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图与网络算法优秀论文51
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图与网络算法优秀论文51
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Society Planning: Model, Simulation And Visualization
Summary
This paper presents a model to maximize both the economic output and job satisfaction for the workforce
with sustainability in the scope. We build a self-adaptive system and define its dynamics. We run simula-
tions of the system with real-world census data(PUMS 2015[1]) to find out the optimal feasible solution.
Based on the solution, we propose strategies to improve the living conditions of human immigrants on
Mars. Our model has capabilities to deal with issues of population scalability, social development modality
and evolution dynamics.
To address the problem of creating an optimal economic-workforce-education system, we decompose
it into six sub-problems.
First, we constructed a parameter frame that integrates variables related to three aspects: income, edu-
cation and social equality. We include basic parameters that exist in the census database, from which we
derive metrics that reveal the characteristics of the society. Through an Analytical Hierarchy Process,
we identify the critical parameters, among which the Happiness Index is an important comprehensive
evaluation of citizens well-being.
Second, we formulate criteria to select 10000 immigrants for Population Zero. In comparison to the
selected group, we generate a random sample by extracting data from PUMS 2015 database of 1,618,489
U.S. citizens. We study the demographics of both the selected group and the random sample. The selected
group shows an obvious advantage in building a successful society.
Third, we construct a model to simulate the dynamic evolution of Population Zero. Consisting of vari-
ous systems such as job, marriage, child generation, education, salary, salvation and migration system, this
model evolves like our real world. We discuss one sample result in details using demographics, economics
and Happiness Index.
In addition, we use this model to find the equilibrium point between two contradictory goals of faster
economic development and better social welfare. By implementing a Principle Component Analysis on the
demographic data, we define the key elements of a successful society as high average family income, high
minimum wage and low standard deviation of income. We solve the three-objective optimization problem
by Elite Genetic Algorithm. We find that the optimal minimum wage is $33526 per year, and the optimal
parental leave pay is $50200 per year.
Next, we merge the models of income, education and social equality into a global model to and test it
in different social groups. We identify the subgroups as professional labors and unskilled workers. The
we build a non-linear programming model to decide the resources allocation strategy among different
subgroups. We find that maximizing the parental leave pay will not reduce the minimum wage and average
income significantly.
Finally, we study the effect of immigrant waves from the view of complex network theory. We generate
a scale-free complex network with small world property to represent the interpersonal relationship among
all individuals including Mars residents and new immigrants. Our model shows strategy of 10000 migrants
every ten years are sustainable, and capable of dealing with a large number of refugees from Earth.
本资料由迈思数模整理www.maisums.com
Team # 64486 Page 1 of 33
1 Policy Recommendation
Honored Director of LIFE,
Thank you for hiring and trusting us. We have seen the great success of planned communities that
are built across Earth. However, after detailed investigation and deliberate consideration, we find that
labor management and society plan of the existing experimental communities can be further optimized.
Therefore, we feel obliged to recommend the optimal strategies to LIFE to ensure the successful launch
of project UTOPIA:2100. Our recommendations are based on precise modeling and computer simulation
based on real-world data, thus we are confident of our proposals.
We study the problem both on a micro and macro level. We consider 3 important balancing factors:
economy, education, and equality in the vision of sustainability. We have run a 2000-year simulation and
validated the robustness of our model. Here we suggest a series of strategies.
Select Educated Immigrants In terms of economic development, we propose that LIFE recruit more
immigrants who own bachelor degree or higher, and increase the ratio of citizens under 40. Individual with
strong innovation ability should be granted privilege in the selection procedure. Our model shows higher
ratio of innovator and higher average education level contribute to faster growth of GDP.
Maximize Minimum Wage Higher minimum wage results in lower standard deviation of income but
lower average income. Nevertheless, concerns about the negative effect of high minimum wage on GDP is
unnecessary. Although average income decreases as the minimum wage grows, the change is negligible.
The slight negative effect can also be compensated by recruiting skilled labor from Earth.
We define a Happiness Index to evaluation the citizens attitude toward life in Mars. Lower variance
of family income leads to higher Happiness Index but lower Net Domestic Product. We balance the two
factors and find the equilibrium point, at which the minimum wage is around $31708 less than the average
personal income. We recommend that minimum wage should be around $33526 and increase as economy
grows.
Emphasize Education The significance of education is amplified by its correlation with the economic
development. Since higher education level leads to higher income and better education of the children,
emphasis on education of Population Zero incurs a virtuous circle. If education of the first generation is
insufficient, chain reaction will lead to a cascade and finally the downfall of Population Zero.
Increase Parental Leave Pay We suggest that LIFE offer parental leave to both fathers and mothers
to maintain the equality and maximize the birthrate. Since population need to expand on Mars to created
more active labor forces, encouraging birth giving by implementing high parental leave pay is beneficial to
the long term development on Mars.
Eliminate Discrimination In our complex network model, we find that larger scale of population
and closer relationship among individuals contribute to higher economic growth speed. Discrimination
between local residents of Mars and new immigrants from Earth should be eliminated, since marriages
between individuals of the two group is fundamental to the stability of population.
Robustness Of Our Model We compare samples of Population Zero with randomly added noises on
database. Results show the optimal strategies do not vary much.Since we do not consider the limitation of
natural resources on Mars, our model may be less effective in modelling a large scale of population. Health
care is not considered, which means additional models should be integrated to our simulation.
We hope that our suggestions are useful for LIFE and the UTOPIA:2100 will be a successful beginning
of migration to Mars.
Sincerely,
Team 64486
本资料由迈思数模整理www.maisums.com
Team # 64486 Page 2 of 33
Contents
1 Policy Recommendation 1
2 Introduction 4
3 Parameter Definition And Specific Outcomes 4
3.1 PUMS Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Three-tier Basic Parameter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Derived Index System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3.1 Income Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3.2 Education Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.3.3 Equality Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.4 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Population Zero: PUMS Dempgraphics And Immigrants Selection 8
4.1 Random Sample Of 10000 People . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Selection Criteria And Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 Comparison Between Population Zero And The Random Sample . . . . . . . . . . . . . . 9
4.3.1 Demographic Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Evolution Model and Dynamic System 11
5.1 Model Structure and Overview Of Sample Results . . . . . . . . . . . . . . . . . . . . . . 11
5.2 Assumptions and Mathematical Expression For Each System . . . . . . . . . . . . . . . . 11
5.3 Job System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.4 Education System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.5 Marriage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.6 New Individuals: Child born And Migration System . . . . . . . . . . . . . . . . . . . . 13
5.6.1 Newly Born Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.6.2 Migration System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6 Trade-offs And Social Equilibrium 15
6.1 Additional Assumptions And Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6.2 Policy For Balance Between Minimum Wage And High Productivity . . . . . . . . . . . . 15
6.3 Best Childcare And Parental Leave Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 16
7 Model’s Function For Different Groups 18
7.1 Outcomes Across Different Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.2 Major Subgroup Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.3 Best Allocation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8 Interpersonal Relationship Network And New Immigrants 20
8.1 Generation Of Interpersonal Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.2 Stationary Increment Model And Impact Of Immmigration Waves . . . . . . . . . . . . . 21
9 Migration Plan Analysis 21
9.1 Influences By Choosing Different Migration Year . . . . . . . . . . . . . . . . . . . . . . 21
9.2 Phased Over and One-Year Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10 Robustness Analysis 23
本资料由迈思数模整理www.maisums.com
Team # 64486 Page 3 of 33
11 Strengths and Weaknesses 23
11.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
11.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References 24
A Appendix 26
A.1 MATLAB Script Of Evolution Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
本资料由迈思数模整理www.maisums.com
Team # 64486 Page 4 of 33
2 Introduction
Background In this year of 2095, a series of short-term planned living experiments have been completed
on Mars. A group of 10000 people, called Population Zero, will migrate to Mars. Besides all the ad-
vanced technologies that make life on Mars possible, an optimal strategy regarding workforce, economy
and education should be designed to facilitate the development of Population Zero.
Restatement and Clarification Our team is bound to construct a policy model, which include a set of
policy recommendations that will create a sustainable life-plan. To find out the optimal strategies, we need
to build models, run simulations and present the visualized results. Our model should be scalable, multi-
tiered and dynamic. However, trade-offs should be made if two objectives contradict, and the 3 balancing
factors are income, education and equality.
We aim to solve the following problems:
• Define a set of parameters and metrics and clarify their relations.
• Select a group of 10000 citizens as Population Zero and analyze the demographic characteristics.
Decide the selection criteria that make UTOPIA:2100 a well-functioning society.
• Define the key elements of a successful society in a 10-year period. Find out the equilibrium between
the optimal minimum wage and salary distribution. Find out the optimal parental leave pay.
• Identify the major subgroups of your workforce, and identify their main priorities. Adjust our mod-
els to balance the needs of different subgroups. Maximize the priority outcomes without sharply
reducing the global outcomes.
• Build a sustainable Small World network model and define the dynamics of evolution. Analyze
the impact of immigration phased over the next 100 years.
• Test the scalability of our network model. Consider a much larger population. Study the robustness
of the model.
3 Parameter Definition And Specific Outcomes
3.1 PUMS Database
The American Community Survey (ACS) Public Use Microdata Sample (PUMS)[1] files are a set of 284
different untabulated records including population and housing unit records with individual information
such as relationship, sex, educational attainment, and employment status, et cetera. It is convenient for
people who are looking for accessibility to inexpensive data for research projects. However, there is a thing
worth noting that PUMS does not contain information of people under 16 years old.
3.2 Three-tier Basic Parameter System
In order to quantify the characteristics of Population Zero, we clarify the fundamental parameters that
would be applied in our models. The parameters are classified according to the objects they describe and
the aspect of the outcomes they contribute to.
There are 3 tiers of parameters, which deliver quantitative information about Population Zero on indi-
vidual level, family level and societal level respectively. In each tier, important factors related to income,
education and equality are adopted as parameters. The Fig.1 below illustrates a clear structure of predomi-
nate parameters whose detailed information is in Tab.1.
本资料由迈思数模整理www.maisums.com
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