Three-way decision based island harmony search algorithm for robust flow-shop scheduling with uncertain processing times depicted by big data

Abstract

This paper discusses an uncertain two-machine permutation flow-shop scheduling problem (2PFSP) with total weighted tardiness and common due date. Uncertain processing times are described by a large set of discrete scenarios, which is a type of big data. The objective is to minimize the schedule performance under the worst-case scenario. Identifying the worst-case scenario for each evaluated schedule is quite time-consuming in the situation that the scenario set size is large so that the objective evaluation might be computationally expensive. To handle this difficulty, three-way decision is used to preprocess the large-size scenario set to get a reduced scenario set so that the concept of surrogate worst-case scenario is adopted. A hybrid harmony search algorithm of combining three-island framework and the scenario-based local search is developed to solve the discussed problem. Based on the single-scenario knowledge of 2PFSP, a problem-specific scenario-dependent neighborhood structure is constructed under the surrogate worst-case scenario. An extensive experiment was carried out. The computational results show that the application of surrogate worst-case scenario based on three-way decision is effective in reducing the time consuming while keeping schedule performance evaluation. Being compared to the worst-case scenario objective evaluation, for an example in the case of the middle bad-scenario ratio, the surrogate worst-case scenario objective evaluation made the solution algorithm save 12.95 % in average CPU time for all instances while the relative performance difference is only 1.809 % in average. Being compared to possible alternative algorithms derived from the state-of-the-art algorithms, the developed algorithm is advantageous for the addressed problems.