A Differential-Based Harmony Search Algorithm With Variable Neighborhood Search for Job Shop Scheduling Problem and Its Runtime Analysis

Abstract

Job shop scheduling problem (JSSP) has drawn a lot of attention as it is one of the vital combinational optimization problems in manufacturing systems. In this paper, a differential-based harmony search (DHS) algorithm with variable neighborhood search (VNS) is proposed for solving JSSP with the objective of minimized makespan. Since the standard harmony search algorithm is constructed for global optimization problems, the smallest position value is introduced to map a harmony vector to an active schedule. The active decoding scheme is employed to improve the search efficiency of DHS. In the pitch-adjustment process, the best individual of the current harmony memory is employed to accelerate the convergence speed. After the pitch-adjustment process, the differential-based enhanced mechanism is designed to maintain the diversity of the population. The modified VNS, which is based on the blocks on the critical path, is embedded into DHS to search for a better solution around the current harmony vector. Besides, the runtime of DHS is analyzed according to the level-based theorem. Compared with various HS-based algorithms and other state-of-the-art algorithms on a set of typical benchmark instances, the DHS is superior to the compared algorithms in terms of solution quality, convergence speed, and stability. The DHS lays a solid foundation for solving optimization problems of expert and intelligent systems.