What solutions do you see for the vast migration to the cities of the least industrialized nations?

First of all, it is not at all clear that there needs to be a solution to urbanization in the least developed countries (LDCs). As we can see in the links below, many experts believe urbanization is a good thing for LDCs. Urbanization brings many people together in one place, allowing them to be more economically productive than possible if they were dispersed out in the country, engaged in subsistence farming. Even in rich countries like the United States, cities are by far the most productive economic areas. Therefore, it is not clear we should try to prevent urbanization in LDCs.
If, however, we assume that we should try to prevent urbanization, then the solution would be to develop more in rural areas. People move to the cities because they want better lives. They do not see opportunities for advancement and wealth in the countryside. Therefore, they go to cities where they hope to find jobs. People also hope their children will be able to attend schools and gain the chance for better lives. 
If these are pull factors attracting migrants to cities, then the solution is to create similar pull factors in places other than cities. Governments would have to create good schools in rural areas. They would also have to build infrastructure in those areas so businesses could develop there. They might have to do things like give tax breaks to people who invest in such areas. By doing these things, the government might be able to create enough economic opportunities to keep people from migrating in large numbers to cities. 
https://population.un.org/wup/

https://www.worldbank.org/en/news/press-release/2013/04/17/developing-countries-need-to-harness-urbanization-to-achieve-mdgs-imf-world-bank-report