A hybridization of PSO and VNS to solve the machinery allocation and scheduling problem under a machinery sharing arrangement

Abstract

This paper presents the hybrid Particle Swarm Optimization and the Variable Neighborhood Search (PSO-VNS) to solve the machinery and equipment allocation and scheduling to help the growers expand the production level to meet the increased demands and growing interest, and to increase profitability. This problem can be formulated as the Machinery and Equipment Allocation and Scheduling Problem (MEASP) which is special type of a hybrid flow shop scheduling problem (HFS) with sequence dependent setup times, machine eligibility, machine grouping, blocking, tooling constraint, and time windows (HFS |SDST, rcrc, Grouping, blocking, Tool, Tw | Cmax). The objective of this research is to minimize the total completion time for sugarcane cultivation. A Mixed Integer Linear Programming (MILP) model was developed to handle small-scale problems. The hybrid Particle Swarm Optimization and the Variable Neighborhood Search (PSO-VNS) was used for large-scale problems. Two new velocity update formulae and a position update formula were incorporated into the Particle Swarm Optimization (PSO), and four types of neighborhood strategies were developed for the VNS. The experimental results show that all the PSO-VNS methods outperform the traditional PSO due to the effectiveness of the newly proposed velocity and position update formulae in finding the optimal solutions, the PSO-VNS-6 methods, on the average, can reduce the computational time by 58.43% from the original PSO and improve the solution quality by 11.71%.