Improved Genetic Algorithm For Solving Multi-objective Optimization Problems

Multi-objective optimization is a difficult problem and a research focus in the fields of science and engineering. How to effectively solve the multi-objective optimization problems has been a goal pursued by scholars. At the early stage, the traditional mathematical programming method is commonly used to solve the multi-objective optimization problems. With evolutionary algorithm being proposed, it is widely used in the optimization fields. As population-based heuristic search methods, evolutionary algorithm has more advantages in solving the multi-objective optimization problems (MOPs). How to make use of evolutionary algorithm to solve multi-objective optimization problems has become a research hotspot in the fields of optimization. Genetic algorithm (GA) as a main branch of evolutionary algorithm has been widely used to solve multi-objective optimization problems, which has strong global search ability and does not rely on specific problems. The NSGA-? use genetic algorithm to solve multi-objective optimization problems. However, there are some deficiencies in the NSGA-? for solving multi-objective optimization problems, such as, insufficient consideration of the diversity of the population, weak local search, high time complexity of fast non-dominated sorting algorithm and so on. This thesis mainly aims at addressing the NSGA-? these deficiencies.The main contents are as follows:1. The relevant background knowledge of multi-objective optimization problems are introduced systematically, and the algorithms for solving the multi-objective optimization problems are introduced in detail. The general process of using the NSGA-? to solve multi-objective optimization problems is focused on. The advantages and disadvantages of NSGA-? are summarized.2. NSGA-? mainly focus on the quality of the solution, and lacks of consideration of the diversity of population in solving multi-objective optimization problems, a new selection operator is proposed. The new selection operator can ensure holding the non-dominated optimal solutions of the population and take into account the diversity of the population. At the same time, the mutation operator is improved to strengthen the local search ability of the NSGA-?. Based on the improvement, this thesis proposes a new improved algorithm ISMNSGA-II, and simulation results show the effectiveness of the algorithm.3. For the multi-objective evolutionary algorithm based on Pareto optimal, constructing non-dominated optimal solution set of population is a crucial step in the algorithm. The key to ensure the quality of the solution is to find the non-dominated optimal solution set of the population accurately. Arena algorithm is a new method to construct the non-dominated optimal solution set of population, and it has a better time performance. Due to some disadvantages exists in arena algorithm, this thesis has made some improvement and proposes an improved arena algorithm. The improved algorithm can find the non-dominated optimal solution set of the population and it can effectively reduce the time needed. The simulation experiment proves the effectiveness of the algorithm.