Graph colorings with restricted bicolored subgraphs: II. The graph coloring game

We use a simulation-based method to consider the effect of different network structures on the propensity for economic producers to develop a complementary division of labor. We use a graph-coloring game, in which nodes are given incentives to find a color that does not match their nearest neighbors, to represent the interdependent coordination problems inherent to the division of labor. We find that a decentralized development of a division of labor is difficult, particularly when too many specializations are chosen. Counterintuitively, a division of labor is more likely to evolve when the ability of agents to specialize is more constrained. The ability to store property also facilitates the development of a division of labor.

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Study on coloring method of airport flight-gate allocation problem

Journal of Mathematics in Industry ◽

10.1186/s13362-019-0068-5 ◽

2019 ◽

Vol 9 (1) ◽

Author(s):

Hongyan Li ◽

Xianfeng Ding ◽

Jiang Lin ◽

Jingyu Zhou

Keyword(s):

Graph Coloring ◽

Programming Model ◽

Weight Vector ◽

Multi Objective ◽

Average Value ◽

Two Factors ◽

Minimum Number ◽

First Come First Serve ◽

Airport Terminals ◽

Single Objective

Abstract With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ w = ( 0.112 , 0.097 , 0.496 , 0.395 ) of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ α = 0.32 and $\beta =0.40$ β = 0.40 , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.

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