How to Solve Evaluation Models: Preprocessing, Weight Calculation, and Integration with Python

1 Solving the Evaluation Model

Overall, the HiMCM 2020 A problem requires little programming skill, but mastering basic Python operations can save time. Input data can be viewed as a table (rows as jobs, columns as attributes) or as a matrix, and we need to perform row‑column transformations.

The evaluation model involves three main computational stages:

Data preprocessing (standardization and normalization)

Weight calculation

Combining weights with data

1.1 Preprocessing

Standardization converts very small, medium, and interval indicators into large‑scale indicators, using piecewise functions, reciprocals, or negatives. In Excel this is done with formulas; in Python you can use either NumPy or Pandas and their built‑in functions together with matrix operations. Detailed methods are described in the referenced material.

Normalization includes range normalization, vector normalization, standardization, and proportion normalization. Functions such as linalg.norm , np.mean , and np.std from NumPy are commonly used. You can also implement these functions yourself, though it is usually unnecessary.

1.2 Weight Calculation

Weight calculation is the most complex part of the evaluation model. Using the entropy weight method as an example, you need an entropy function and must ensure the probability p is not zero (replace zero with a very small number if needed). The method is detailed in the referenced material.

The Analytic Hierarchy Process (AHP) requires knowledge of eigenvalues and eigenvectors from linear algebra. In Python this can be obtained with numpy.linalg.eig . Understanding these concepts is essential for correctly presenting the weight derivation.

1.3 Combining Weights and Data

Common combination methods include linear weighting, exponential weighting, and logarithmic weighting. Linear weighting, the most frequently used, treats weights as coefficients and performs matrix multiplication. In Python you can use dot or the @ operator for this purpose.

2 Summary

For most students familiar with mathematical modeling, the evaluation model computation is not the main difficulty; the focus lies on model innovation and interpretation. Familiarity with basic Python libraries such as NumPy or Pandas is sufficient, while additional model types may require specific programming knowledge.