Biogeography-Based Multi-Objective Discrete Optimization with Constraints

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Biogeography-based optimization (BBO) is an evolutionary algorithm that enhances search capabilities through adaptive migration.
• The original BBO is limited to continuous, single-objective problems, excluding discrete and multi-objective optimization challenges.

Purpose of the Study:

• To propose an improved Biogeography-based optimization (BBO) algorithm capable of solving multi-objective discrete optimization problems with multiple constraints.
• To enhance the diversity and convergence of search solutions for complex optimization tasks.

Main Methods:

• Defined decision matrix and objective vector to adapt variables and objective functions for multi-objective discrete optimization.
• Introduced ideal point and utility function for evaluating candidate solutions.
• Proposed similarity, repeatability, cost, and stagnation thresholds to balance solution diversity and convergence.

Main Results:

• The improved BBO algorithm effectively addresses multi-objective discrete optimization problems with multiple constraints.
• Experimental results on NP-hard composite functions validate the approach's effectiveness and efficiency.
• The proposed thresholds contribute to improved search diversity and convergence.

Conclusions:

• The developed BBO algorithm offers a robust solution for complex discrete, multi-objective optimization problems.
• The methodology provides a framework for enhancing evolutionary algorithms in handling constrained optimization tasks.
• The study confirms the practical applicability and efficiency of the proposed BBO enhancements.