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A Novel Binary Dream Optimization Algorithm with Data-Driven Repair for the Set Covering Problem.

Broderick Crawford1, Hugo Caballero1, Gino Astorga2

  • 1Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile.

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Summary
This summary is machine-generated.

This study adapts the Dream Optimization Algorithm for the Set Covering Problem, a critical NP-hard optimization task. The enhanced approach effectively handles constraints and improves solution quality for complex industrial applications.

Keywords:
combinatorial optimizationdream optimization algorithmmachine learning–based controlmetaheuristicsrepair strategiesset covering problem

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Area of Science:

  • Combinatorial Optimization
  • Metaheuristic Algorithms
  • Computational Complexity

Background:

  • The Set Covering Problem is a fundamental NP-hard problem with broad industrial applications.
  • Large-scale, constrained instances necessitate metaheuristic approaches over exact methods.
  • Adapting continuous optimization algorithms to discrete, constrained problems presents unique challenges.

Purpose of the Study:

  • To propose a discrete adaptation of the Dream Optimization Algorithm for the Set Covering Problem.
  • To address challenges in applying continuous algorithms to binary and constrained models.
  • To develop effective feasibility restoration and search progression mechanisms.

Main Methods:

  • A discrete adaptation of the Dream Optimization Algorithm was developed.
  • A fixed discretization scheme mapped continuous search to the binary decision space.
  • An adaptive control mechanism using bandit-driven operator selection managed repair procedures.

Main Results:

  • The proposed approach consistently achieved high-quality solutions.
  • Low relative deviation from known optima was observed.
  • Stable performance across independent runs was demonstrated.

Conclusions:

  • The discrete Dream Optimization Algorithm effectively solves constrained Set Covering Problems.
  • The adaptive repair mechanism enhances feasibility restoration and search progression.
  • The method offers a robust metaheuristic for complex optimization tasks.