Estimation of efficiency of production and infrastructure subsystems
Macrosystem dynamics
V.V. Topka Multidimensional Knapsack problem: an effective solution method and its applying
MATHEMATICAL MODELING
System analysis in medicine and biology
V.V. Topka Multidimensional Knapsack problem: an effective solution method and its applying

Abstract.

Recently, there is an urgent need to develop an effective model and algorithmic apparatus for the top level of the project management system, on which there should be a subsystem for selecting and managing the portfolio of projects to be implemented. In this paper, we consider the optimal selection of the project portfolio and the allocation of resources for its implementation in the form of a discrete optimization problem – the multidimensional Knapsack problem. The paper presents known theoretical results for a greedy heuristic for solving a one-dimensional Knapsack problem. Necessary and sufficient conditions for optimality; estimation of the error of the algorithm and its asymptotic error for the behavior in the mean. A direct greedy heuristic at unit cost is proposed for solving the multidimensional Knapsack problem. To improve its effectiveness, we use a local limited search, which improves the greedy solution, as well as the addition and local optimization of the previous stages. Greedy heuristics are fast, with a polynomial time complexity.

Keywords:

knapsack problem, multidimensional Knapsack problem, project portfolio, improved greedy heuristic, local limited search, polynomial time complexity.

PP. 54-64.

DOI: 10.14357/20790279190206

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