Improved estimation of distribution algorithm for the problem of single-machine scheduling with deteriorating jobs and different due dates

Abstract

This paper investigates single-machine scheduling problem, which is an NP-hard problem, with deteriorating jobs and different due dates to minimize total tardiness. First, two special polynomially solvable cases of the problem and a mixed-integer programming (MIP) model are proposed. Since the large-scale problem needs a long time when the MIP is solved using the CPLEX, the improved estimation of distribution algorithm (EDA) is proposed to solve the problem with a large size. EDA depends on the probabilistic model, which denotes the distribution of decision variables in the feasible region space. Meanwhile, EDA owns efficient search capability and convergence. To obtain an improved initial population, an efficient initialization scheme based on the feature of two special cases and a heuristic algorithm are adopted in the process of constructing the initial population. The probabilistic model is composited based on elite solutions from each generation. Simultaneously, mutation is embedded to maintain the diversity of the population. Compared with the results, numerical experiments show that the proposed algorithm can obtain good near-optimal solutions within a short period.