Feasible solution of the time table assignment problem to faculty

IMPROVED PROJECTION HOPFIELD NETWORK FOR THE QUADRATIC ASSIGNMENT PROBLEM

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622008002818 ◽

2008 ◽

Vol 07 (01) ◽

pp. 53-70 ◽

Cited By ~ 2

Author(s):

KEIJI TATSUMI ◽

TETSUZO TANINO

Keyword(s):

Assignment Problem ◽

Feasible Solution ◽

Quadratic Assignment Problem ◽

Hopfield Neural Network ◽

Hopfield Network ◽

Quadratic Assignment ◽

Feasible Region ◽

Projection Technique ◽

Proposed Model ◽

Theoretical Results

The continuous-valued Hopfield neural network (CHN) is a popular and powerful metaheuristic method for combinatorial optimization. However, it is difficult to select appropriate penalty parameters for constraints so as to obtain a feasible and desirable solution by CHN. Thus, various improved models have been proposed. Matsuda proposed a CHN named optimal CHN and showed theoretical results on selecting parameters. On the other hand, Smith et al. proposed the projection CHN which projects a solution onto the feasible region and thus needs not select penalty parameters. In this paper, we point out some drawbacks of these two models and propose a new CHN with an efficient projection technique for the quadratic assignment problem, which overcomes these drawbacks. Moreover, we show that the proposed model can always find a feasible solution and that it has the local convergence property. Finally, we verify advantages of the proposed model through some numerical experiments.

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Research on DNA Nanostructures Based on the Hybrid Chain Reaction for the Assignment Problem

Journal of Mathematics ◽

10.1155/2021/5570737 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Risheng Wang ◽

Zhixiang Yin ◽

Jing Yang ◽

Xinmu Yang ◽

Zhen Tang

Keyword(s):

Information Processing ◽

Assignment Problem ◽

Feasible Solution ◽

Optimal Solution ◽

Dna Origami ◽

Hairpin Structure ◽

Dna Nanostructures ◽

Chain Reaction ◽

Light Emitting ◽

Starting Point

Nanostructures with information processing play an important role in many fields. It is an excellent approach to the application that DNA nanostructures represented by DNA origami molecules combine with the hybrid chain reaction. In this paper, the assignment problem is mapped to a combinatorial graph on the DNA origami substrate. The graph has several modules corresponding to the time efficiency matrix of the assignment problem. The starting chain of the corresponding module is hybridized with the hairpin structure of the starting point, and the corresponding module is opened to emit light. The feasible solution to the problem can be obtained by observing the light-emitting fluorescent numbers of the opened modules. The fluorescent numbers of all the opened modules are added up on the same origami substrate, then different opening methods in different test tubes are compared, and the optimal solution is obtained.

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