# An Improved NSGA-II Algorithm Based on Adaptive Weighting and Searching Strategy
## 1 Introduction  
The principle of multi-objective optimization [1] is that when multiple conflicting objectives need to be achieved in a particular situation, the optimization of one objective is often accompanied by degradation of the performance of other objectives, so it is necessary to find a set of solutions [2] that balance multiple sub-objectives to obtain the best optimization for each sub-objective.  
Traditional mathematical methods cannot achieve more satisfactory results because multi-objective optimization problems are computationally difficult. Evolutionary algorithms [3] can be a good solution [4]. The most widely used evolutionary multi-objective optimization algorithm for discovering Pareto optimal solutions is known as the non-dominated sorting genetic algorithm II. In 1989, [PERSON] proposed the concept of Pareto-based optimal solutions and the calculation of the individual fitness method, where the population evolves toward the Pareto optimal solution through non-inferior solutions and the corresponding selection operations.  
The NSGA algorithm, which was first proposed by Professors [PERSON] and [PERSON] in the early 1990s, is based on classifying all individuals in a population at different levels. NSGA uses a non-dominated sorting method that allows good individuals to have a greater chance of being inherited by the next generation, and an adaptation sharing strategy that allows individuals to be evenly distributed and maintains population diversity. Indian scientistDeb proposed a non-dominance ranking genetic algorithm based on the NSGA algorithm in 2002 [5] and used an elite strategy by applying the Pareto dominance relationship and crowding distance mechanism to update the population.  
NSGA-II has better convergence and distribution [6] because of the use of fast non-dominated sorting and crowded-distance-sorting mechanisms. However, NSGA-II has a slow convergence speed due to the use of an inefficient simulated binary crossover algorithm. It has poor convergence speed and optimization finding ability when solving complex problems [7]. With the NSGA-II algorithm applied to a wider range, some problems have gradually emerged. In the genetic operation, constant genetic parameters lead to a smaller moving space and poorer search performance during the iteration of the algorithm. Meanwhile, the NSGA-II algorithm shows the problem of falling into local optimal solutions.  
The principal contributions of this study are summarized as follows:  
1. An improved non-dominated ranking genetic algorithm is proposed to enhance the search ability by using Levy flight and random walk strategy, which can provide a larger search range and better local search ability.
2. To improve the accuracy and speed of convergence, an adaptive parameter is designed, which balances the exploration and development periods.  
In the remainder of the paper, we first introduce some fundamental conceptions of multi-objective optimization problems and discuss some existing works in Section 2. At the beginning of Section 3, we present some background on NSGA-II, then introduce Levy distribution and random walk-in detail, while designing an adaptive weight to balance global exploration and local exploitation. After that, we propose the improved NSGA-II algorithm. In Section 4, we submit the results on standard test functions and a mathematical model for the parallel chillers. At the end of the article, we outline the conclusions of the study.