BRKGA-VNS for Parallel-Batching Scheduling on a Single Machine with Step-Deteriorating Jobs and Release Times

This paper investigates the problem of scheduling step-deteriorating jobs with release times on a single parallel-batching machine. The processing time of each job can be represented as a simple non-linear step function of its starting time. The machine can process up to \( c \) jobs simultaneously as a batch. The objective is to minimize the makespan, and we show that the problem is strongly NP-hard. Then, a hybrid meta-heuristic algorithm BRKGA-VNS combining biased random-key genetic algorithm (BRKGA) and variable neighborhood search (VNS) is proposed to solve this problem. A heuristic algorithm H is developed based on the structural properties of the problem, and it is applied in the decoding procedure of the proposed algorithm. A series of computational experiments are conducted and the results show that the proposed hybrid algorithm can yield better solutions compared with BRKGA, PSO (Particle Swarm Optismization), and VNS.

[1]  T. C. E. Cheng,et al.  Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan , 2010, Eur. J. Oper. Res..

[2]  Gur Mosheiov,et al.  Batch scheduling with step‐deteriorating processing times to minimize flowtime , 2012 .

[3]  Purushothaman Damodaran,et al.  Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times , 2010 .

[4]  Reha Uzsoy,et al.  Minimizing makespan on a single batch processing machine with dynamic job arrivals , 1999 .

[5]  Pierre Hansen,et al.  Variable Neighborhood Decomposition Search , 1998, J. Heuristics.

[6]  T. C. Edwin Cheng,et al.  "Product Partition" and related problems of scheduling and systems reliability: Computational complexity and approximation , 2010, Eur. J. Oper. Res..

[7]  T. C. Edwin Cheng,et al.  Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan , 2011, Eur. J. Oper. Res..

[8]  Celso C. Ribeiro,et al.  Biased Ranom-Key Genetic Algorithms: An Advanced Tutorial , 2016, GECCO.

[9]  Mauricio G. C. Resende,et al.  Biased random-key genetic algorithms for combinatorial optimization , 2011, J. Heuristics.

[10]  J. A. Hoogeveen,et al.  Scheduling a batching machine , 1998 .

[11]  T. C. Edwin Cheng,et al.  Batch scheduling of deteriorating reworkables , 2008, Eur. J. Oper. Res..

[12]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .