Nature-Inspired-DMU-Selection-and-Evaluation-in-Data-Envelopment-Analysis

Nature-Inspired DMU Selection and Evaluation in Data Envelopment Analysis

Link to the paper:

• https://link.springer.com/chapter/10.1007/978-3-031-24475-9_17
• DOI: https://doi.org/10.1007/978-3-031-24475-9_17

Please cite:

• Mousavi, Seyed Muhammad Hossein. "Nature-Inspired DMU Selection and Evaluation in Data Envelopment Analysis." The International Symposium on Computer Science, Digital Economy and Intelligent Systems. Cham: Springer Nature Switzerland, 2022.

Nature-inspired DMU Selection and Evaluation in Data Envelopment Analysis

This repository contains the implementation of the research paper "Nature-inspired DMU Selection and Evaluation in Data Envelopment Analysis" by Seyed Muhammad Hossein Mousavi. The study explores the use of Biogeography-Based Optimization (BBO) for selecting Decision Management Units (DMUs) in Data Envelopment Analysis (DEA) to enhance system efficiency. It also introduces Fuzzy Firefly Regression for post-selection evaluation.

---

Abstract

DMU selection is a critical step in optimizing efficiency in DEA. This research leverages nature-inspired optimization algorithms, particularly Biogeography-Based Optimization (BBO), to select the most effective DMUs for business and management datasets. Post-selection evaluation is performed using Fuzzy Firefly Regression, resulting in improved efficiency and correlation coefficients compared to traditional methods.

---

Key Features

1. Nature-inspired Optimization:

   • Utilizes Biogeography-Based Optimization (BBO) for DMU selection.
   • Removes weak DMUs with high Mean Square Error (MSE) values.

2. DEA Evaluation:

   • Evaluates DMU efficiency using four DEA methods:
     • CCR
     • Input-Oriented BCC (IOBCC)
     • Output-Oriented BCC (OOBCC)
     • Additive models.

3. Post-selection Regression:

   • Applies Fuzzy Firefly Regression for enhanced correlation modeling.
   • Uses Fuzzy C-means clustering and Sugeno inference systems for optimization.

4. Dataset Support:

   • Works with various datasets, including:
     • Clickstream Data for Online Shopping
     • Daily Demand Forecasting Orders
     • Online News Popularity
     • Statlog (Australian Credit Approval).

---

Workflow

Step 1: DMU Selection

• Input data is processed using the BBO algorithm.
• DMUs are ranked based on their efficiency and suitability for the system.

Step 2: DEA Evaluation

• The selected DMUs are evaluated using DEA methods.
• Efficiency is calculated for subsets (25%, 50%, 75%) of the features.

Step 3: Post-selection Regression

• Selected DMUs are used in Fuzzy Firefly Regression.
• The regression model is optimized using Firefly algorithm parameters (light intensity, absorption, and attraction coefficients).

---

Results

DEA Results

Method	Rank (Features)	Clickstream	Daily Demand	Online News	Statlog
Original DEA	All	0.837	0.926	0.844	0.883
Lasso DEA	25%	0.588	0.754	0.694	0.758
GA DEA	25%	0.767	0.867	0.805	0.796
PSO DEA	25%	0.772	0.876	0.800	0.856
BBO DEA	25%	0.803	0.900	0.840	0.883

Regression Results

Method	Rank (Features)	CC (Train)	CC (Test)	MSE (Train)	MSE (Test)
Fuzzy Regression	25%	0.783	0.783	0.319	0.319
Fuzzy Firefly	25%	0.987	0.987	0.032	0.032

---

Algorithms Used

Biogeography-Based Optimization (BBO)

• Parameters:
  • Iterations: 1000
  • Population: 20
  • Immigration Rate (λ): 0.3
  • Emigration Rate (μ): 0.2
  • Mutation Probability: 0.1
• Objective: Minimize MSE and select DMUs with the highest efficiency.

Fuzzy Firefly Regression

• Parameters:
  • Population: 15
  • Iterations: 1000
  • Light Absorption Coefficient (γ): 0.1
  • Attraction Coefficient (β): 2
• Objective: Optimize fuzzy parameters for regression.