The nonlinear knapsack problem – algorithms and applications

Bretthauer, Kurt M.; Shetty, Bala

doi:10.1016/s0377-2217(01)00179-5

Cited by 201 publications

(115 citation statements)

References 42 publications

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“…Third, and the most important distinguishing feature, is that for the sake of system stability, any solution to the resource allocation problem must employ incremental resource adjustments, instead of reallocating resources from scratch, and such resource change is constrained according to Equation 3. This additional constraint makes resource allocation substantially more challenging precluding existing solutions to multi-dimensional, nonlinear knapsack problems [7]. Furthermore, the reduction of an instance of the dynamic resource allocation problem to a complex variant of knapsack is possible only by eliminating Equation 3.…”

Section: Other Heuristic Solutionsmentioning

confidence: 99%

Revenue Driven Resource Allocation for Virtualized Data Centers

Kundu

Rangaswami

Zhao

et al. 2015

2015 IEEE International Conference on Autonomic Computing

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Abstract-The increasing VM density in cloud hosting services makes careful management of physical resources such as CPU, memory, and I/O bandwidth within individual virtualized servers a priority. To maximize cost-efficiency, resource management needs to be coupled with the revenue generating mechanisms of cloud hosting: the service level agreements (SLAs) of hosted client applications. In this paper, we develop a server resource management framework that reduces data center resource management complexity substantially. Our solution implements revenuedriven dynamic resource allocation which continuously steers the resource distribution across hosted VMs within a server such as to maximize the SLA-generated revenue from the server. Our experimental evaluation for a VMware ESX hypervisor highlights the importance of both resource isolation and resource sharing across VMs. The empirical data shows a 7%-54% increase in total revenue generated for a mix of 10-25 VMs hosting either similar or diverse workloads when compared to using the currently available resource distribution mechanisms in ESX.

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Section: Other Heuristic Solutionsmentioning

confidence: 99%

Revenue Driven Resource Allocation for Virtualized Data Centers

Kundu

Rangaswami

Zhao

et al. 2015

2015 IEEE International Conference on Autonomic Computing

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“…Once the optimal shelf space allocation variables are found, the corresponding optimal order quality and surplus can be decided efficiently. In this sense, the problem can be reduced to a nonlinear bounded knapsack problem, which is still NPHard (Bretthauer and Shetty, 2002). In the following sections, some heuristic and meta-heuristic approaches will be adapted to the problem and their computational performance will be reported and compared against each other.…”

Section: Addressing Multi-item Problemsmentioning

confidence: 99%

Heuristic, meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation

Bai

Burke

Kendall

2008

Journal of the Operational Research Society

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The allocation of fresh produce to shelf space represents a new decision support research area which is motivated by the desire of many retailers to improve their service due to the increasing demand for fresh food. However, automated decision making for fresh produce allocation is challenging because of the very short lifetime of fresh products. This paper considers a recently proposed practical model for the problem which is motivated by our collaboration with Tesco. Moreover, the paper investigates heuristic and meta-heuristic approaches as alternatives for the generalized reduced gradient algorithm, which becomes inefficient when the problem size becomes larger. A simpler single-item inventory problem is firstly studied and solved by a polynomial time bounded procedure. Several dynamic greedy heuristics are then developed for the multi-item problem based on the procedure for the single-item inventory problem. Experimental results show that these greedy heuristics are much more efficient and provide competitive results when compared to those of a multi-start generalized reduced gradient algorithm. In order to further improve the solution, we investigated simulated annealing, a greedy randomized adaptive search procedure and three types of hyper-heuristics. Their performance is tested and compared on a set of problem instances which are made publicly available for the research community.

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“…Specifically, by invoking the KKT conditions, all the variables can be expressed as a function of the Lagrange multiplier λ of the resource-usage constraint, i.e. [2,3,13]). In case of quadratic knapsack problems, the function g(λ) is continuous, monotonic and piecewise linear.…”

Section: Introductionmentioning

confidence: 99%

A breakpoint search approach for convex resource allocation problems with bounded variables

Waegenaere

Wielhouwer

2011

Optim Lett

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We present an efficient approach to solve resource allocation problems with a single resource, a convex separable objective function, a convex separable resource-usage constraint, and variables that are bounded below and above. Through a combination of function evaluations and median searches, information on whether or not the upper-and lowerbounds are binding is obtained. Once this information is available for all upper and lower bounds, it remains to determine the optimum of a smaller problem with unbounded variables. This can be done through a multiplier search procedure. The information gathered allows for alternative approaches for the multiplier search which can reduce the complexity of this procedure.

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The nonlinear knapsack problem – algorithms and applications

Cited by 201 publications

References 42 publications

Revenue Driven Resource Allocation for Virtualized Data Centers

Revenue Driven Resource Allocation for Virtualized Data Centers

Heuristic, meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation

A breakpoint search approach for convex resource allocation problems with bounded variables

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