Multi-objective temporal bin packing problem: An application in cloud computing

Abstract

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Overlap Detection in 2D Amorphous Shapes for Paper Optimization in Digital Printing Presses

“…One proposal is to parallelize the overlap detection algorithm to speed up reading the masks' pixels that detect overlaps. Works with distributed processing have been done using cloud computing to solve the bin packing problem [23]. To reduce the residual area, the developed neighborhood structure can also be improved by applying movements such as insertion in pairs of figures, translation, rotation, and a combination of these movements.…”

“…For the i-th group of data generated by the i-th algorithm, (13) where ni is the sample size of the i-th algorithm, s 2 w,i is the winsorized variance (of the trimmed data), hi is the adequate sample size of the i-th group (number of observations remaining after the cut-off). ( 14) Welch's test, defined by Equations ( 13)- (23), uses weights w i to reduce the data heterogeneity. The weights w i in Equation ( 13) are based on the sample size n i of the data generated by the i-th algorithm and the observed variance s 2 w , i for each i-th group of data generated by the i-th algorithm.…”

Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

“…In this study, we propose an adaptation of the Positions and Covering (P&C) methodology, used by [ 10 ] to obtain optimal solutions for the two-dimensional bin packing problem. Considering the similarity of the 2SP with other packing problems, some potential applications for the P&C methodology can be found in agricultural fields to delineate rectangular and homogeneous management zones [ 11 – 13 ], in scheduling problems applied to environmental, automotive, ferry, and manufacturing industries to ensure maximum use of materials [ 14 – 16 ], in healthcare applied to operating rooms schedules [ 17 – 19 ], in cloud computing where a set of jobs must be processed on virtual machines of physical servers with the aim of improves the energy efficiency [ 20 – 22 ], and in optimal deliveries in e-commerce where the objective is optimizing the total number of containers to integrate into several delivery trips [ 23 ].…”

Variable and constraint reduction techniques for the temporal bin packing problem with fire-ups

“…A server restart is called a fire-up, see also Fig. 1 for a graphical representation, and-from the perspective of energy-efficiency-this naturally leads to a second optimization goal, introduced in [3]. The authors of that article propose two compact ILP formulations (denoted M1 and M2) taking into consideration two different objectives: (i) the number of servers and (ii) the number of fire-ups.…”

“…This new objective function is a weighted-sum, using the input parameter γ > 0 to scale the contribution of the fire-ups. In this way, a multi-objective variant of the TBPP has been proposed in [3], hereinafter referred to as the temporal bin packing problem with fireups (TBPP-FU). The models M1 and M2 of [3] are based on the classic Kantorovichtype structure for the BPP, see [15], and the experiments show that the proposed exact solution method using these models is very challenging from a computational Fig.…”