Determining the K-best solutions of knapsack problems

Leão, Aline Aparecida de Souza; Cherri, Luiz Henrique; Arenales, Marcos Nereu

doi:10.1016/j.cor.2014.03.008

Cited by 7 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Otherwise, all solutions are computed by issuing a call to the Knapsack01AllSolutions procedure at line 11. The Knapsack01OneSolution procedure can be implemented using dynamic programming [Andonov et al 2000] or branch and bound [Vance 1993] approaches, while the Knapsack01AllSolutions procedure can be carried out using techniques for computing k-best solutions of knapsack problems [Leão et al 2014].…”

Section: Knapsack Searchmentioning

confidence: 99%

Impact-Driven Process Model Repair

Polyvyanyy

Aalst

Hofstede

et al. 2016

ACM Trans. Softw. Eng. Methodol.

View full text Add to dashboard Cite

The abundance of event data in today's information systems makes it possible to "confront" process models with the actual observed behavior. Process mining techniques use event logs to discover process models that describe the observed behavior, and to check conformance of process models by diagnosing deviations between models and reality. In many situations it is desirable to mediate between a preexisting model and observed behavior. Hence, we would like to repair the model while improving the correspondence between model and log as much as possible. The approach presented in this paper assigns predefined costs to repair actions (allowing inserting or skipping of activities). Given a maximum degree of change, we search for models that are optimal in terms of fitness, i.e., the fraction of behavior in the log not possible according to the model is minimized. To compute fitness we need to align the model and log and this can be time consuming. Hence, finding an optimal repair may be intractable. We propose different alternative approaches to speed-up repair. The number of alignment computations can be reduced dramatically while still returning near-optimal repairs. The different approaches have been implemented using the process mining framework ProM and evaluated using real-life logs. CCS Concepts: •Theory of computation → Design and analysis of algorithms; •Information systems → Information systems applications; •Mathematics of computing → Combinatorial optimization;

show abstract

Section: Knapsack Searchmentioning

confidence: 99%

Impact-Driven Process Model Repair

Polyvyanyy

Aalst

Hofstede

et al. 2016

ACM Trans. Softw. Eng. Methodol.

View full text Add to dashboard Cite

show abstract

“…Resource allocation approaches are categorized into two methods: auction-based and optimization (Ghobaei-Arani et al, 20202023;Li and Sun 2021). Many resource allocation problems can be transformed into a knapsack problem (Leao et al, 2014;Angelelli and Filippi, 2011). For this reason, resource providers have introduced auction mechanisms in fog computing to obtain more profit, allowing idle resources to be sold at dynamic prices (Zhang et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

A combinatorial auction mechanism for time-varying multidimensional resource allocation and pricing in fog computing

Li,

Zhang,

Sun

et al. 2023

International Journal of Applied Mathematics and Computer Scien

View full text Add to dashboard Cite

It is a hot topic to investigate resource allocation in fog computing. However, currently resource allocation in fog computing mostly supports only fixed resources, that is, the resource requirements of users are satisfied with a fixed amount of resources during the usage time, which may result in low utility of resource providers and even cause a waste of resources. Therefore, we establish an integer programming model for the time-varying multidimensional resource allocation problem in fog computing to maximize the utility of the fog resource pool. We also design a heuristic algorithm to approximate the solution of the model. We apply a dominant-resource-based strategy for resource allocation to improve resource utilization as well as critical value theory for resource pricing to enhance the utility of the fog resource pool. We also prove that the algorithm satisfies truthful and individual rationality. Finally, we give some numerical examples to demonstrate the performance of the algorithm. Compared with existing studies, our approach can improve resource utilization and maximize the utility of the fog resource pool.

show abstract

“…In many real-life combinatorial optimization problems is of great interest for the decision-maker to have not only one solution, but the set of all optimal solutions (see [10] or [7], for example). The information provided by this set can give some additional information about the solutions, and sometimes is a first step for multi-objective optimization.…”

Section: Introductionmentioning

confidence: 99%