**Author(s): ** А.А. Bоsоv |

А.В. Gоrbоvа |

Н.В. KHalipovа**Journal: ** Science and Transport Progress ISSN 2307-3489

**Issue: ** 42;

**Start page: ** 170;

**Date: ** 2013;

Original page**Keywords: ** knapsack problem |

set functions |

vector optimization |

the task of investing**ABSTRACT**

Introduction: Formed knapsack problem in terms of set functions and is a heuristic algorithm. The goal: to prove that the heuristic algorithm is essential. Some facts from [2]. The equivalence of the limit order to E.Borelyu and convergence in measure. The theorem about the need to set a maximum of function. The situation is quite the algorithm: We present three cases where a heuristic algorithm is sufficient. Counterexample: An Rear take from [1], and given the addition heuristic algorithm, which allows to obtain the solution of the knapsack problem. Vector optimization: With the knapsack problem is tied vector optimization of investment activities. Conclusions: The proposed algorithm for solving the knapsack problem and for additive functions algorithm for Pareto solutions of vector optimization for the two indicators. Appendix: an agenda for the Maple solutions knapsack problem.

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