MCM 2023: Global Meritorious Winner — Policy Optimization & Animal Population Modeling
Global Meritorious Winner (Top ~10% among 11,296 teams). The only high school team to achieve this on Problem B. Built optimization models using simulated annealing, logistic models, and Euler Method.
Global Meritorious Winner — Top ~10% among 11,296 teams. The only high school team to achieve this on Problem B (among 728 teams).
Methodology
We first built an optimization model by subtracting the predicted economic profit using the modeled negative impacts, and conducted simulated annealing to obtain the value of each variable for the optimized policy.
To account for changes in animal populations and propose an alternative policy that preserves these populations, we developed our animal population model using the logistic model framework. This model includes the additional mortality rate resulting from policies that permit hunting.
We converted the differential equation into a recursive form using the Euler Method to solve it. To estimate the natural growth rates of various animals within the national reserve, we employed an exponential growth model, aligning it with the existing population data. The main model was refined by incorporating a constraint derived from the differential equation.
IMMC 2023: Land Development Strategy Optimization via Machine Learning
Advanced to Final Defense (Top 26 among 900+ teams) at IMMC Greater China International Round. Applied Entropy Weight and K-Means clustering for optimized land development strategy.
Advanced to Final Defense — Top 26 among 900+ teams at the IMMC Greater China International Round.
Approach
Applied machine learning methods — Entropy Weight and K-Means clustering — to evaluate different development plans for a 5-square-kilometer land area. The model considered three key dimensions:
- Environmental impacts — ecological footprint and sustainability metrics
- Economic profits — projected returns and cost-benefit analysis
- Community utilities — social infrastructure and quality of life factors
The optimization framework balanced these competing objectives to find the most effective land development strategy.
HiMCM 2023: Dandelion Spread PDE Model — Finalist Award
Finalist Award (Top ~7% globally) at HiMCM 2023. Constructed a system of four coupled PDEs modeling dandelion population dynamics with Fisher logistic growth, advection-diffusion, and Brownian dispersal.
Finalist Award — Top ~7% globally at the 2023 High School Mathematical Contest in Modeling.
The Model
We constructed a Dandelion Spread PDE Model (DSM) — a system of four coupled partial differential equations that model population densities of:
- Settled dandelion seeds
- Dandelion plants
- Puffballs
- Drifting seeds
We corrected the Fisher model by multiplying a logistic term to obtain a logistic population growth that depicts the effect of intraspecific competition on the dandelion population.
For the PDE of drifting seeds, we used the advection-diffusion equation by adding Brownian Random Dispersal. This allows us to effectively predict the spread of dandelions in various kinds of winds.
Computation & Analysis
We used FEniCS to obtain the final predictions of the DSM model, followed by a sensitivity analysis. Finally, we used the Analytic Hierarchy Process to measure the dandelions’ invasiveness, with total biomass calculated using the DSM model.
IMMC 2023: Lizard Species Classification via Machine Learning
Advanced to International Round at IMMC Greater China National Round. Applied logistic regression, decision tree, and random forest to classify lizards into 26 species.
Advanced to International Round at the IMMC Greater China National Round.
Approach
Applied machine learning classification methods to classify lizards into 26 species:
- Logistic Regression — baseline linear classifier
- Decision Tree — interpretable tree-based model
- Random Forest — ensemble method for improved accuracy
The models were trained on morphological and behavioral features to achieve reliable multi-class species identification.