Hybrid Genetic Algorithms for the Asymmetric Distance-Constrained Vehicle Routing Problem

Algorithm 3

Sequential constructive crossover algorithm.

	Input: , Pair of parent chromosomes.
	Output: Offspring chromosome.
	Generate a random number .
	if () then do
	Set.
	The offspring chromosome contains only “city 1.”
	forto n do
	In each chromosome consider the first “legitimate” (un-visited) city existed after “city p.”
	if no legitimate city is existed in a parent, then
	Examine from starting of the parent and choose the first legitimate city existed after “city p.”
	end if
	Assume that “city α” and “city β” are selected from 1st and 2nd parents, respectively.
	if () then do
	Add “city α” to the offspring chromosome.
	else
	Add “city β” to the offspring chromosome.
	end if
	If after combining the current city,
	then
	Drop the current city and add a dummy depot in the route as the end city of the route.
	end if
	Rename the present city as “city p” and continue.
	end for
	end if
	Return the offspring chromosome