Precedence constrained sequencing problem (PCSP) is related to locate the optimal sequence with the shortest traveling time among all feasible sequences. In PCSP, precedence relations determine sequence of traveling between any two nodes. Various methods and algorithms for effectively solving the PCSP have been suggested. In this paper we propose a cuckoo search algorithm (CSA) for effectively ...

This paper deals with finding a lower and an upper bound for the minimum number of vehicles needed to serve all locations of the multiple traveling salesman problem with time windows. The two types of precedence graphs are introduced – the start-time precedence graph and the end-time precedence graph. The bounds are generated by covering the precedence graph with minimum number of paths. Instan...