An effective operations permutation-based discrete harmony search approach for the flexible job shop scheduling problem with makespan criterion

The Flexible Job Shop Scheduling Problem (FJSSP) represents a challenging applicative problem for metaheuristic algorithms because it imposes the development of innovative domain-dependent search operators that have to deal both with its combined discrete and permutation nature. Emerging as an effective approach for the resolution of a broad spectrum of hard optimization problems, some few discrete declinations of the Harmony Search (HS) algorithm have been recently proposed for tackling the FJSSP. Recent advances include an investigation of an innovative and promising permutation-based proposal. Accordingly, this paper proposes an Effective Operations Permutation-based Discrete Harmony Search (EOP-DHS) approach for FJSSP with Makespan criterion. The approach adopts an integrated two-part “affectation-sequencing” representation of the solution harmony and a dedicated improvisation operator particularly adapted to the integer-valued and operations permutation-based used coding scheme. Besides, a Modified Intelligent Mutation (MIM) operator is integrated to the adopted framework in order to enhance its overall search ability. Mainly, by balancing maximum machine workload during the overall search process, MIM operator allows essentially maintaining and enhancing the reciprocal equilibrium of diversification and intensification abilities of the proposed EOP-DHS algorithm. Conducted numerical experimentations on 188 benchmarking instances validate the proposal comparatively to a representative set of previously deployed metaheuristic approaches to FJSSP with Makespan criterion. Furthermore, main contribution of the paper is extended with an experimental procedure proving the effectiveness of the adopted permutation-based HS scheme for the resolution of combinatorial optimization problems. Hard benchmarking instances of the classical Job Shop Scheduling Problem (JSSP) are thus considered for exemplification.