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

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.