On the Single and Flow Shop Scheduling Problems

In the first part of this book, we investigate the single machine scheduling problems. We begin with minimize four cost functions simultaneously. To find an approximate set of non dominated solutions for this problem, two propositions and two multi-objective heuristic algorithms are proposed. We implement a multi-objective genetic algorithm which, also a multi-objective variable neighborhood search algorithm proposed and a modification using these two algorithms proposed. Some special cases are studied. We propose a BAB algorithm, and proposed the local search algorithms to find the near optimal solution. In the second part, m-machine permutation flowshop scheduling problems are studied, to minimize simultaneously some combination of the cost functions, we implement the multi-objective partial enumeration algorithm and propose a modification algorithm using multiobjective variable neighborhood. Two multi-objective genetic algorithms are implemented and a modifications proposed. Finally we study the two machine permutation flowshop problem to minimize some combinations of cost functions. We propose two propositions to solve the problem and three special cases are studied.