introductionmentioning

confidence: 99%

Solving the circular open dimension problem by using separate beams and look-ahead strategies

Akeb¹,

Hifi²

2013

Computers & Operations Research

Self Cite

View full text Add to dashboard Cite

“…Beam search was used to solve different combinatorial problems, such as Scheduling [18] and Cutting-and-Packing problems [1]. In its width-first implementation, the method starts by creating the root node which may contains an initial (starting) partial solution.…”

Section: The Building Stage (Beam Search For Computing Routes)mentioning

confidence: 99%

A Three-Stage Heuristic for the Capacitated Vehicle Routing Problem with Time Windows

Akeb

Bouchakhchoukha

Hifi

2014

Recent Advances in Computational Optimization

Self Cite

View full text Add to dashboard Cite

In this paper we propose to solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) by using a three-stage solution procedure. CVRPTW is defined by a set of customers (with associated demands and time windows) and a set of vehicles (with a given capacity) and the aim of the problem is to serve all the customers inside their respective time windows. There are two objectives to optimize, the first one consists in using the minimum number of vehicles and the second one is to minimize the total distance traveled by all the vehicles. The proposed heuristic combines (i) a clustering stage in which the set of customers is divided into disjoint clusters, (ii) a building stage that serves to provide a feasible tour in each cluster and, (iii) a local-search stage that is applied in order to try to improve the quality of the solutions obtained from the second stage. The computational investigation, conducted on a class of benchmark instances of the literature, shows that the results reached by the proposed heuristic remain competitive when compared to the best known solutions taken from the literature.

show abstract

Algorithms for the circular two‐dimensional open dimension problem

Cited by 24 publications

References 15 publications

Iterated tabu search for the circular open dimension problem

Iterated tabu search for the circular open dimension problem

Solving the circular open dimension problem by using separate beams and look-ahead strategies

A Three-Stage Heuristic for the Capacitated Vehicle Routing Problem with Time Windows

Contact Info

Product

Resources

About