Citation: Yang, W.; Yang, Z.; Chen, Y.;
Peng, Z. Modified Whale
Optimization Algorithm for
Multi-Type Combine Harvesters
Scheduling. Machines 2022, 10, 64.
https://doi.org/10.3390/
machines10010064
Academic Editor: Dario Richiedei
Received: 12 December 2021
Accepted: 13 January 2022
Published: 17 January 2022
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Article
Modified Whale Optimization Algorithm for Multi-Type Combine
Harvesters Scheduling
Wenqiang Yang
1,2
, Zhile Yang
3,
*, Yonggang Chen
1,2
and Zhanlei Peng
1,2
1
Postdoctoral Station, Henan University of Science and Technology, Luoyang 471000, China;
yangwqjsj@hist.edu.cn (W.Y.); happycygzmd@hist.edu.cn (Y.C.); zl.peng@stu.hist.edu.cn (Z.P.)
2
Postdoctoral Research Base, Henan Institute of Science and Technology, Xinxiang 453003, China
3
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
* Correspondence: zl.yang@siat.ac.cn
Abstract:
The optimal scheduling of multi-type combine harvesters is a crucial topic in improving
the operating efficiency of combine harvesters. Due to the NP-hard property of this problem,
developing appropriate optimization approaches is an intractable task. The multi-type combine
harvesters scheduling problem considered in this paper deals with the question of how a given
set of harvesting tasks should be assigned to each combine harvester, such that the total cost is
comprehensively minimized. In this paper, a novel multi-type combine harvesters scheduling
problem is first formulated as a constrained optimization problem. Then, a whale optimization
algorithm (WOA) including an opposition-based learning search operator, adaptive convergence
factor and heuristic mutation, namely, MWOA, is proposed and evaluated based on benchmark
functions and comprehensive computational studies. Finally, the proposed intelligent approach
is used to solve the multi-type combine harvesters scheduling problem. The experimental results
prove the superiority of the MWOA in terms of solution quality and convergence speed both in the
benchmark test and for solving the complex multi-type combine harvester scheduling problem.
Keywords:
multi-type combine harvesters scheduling; whale optimization algorithm;
opposition-based learning; adaptive convergence factor; heuristic mutation
1. Introduction
As a modern agricultural machine, the combine harvester achieves harvesting at
a high speed, playing a significant role in the harvest season [
1
]. Combine harvesters
scheduling, which aims to obtain a reasonable scheduling scheme with the least cost while
satisfying various constraints, has attracted research interest across the world. For wheat
farms with high yield, harvesters with low capacity may not be suitable. Nik et al. adopted
multi-criteria decision-making to optimizing the feed rate in order to match harvesters
with farms [
2
]. In order to improve the harvesting efficiency, Zhang et al. proposed a path-
planning optimization scheme based on tabu search and proportion integral differential
(PID) control, which effectively shortens the harvesting path [
3
]. In order to obtain a corner
position from the global positioning system, a conventional AB point method is generally
adopted, but this is fairly time-consuming. In the light of this, Rahman et al. presented an
optimum harvesting area of a convex and concave polygon for the path planning of a robot
combine harvester, which reduces crop losses [
4
]. Due to changes in the location of fruit in
the picking process, locating fruits and path planning, which have to be performed on-line,
are computationally expensive operations, and hence Willigenburg et al. presented a new
method for near-minimum-time collision-free path planning for a fruit-picking robot [
5
].
Saito et al. developed a robot combine harvester for beans, and this robot can unload
harvested grain to an adjacent transport truck during the harvesting operation, improv-
ing the harvesting capacity by approximately 10% [
6
]. The minimization of harvesting
distance and the maximization of sugarcane yield, which are conflicting, are treated as
Machines 2022, 10, 64. https://doi.org/10.3390/machines10010064 https://www.mdpi.com/journal/machines
