Integrated LI-NSGA-II Approach for Solving the Non-linear Multi-objective Optimization Problem - Muskan Kapoor; Bhupendra Kumar Pathak; Rajiv Kumar (Austrian Journal of Statistics)
Real-world engineering projects frequently involve complex, non-linear multi-objective optimization challenges. Traditional methods like PERT/CPM and basic heuristics often fail to provide optimal solutions in such scenarios. Multi-objective evolutionary algorithms, such as genetic algorithms and non-dominated sorting genetic algorithms, are more effective for identifying true Pareto solutions. Among these, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is a well-known algorithm for solving multi-objective optimization problems. This study presents an integrated approach, called LI-NSGA-II, which combines Lagrange's Interpolation (LI) with NSGA-II to solve non-linear multi-objective optimization problems in real-world projects. In this LI-NSGA-II approach, LI is used to handle the non-linearity of competing objectives, whereas NSGA-II optimizes these objectives to find optimal solutions. The outcomes achieved through the LI-NSGA-II approach are ideal for real-time monitoring and control of non-linear multi-objective optimization problems.