Disk Packing in a Square: A New Global Optimization Approach

Addis, Bernardetta; Locatelli, Marco; Schoen, Fabio

doi:10.1287/ijoc.1080.0263

Cited by 56 publications

(19 citation statements)

References 28 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…proposed a simulated annealing approach which also combines the gradient descent method with several configuration transformation strategies. Moreover, for the situation of circular container, several efficient perturbation-based algorithms exist, such as the quasi-physical quasi-human algorithm (Wang et al, 2002), the population basin hopping method (Addis et al, 2008a), the simulated annealing approach (Müller et al, 2009), and the energy landscape paving method (Liu et al, 2009), etc. On the other hand, UCP has also been extensively investigated and many efficient approaches exist, such as the non-linear programming solver(MINOS) (Maranas et al, 1995), the billiard simulation approach (Boll et al, 2000), the population basin hopping method (Addis et al, 2008b;Grosso et al, 2010), the greedy vacancy search strategy (Huang and Ye, 2010), the quasiphysical global optimization method (Huang and Ye, 2011), etc. In addition, as mentioned above, due to the extremely challenging combinatorial feature of ACP, the approaches proposed for ACP are usually quite different from those proposed for UCP.…”

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

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: 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

“…In order to have total coverage, the whole deployment area should be filled with the minimal number of sensing disks without leaving any uncovered region. Many algorithms, based on the disk packing theory, have been proposed for solving such problems [24], [25], [26]. These algorithms aim at packing equal disks, in an optimal manner, into a square area.…”

Section: Coverage Problemmentioning

confidence: 99%

Controlled Mobility Sensor Networks for Target Tracking Using Ant Colony Optimization

Mourad

Chehade

Snoussi

et al. 2012

IEEE Trans. on Mobile Comput.

View full text Add to dashboard Cite

Abstract-In mobile sensor networks, it is important to manage the mobility of the nodes in order to improve the performances of the network. This paper addresses the problem of single target tracking in controlled mobility sensor networks. The proposed method consists of estimating the current position of a single target. Estimated positions are then used to predict the following location of the target. Once an area of interest is defined, the proposed approach consists of moving the mobile nodes in order to cover it in an optimal way. It thus defines a strategy for choosing the set of new sensors locations. Each node is then assigned one position within the set in the way to minimize the total traveled distance by the nodes. While the estimation and the prediction phases are performed using the interval theory, relocating nodes employs the ant colony optimization algorithm. Simulations results corroborate the efficiency of the proposed method compared to the target tracking methods considered for networks with static nodes.

show abstract

“…The critical steps of the algorithm are as described above. Three algorithm parameters must be specified for implementation: the population size M, the selection parameter τ and the variable screening/selection parameter η. sEDA uses truncation selection: a fraction τ of the population with the best objective function values are retained for building/adapting the search model 1 . The mean (m) of the selected population is then calculated for expanding the population.…”

Section: Incorporating Variable Screening (Morris Method) In An Edamentioning

confidence: 99%

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

Mishra¹

View full text Add to dashboard Cite

Optimization problems occur widely in various domains and are of great practical importance. Better solutions to optimization problems translate into increased production or efficiency, or less waste or error. As a result, the development of optimization algorithms is a large and active area of research. Although there is a large amount of theory and techniques for solving optimization problems, there are also many open issues and questions in understanding the relationship between optimization algorithms and the problems that they are applied to.In any optimization problem, the influence of each solution variable on the objective function, as well as the interactions between variables are very important. For example, if the variables in a problem are independent, then it might be efficiently solved by decomposition. If important dependencies exist between variables, an algorithm that is able to capture these dependencies may be able to exploit them to find good solutions. Alternatively, if a variable has a strong influence on the objective function, then an algorithm may be better off focusing its search on this variable, compared with another variable that has very little influence on the objective function.Estimation of Distribution Algorithms (EDAs) are a class of black-box optimization algorithms that learn and sample from a probabilistic model over the solution variables to carry out the search process. The explicit model in an EDA clearly specifies how the algorithm handles problem variables during the search process. A major focus in EDA research has been the incorporation of dependency modeling using models of varying complexity (e.g. probabilistic graphical models). The intuition behind this work is that if the algorithm model is capable and successful at capturing the structure of the problem, it will produce good performance on that problem. Experimental results have confirmed this intuition, for example EDAs that model dependency information have outperformed EDAs that do not model dependencies on certain problems.While EDAs have shown good performance results, little work has analyzed the dynamics of EDA models in practice. In fact, it is not clear what kind of problem structure EDAs can successfully model, or to what extent it is necessary to successfully model problem structure in order to achieve good performance. To provide insight into these issues, a more detailed analysis of EDAs applied to specific problems is needed.In this thesis, an experimental methodology is proposed to analyze the features of variables in continuous optimization problems and continuous EDAs. The approach is based on sampling points from the problem fitness landscape and/or the history of points visited by an EDA during the search process. These samples are then analyzed in three different ways, to identify key structural variables, variable dependencies and important variables. The techniques are used to analyze a variety of test problems and EDAs optimizing the same problem set. The results confirm that the i...

show abstract

Disk Packing in a Square: A New Global Optimization Approach

Cited by 56 publications

References 28 publications

Iterated tabu search for the circular open dimension problem

Iterated tabu search for the circular open dimension problem

Controlled Mobility Sensor Networks for Target Tracking Using Ant Colony Optimization

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

Contact Info

Product

Resources

About