Modified discrete firefly algorithms with mutation operators as local search for makespan minimization of the permutation flowshop scheduling problem - Pabrua, Lerr Dwaine Badoy (2011)
Combinatorial optimizations the discipline in the area of discrete mathematics that deals with decision making in the case of discrete alternatives. A famous combinatorial optimization problem is the Permutation Flowshop Scheduling Problem (PFSP-a decision problem that deals with how to schedule n jobs on m machines with consideration to a specific criterion. In this study, novel variants of the Discrete Firefly Algorithm (DFA), generally called Modified Discrete Firefly Algorithms (MDFAs) are introduced. Modification was done by replacing the logistic sigmoid function (sigmoid) with the hyperbolic tangent function (tanh). Three mutation operators are used as local search methods producing 3 MDFAs called MDFA with exchange mutation (MDFA-EM), MDFA with insertion mutation (MDFA-ISM )and MDFA with simple inversion mutation (MDFA-SIM). DFA and the proposed algorithms were subjected to known PFSP benchmarks with makespan criterion as the objective function. In terms of solution quality, an MDFA variant, specifically MDFA-EM, produced more minimum makespan and average minimum values. regarding solution time, MDFA found optimal solutions faster compared to DFA, on the average case. In terms of performance, tanh also matched that of sigmoid while some instances had shown the better performance of tanh.