An Improved Quantum Differential Algorithm for Stochastic Flow Shop Scheduling Problem

In this paper, an Improved Quantum Differential Algorithm (IQDA) is proposed for a stochastic flow shop scheduling problem with the objective to minimize the expected value of makespan. We set up a stochastic expected value model, where the processing times are subjected to independent normal distributions. In the algorithm, a new strategy named big fish eating small fish is developed during the process of population growth. Based on the concepts of quantum theory and differential knowledge, this algorithm applies the mutation operator and crossover operator of Differential Evolution (DE) to generate new Q-bit representations. The experiment results achieved by IQDA are compared with Quantum Genetic Algorithm (QGA) and standard Genetic Algorithm (GA), which shows that IQDA has better feasibility and effectiveness.