Abstract
There are many applications of the optimal solution problems such as the traveling salesman
problem (TSP) and the location pickup and delivery problem (LPDP ) , the group theory is
widely used to solve such problems where the solution space of these problems become larger
and larger as the nodes of the problem increase and the searching begin by constructing a
neighborhood of the known solution and then lock for the optimal solution in this
neighborhood and in the other neighborhood if these neighborhood are communicated , but if
they are non-communicated the searching will stuck in one neighborhood and will never find
the optimal solution if it was in another neighborhood . For this the searching in this case was
began in 1999 see [1] . In this research we will study the constructing neighborhood using
template strategy under the action of a conjugation classes of n-cycles and under the action of
subgroups of n S and their transition matrices. And using conjugation strategy under the
sylow p-subgroup of p S and discuss their transition matrices.
problem (TSP) and the location pickup and delivery problem (LPDP ) , the group theory is
widely used to solve such problems where the solution space of these problems become larger
and larger as the nodes of the problem increase and the searching begin by constructing a
neighborhood of the known solution and then lock for the optimal solution in this
neighborhood and in the other neighborhood if these neighborhood are communicated , but if
they are non-communicated the searching will stuck in one neighborhood and will never find
the optimal solution if it was in another neighborhood . For this the searching in this case was
began in 1999 see [1] . In this research we will study the constructing neighborhood using
template strategy under the action of a conjugation classes of n-cycles and under the action of
subgroups of n S and their transition matrices. And using conjugation strategy under the
sylow p-subgroup of p S and discuss their transition matrices.