A novel hybrid fuzzy–metaheuristic approach for multimodal single and multi-objective optimization problems

In this paper, we propose a novel hybrid fuzzy–metaheuristic approach with the aim of overcoming premature convergence when solving multimodal single and multi-objective optimization problems. The metaheuristic algorithm used in our proposed approach is based on the imperialist competitive algorithm (ICA), a population-based method for optimization. The ICA divides its population into sub-populations, known as empires. Each empire is composed of a high fitness solution—the imperialist—and some lower fitness solutions—the colonies. Colonies move towards their associated imperialist to achieve better status (higher fitness). The most powerful empire tends to attract weaker colonies. These competitions and movements can be enhanced for better algorithm performance. In our hybrid approach, a global learning strategy is devised for each colony to learn from its best-known position, its associated imperialist and the global best imperialist. A fast-evolutionary elitism local search is used to enhance the collaborative search mechanism (competition) in each empire, and thus the overall optimization performance may be improved. Other main evolutionary operators include velocity adaptation and velocity divergence. To address parameterization and computational cost evaluation issues, two fuzzy inferencing mechanisms are designed and used in parallel: one is a learning strategy adaptor in each run, and the other is a smart evolution selector in each running window. For Pareto front approximation, fast-elitism non-dominated sorting is applied to the solutions, and a novel penalized sigma diversity index is designed to estimate the diversity (power) of solutions in the same rank. Comprehensive experimental results based on 22 single-objective and 25 multi-objective benchmark instances clearly show that our proposed approach provides better solutions compared with other popular metaheuristics and state-of-the-art ICA variants. The proposed approach can be used as an optimization module in any intelligent decision-making systems to enhance efficiency and accuracy. The designed fuzzy inferencing mechanisms can also be incorporated into any single- or multi-objective optimizers for parameter tuning purposes, to make the optimizers more adaptive to new problems or environments.