ORIGINAL ARTICLE A simple yet effective grouping evolutionary strategy (GES) algorithm for scheduling parallel machines Ali Husseinzadeh Kashan 1 • Marziehsadat Keshmiry 2 • Jalil Heidary Dahooie 3 • Amin Abbasi-Pooya 1 Received: 12 August 2015 / Accepted: 17 December 2016 Ó The Natural Computing Applications Forum 2016 Abstract As a novel evolutionary technique, grouping evolutionary strategy (GES) has proved efficient and effective on grouping problems in which the task is to partition a set of items into disjoint groups. This paper investigates the first application of GES to tackle the par- allel-machines scheduling problem as a well-known grouping problem in which machines can be treated as groups and jobs can be regarded as the items and the task is to partition a set of jobs into disjoint groups (and process all jobs in a same group by the same machines) to mini- mize makespan (C max ) criterion. The main features of GES algorithm that make it different from the typical evolu- tionary approaches proposed for the parallel-machines scheduling problem, lie in exploiting a suitable chromoso- mal representation and a well-designed mutation operator that works with the set of jobs assigned to each machine instead of jobs isolatedly, and uses a two-phase procedure to generate the new schedules more effectively. In addition, we hybridized GES with an efficient local search heuristic and proved that it has an important descent property. To verify the performance of our proposed algorithm, com- parisons are made using available methodologies in the literature. Computational results signify that the proposed approach is fast and competitive in providing high quality results. Keywords Scheduling  Parallel-machines  Makespan  Grouping evolutionary strategy 1 Introduction Identical parallel-machines scheduling problem is formally described as follows: a set of n independent jobs, J ¼fJ 1 ; J 2 ; ...; J n g, each having an associated processing time p i , i = 1,…,n, are to be processed on a set M ¼ fM 1 ; M 2 ; ...; M m g of m machines. Each job should be processed on one of the machines, and preemption is not allowed during processing. The subset of jobs assigned to machine M j in a schedule is denoted by S M j . Furthermore, each machine can only process one job at a time, and there is no precedence relation between jobs. The paper inves- tigates the problem of optimal assignment of jobs to machines in order to minimize the completion time of the last job, i.e., the makespan criterion (C max ). Due to the fact that this problem is NP-hard [13], it is unlikely to obtain the optimal schedule through polynomial time-bounded algorithms. Over the years extensive research has been carried out to develop efficient approaches for the problem. As a member of a family of algorithms known as list- scheduling algorithms, the well-known longest processing time (LPT) rule of Graham [15] has received considerable attention because it tends to perform better in terms of performance guarantee. According to LPT rule, we start with an empty schedule and iteratively assign a non- scheduled job with the longest processing time of all remaining jobs to the machine with currently minimal workload. This method generates a schedule that is no worse than C max ðLPT Þ C  max  4 3  1 3m , where C max (LPT) denotes the makespan obtained based on the LPT rule. Coffman & Ali Husseinzadeh Kashan A.kashan@modares.ac.ir 1 Department of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran 2 Department of Industrial Engineering, Kowsar University, Bojnourd, Iran 3 Faculty of Management, University of Tehran, Tehran, Iran 123 Neural Comput & Applic DOI 10.1007/s00521-016-2789-3