Multi-Objective Optimization Based on Improved Distribution of Solutions

For low-dimensional multi-objective optimization problems, the existing multi-objective optimization algorithms have been able to ensure the proximity to the optimal front of the problem, and balance the convergence and the diversity of solution sets. However, the uniformity of the solution is ignored in most algorithms. In the multi-objective optimization problem with irregular Pareto front, the more uniform the distribution of solution is, the more the solution can reflect the true distribution of the optimal front of the problem, and the more reasonable the choices provided to decision makers. To improve the uniform distribution of solutions, a new multi-objective optimization algorithm CM-SPEA2 is proposed based on SPEA2 algorithm and the improved individual fitness calculation. In this algorithm, firstly, the initial population is divided into different clusters by means of hierarchical clustering. Next, the original calculation method of messy degree is improved to measure the messy degree of individuals in their clusters, and the individuals with the lowest messy degree are selected as reference points. Then, based on the Manhattan distance between other individuals and the reference point, the operator representing distribution is calculated and the fitness function is improved. Finally, the fitness threshold is set to screen non-dominated individuals near the reference point, so as to indirectly adjust the environmental selection strategy, make the distribution of retained individuals more uniform, thus improving the convergence and diversity. As compared with some similar multi-objective optimization algorithms, the proposed CM-SPEA2 algorithm has certain advantages in solving IMOP, ZDT and VNT test problems.