Multi-objective optimization problems exist everywhere in life, and solving these problems can bring many benefits to society. Multi-objective optimization is to optimize all the objective functions in the problem, but in general, there is a little conflict between these objective functions, so it is difficult to achieve multi-objective optimization. So far, many experts and scholars have carried out research on multi-objective optimization problems and have achieved a series of results. This article starts from the basic description of multi-objective optimization problems and the research status so far. There are many methods to solve multi-objective optimization problems, such as objective optimization method. Such traditional methods as well as intelligent algorithms such as particle swarm optimization and differential evolution algorithm provide a comprehensive overview of multi-objective optimization problems.