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Multi-scale quantum resonance solving algorithm for multi-choice multi-dimensional knapsack problem

A knapsack problem and multi-scale technology, applied in the field of operations research, can solve problems that cannot be directly applied and take a long time

Inactive Publication Date: 2019-01-25
CHENGDU UNIV OF INFORMATION TECH
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Problems solved by technology

When this algorithm is applied to integer programming, compared with the quantum particle swarm algorithm and the corresponding improved algorithm, it has better solution accuracy and convergence speed, but the problem it solves is much simpler than that of MMKP, and is suitable for large-scale problems. It takes a long time and cannot be directly applied

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  • Multi-scale quantum resonance solving algorithm for multi-choice multi-dimensional knapsack problem
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  • Multi-scale quantum resonance solving algorithm for multi-choice multi-dimensional knapsack problem

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Embodiment Construction

[0065] The present invention will be further described below in conjunction with accompanying drawing:

[0066] The knapsack problem is a combinatorial optimization problem proposed by Merkel and Hellman. Among its extended problems, MMKP is the most difficult problem to solve. It is built on the multi-choice knapsack problem and multidimensional knapsack problem, which can be described as follows:

[0067] There are some items with different benefits that need to be put into the backpack. These items are divided into mutually exclusive groups, and each item selected needs to consume one or more resources. The purpose of MMKP is to select from each group and only An item can be selected so that the total income of the selected item is maximized, and the consumption of each resource does not exceed a given upper limit (knapsack constraint).

[0068] If there are n mutually exclusive groups G={G 1 ,G 2 ,...,G n}, G i ∩G j =φ, 1≤i≠j≤n, I={1,2,…,n} is the group index set, g ...

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Abstract

The invention discloses a classical combinatorial optimization problem in the field of operational research, i.e., the multi-scale quantum resonance solving algorithm for a multi-choice and multi-dimensional knapsack problem, firstly, the Lagrange relaxation dual model is established for the original problem model, which greatly reduces the constraint conditions and evaluates the value of the items in the group by using Lagrange value. On this basis, the MMKP approximate kernel problem is introduced, which is heuristic to find the optimal solution and reduces the scale of the problem. In addition, based on the approximate kernel problem, a mixed Gaussian sampling model is constructed to guide the algorithm to intensify the search in the trusted region and to uniformly search in the untrusted region, which improves the solution accuracy and convergence speed.

Description

technical field [0001] The invention relates to the field of operations research, in particular to a classic combinatorial optimization problem in the field of operations research, that is, a multi-scale quantum resonance algorithm for solving the multi-choice multi-dimensional knapsack problem. Background technique [0002] The knapsack problem (Knapsack Problem, KP) is a classic combinatorial optimization problem in the field of operations research, which has been proved to be NP-hard. [0003] If only multiple resource constraints are considered, it is the multi-dimensional knapsack problem (Multi-dimensional KP, MKP); [0004] If the selection of items is constrained, that is, the items are divided into several categories, and each type of item can only be selected to be loaded into the backpack, which is the multi-choice knapsack problem (Multi-Choice KP, MCKP), but each item in MCKP has only a single resource limit; [0005] If multiple resource constraints are added,...

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Application Information

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IPC IPC(8): G06N99/00
Inventor 安俊秀文仁强陆志君
Owner CHENGDU UNIV OF INFORMATION TECH
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