Forward VNS, Reverse VNS, and Multi-VNS Algorithms for Job-Shop Scheduling Problem

This paper proposes a number of forward VNS and reverse VNS algorithms for job-shop scheduling problem. The forward VNS algorithms are the variable neighborhood search algorithms applied to the original problem (i.e., the problem instance with the original precedence constraints). The reverse VNS algorithms are the variable neighborhood search algorithms applied to the reversed problem (i.e., the problem instance with the reversed precedence constraints). This paper also proposes a multi-VNS algorithm which assigns an identical initial solution-representing permutation to the selected VNS algorithms, runs these VNS algorithms, and then uses the best solution among the final solutions of all selected VNS algorithms as its final result. The aim of the multi-VNS algorithm is to utilize each single initial solution-representing permutation most efficiently and thus receive its best result in return.