This book introduces a novel two-phase algorithm for multiobjective optimization, integrating genetic algorithms with rough set theory. The first phase employs a multiobjective genetic algorithm, utilizing co-evolution and a repair algorithm for nonlinear constraints, to approximate the true Pareto front and maintain a finite archive of non-dominated solutions updated via ε-dominance. The second phase then applies rough set theory as a local search engine to enhance the spread of these solutions. The proposed algorithm demonstrates promising results on benchmark problems when compared to existing methods, suggesting its applicability to real-world challenges such as the Economic Environmental Dispatch of Power Systems.

The presented methodology offers a sophisticated approach to multiobjective optimization, combining established techniques with novel applications of rough set theory. The authors detail a two-phase algorithm designed to efficiently generate and refine Pareto optimal solutions, demonstrating its efficacy through benchmark tests and a practical application in power systems dispatch. The results suggest a competitive performance against existing algorithms, highlighting the potential of this integrated approach for complex real-world problems.