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

  • Chunfeng Ma
  • Min Kong
  • Jun PeiEmail author
  • Panos M. Pardalos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10710)


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.


Parallel-batching Step-deteriorating Release times Makespan 



This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71601065, 71690235, 71501058, 71690230, 71601060), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167). Panos M. Pardalos is partially supported by the project of Distinguished International Professor by the Chinese Ministry of Education (MS2014HFGY026).


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Chunfeng Ma
    • 1
  • Min Kong
    • 1
  • Jun Pei
    • 1
    • 2
    Email author
  • Panos M. Pardalos
    • 2
  1. 1.School of ManagementHefei University of TechnologyHefeiChina
  2. 2.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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