Before revision:  This paper addresses this problem by proposing what we called alazy listing algorithm. By this we mean that, instead of listing all solutions , we list, in an efficient way, directly only the equivalence classes or  one representative per class . Besides the need to then provide ana priori relation of equivalence between solutions, we place ourselves in the special context where the problem to be addressed , either after some preliminary polynomial time dynamic programming computation or directly from the start, leads to a decomposable tropical circuit .
After revision:  This paper addresses this problem by proposing what we called alazy listing Furthermore, depending on the application, many of these solutions can be considered equivalent. The problem of an efficient enumeration of the equivalence classes or one representative per class . Besides the need to then provide ana priori relation of equivalence between solutions, we place ourselves in the special context where the problem to be addressed , either after some preliminary polynomial time dynamic programming computation or directly from the start, leads to a decomposable tropical circuit .