Matrix Method for Non-Dominated Sorting and Population Selection for Next Generation in Multi-Objective Problem Solution
Prince Rajpoot, Pragya Dwivedi · 2018
The Multi-Objective problem solution methods consider two or more conflicting objectives simultaneously. The method selects the initial population and rectifies it for generating better solution using different operations like: crossover, mutation etc. Finally, it generates pareto-optimal solutions for the given problem after satisfying some conditions. In order to rectify the current population, after performing operations on the population, it generates fronts and selects the best populations from the higher to lower fronts according to the needs. Crowding distance concept comes into existence and plays an important role when the number of solutions presents in the particular front has been exceeded then the remaining needed solutions. Due to the limitation of time, we need to stop the rectifying process after a limited period of time. It shows that due to its higher convergence power, the algorithm with lower computational complexity can generate efficient solution within that period of time as compared to the algorithm with higher computational complexity. In recent years, several algorithms provide solutions for multi-objective optimization problem based on non-dominated sorting but the computational complexity of such algorithms is high and implementation in complex in nature. In this paper, we propose an alternative method based on matrix approach for front generation and selection of next-generation population so that it can magnify the convergence power by decreasing the time consumption in these phases of algorithms. The computational complexity of the proposed method is calculated. The proposed algorithm has been applied to various cases of a case study and it selects the same population for next generation as NSGA algorithm, but with a lower computation effort. This algorithm is also very easy to learn and implement.