We can summarize Popper’s criticism of the scientific method in the following statement:
A theory is not provable, but it is only falsifiable.
He did not agree with the justification of induction as a sound scientific method, because of the lack of falsifiability. Induction is a mechanism wich can be described with the following statement:
A lot of theories are formed basically by generalization of two or more other theories.
But look for example how, first, the movement of planets and stars are described in a very elaborative way for each planet or group of stars. Then there are successive generalization steps by Ptomelaeus (the earth in the centre, epicycles) followed by Copernicus (the sun in the centre), Keppler (laws) and Newton (gravity). The gain is clear: Each time it leads to fewer equations. The physical scientists suggest that they will find te ultimate generalization, the Unified Theory. So, induction had a lot of succes, and nowadays a lot of philosophical scientists defend it and build a more sound basis for it, e.g. by the Confirmation Theory.
So, we think that we can start form induction, but we will use also the merits of the objections of Popper in the earliest stages of a research of a hypothesis, certainly if it is in a very out-of-the box, provocative think experiment. We combine therefore the two statements into the following guidance in theorizing.
One can use a generalization in theorizing, when there is any indication for it, if one immediately searches for falsifications.
The merit is that we start to find as early as possible falsifications to avoid ridiculous generalizations, i.e. those who can be rejected easely by opponents. Later, once the hypothesis becomes more theory, we can focus more on confirmations.
Notice: We want this guidance certainly only apply to natural sciences. In social sciences it is really questionable to find fast falsifications (Popper) and then the danger is that generalizations will be used while not justified, causing possibly a wrong social impact, even damage.