Energy-Conscious Scheduling Problem in a Flexible Job Shop Using a Discrete Water Wave Optimization Algorithm

Yi Lu,Jiacheng Lu,Tianhua Jiang

doi:10.1109/access.2019.2930281

Abstract

As more and more attention is paid to green manufacturing, production scheduling has been proved to be an efficient method for the reduction of environmental pollution. It is well-known that the flexible job shop scheduling problem (FJSP) is a very complex combinatorial optimization problem with strong theoretical and background for application. However, the problem has been extensively investigated and historically concerned with some indicators related to time, e.g., flow time, makespan, and workload. In this study, an energy-conscious FJSP is investigated with the consideration of the energy consumption. First, a mathematical model of the energy-conscious FJSP is built with the objective of optimizing the sum of the energy consumption cost and the completion-time cost. Due to the fact that the basic water wave optimization (WWO) was developed for various continuous problems, a discrete water wave optimization (DWWO) algorithm is proposed to solve the model. In our DWWO algorithm, a three-string encoding approach is first adopted to represent each individual wave. To make the algorithm adapt for the considered scheduling problem, three discrete evolutionary operations are redesigned according to the characteristics of the problem, i.e., propagation, refraction, and breaking. Finally, extensive experimental simulations are conducted to test the proposed DWWO algorithm. The comparison results demonstrate that the proposed DWWO algorithm is efficient for the energy-conscious FJSP.

Highlights

Flexible job shop scheduling problem (FJSP) is an extended version of the job shop scheduling problem (JSP), which presents a closer approximation to the real-life production than the JSP
Lu et al [21] established a mathematical model of a permutation flow shop scheduling problem and presented a hybrid backtracking search algorithm to optimize the makespan and the energy consumption
If Oij is processed on machine k at speed vd, the actual processing time pijkd equals to qijk /vd, and the energy consumption cost per unit time is measured by Ekd

Summary

INTRODUCTION

TO THE BASIC WATER WAVE OPTIMIZATION Water wave optimization (WWO) algorithm is inspired from shallow wave models and proposed by Zheng [43] for solving various continuous optimization problems. Three operations (propagation, refraction and breaking) are involved in the algorithm and performed to waves. The breaking operation in Equation (12) will be performed to each selected dimension to generate kk new waves. ENCODING AND DECODING APPROACH As stated above, WWO was originally proposed for solving continuous optimization problems. The first string defines the machine assignment, the second shows the speed level selection, and the third is the operation permutation. Each element is the selected speed level for processing each operation. In order to obtain a feasible scheduling scheme, the decoding procedure can be described as follows: Step 1: Scan the operation permutation in the first string from left to right, read the machine information in the first string, and find the speed level of the assigned machine in the second string.

MATHEMATICAL MODEL OF THE ENERGYCONSCIOUS FJSP

PROPAGATION OPERATOR

COMPUTATIONAL EXPERIMENTS

CONCLUSION