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A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment

Martin Gonzalez1, Jose J López-Espín1, Juan Aparicio1

  • 1Center of Operations Research, Universidad Miguel Hernández de Elche, Elche, Spain.

Peerj. Computer Science
|February 17, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel hyper-matheuristic for solving complex Mixed Integer Linear Programs (MILPs) in Data Envelopment Analysis (DEA). The new method decomposes problems, outperforming global metaheuristics for technical efficiency scores.

Keywords:
Exact methodsHyper-matheuristicMILP decompositionMathematical optimizationMetaheuristicsMixed integer problems

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Area of Science:

  • Operations Research
  • Mathematical Optimization
  • Data Envelopment Analysis

Background:

  • Mixed Integer Linear Programs (MILPs) are computationally challenging NP-hard problems.
  • Metaheuristics offer potential solutions for large-scale MILPs.
  • Data Envelopment Analysis (DEA) frequently utilizes MILPs to assess the technical efficiency of Decision Making Units (DMUs).

Purpose of the Study:

  • To propose a new hyper-matheuristic approach for solving MILPs within the DEA framework.
  • To enhance the efficiency and accuracy of technical efficiency score determination in DEA.

Main Methods:

  • A MILP-based decomposition strategy dividing the problem into hierarchical subproblems.
  • Separate optimization methods for discrete (metaheuristics) and continuous (exact methods) variables.
  • An indirect solution representation for metaheuristics, decoded by exact methods.

Main Results:

  • The proposed hyper-matheuristic approach yields superior solutions compared to global metaheuristic methods.
  • Experimental results on simulated DEA data validate the effectiveness of the decomposition technique.
  • Identified optimal algorithm selection through cooperative metaheuristics and exact optimization algorithms.

Conclusions:

  • The novel hyper-matheuristic effectively addresses MILPs in DEA, improving technical efficiency assessments.
  • Decomposition into discrete and continuous subproblems is a viable strategy for complex optimization tasks.
  • Cooperative optimization algorithms demonstrate strong performance in this specialized problem context.