A Pareto-Based Adaptive Variable Neighborhood Search for Biobjective Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup Time

Huixin Tian,Wei Liu,Kun Li

doi:10.1155/2016/1257060

Abstract

Different from most researches focused on the single objective hybrid flowshop scheduling (HFS) problem, this paper investigates a biobjective HFS problem with sequence dependent setup time. The two objectives are the minimization of total weighted tardiness and the total setup time. To efficiently solve this problem, a Pareto-based adaptive biobjective variable neighborhood search (PABOVNS) is developed. In the proposed PABOVNS, a solution is denoted as a sequence of all jobs and a decoding procedure is presented to obtain the corresponding complete schedule. In addition, the proposed PABOVNS has three major features that can guarantee a good balance of exploration and exploitation. First, an adaptive selection strategy of neighborhoods is proposed to automatically select the most promising neighborhood instead of the sequential selection strategy of canonical VNS. Second, a two phase multiobjective local search based on neighborhood search and path relinking is designed for each selected neighborhood. Third, an external archive with diversity maintenance is adopted to store the nondominated solutions and at the same time provide initial solutions for the local search. Computational results based on randomly generated instances show that the PABOVNS is efficient and even superior to some other powerful multiobjective algorithms in the literature.

Highlights

In a typical hybrid flow shop scheduling (HFS) problem (Figure 1), a set of n jobs need to be processed through M production stages and at each stage k there are mk identical parallel machines
Different from most researches focused on the single objective hybrid flowshop scheduling (HFS) problem, this paper investigates a biobjective HFS problem with sequence dependent setup time
The HFS problem has been one of the important research issues in the production scheduling since proposed because many practical production scheduling problems can be modeled as a HFS problem [2, 3]

Summary

Introduction

In a typical hybrid flow shop scheduling (HFS) problem (Figure 1), a set of n jobs need to be processed through M production stages and at each stage k there are mk identical parallel machines. The task of the HFS problem is to establish a production schedule so that some performance can be optimized (e.g., minimization of makespan, total weighted completion time, and tardiness of jobs [1]). Different from the single objective HFS problem in the literature, in practical production decision makers usually need to consider multiple objectives during scheduling, for example, (1) minimization of the total sequence-dependent setup times between consecutive jobs and (2) minimization of the total tardiness of all jobs. In this paper we consider the biobjective HFS and develop a Pareto-based adaptive biobjective variable neighborhood search (PABOVNS) algorithm to solve it.

Literature Review

Problem Statement

Pareto-Based Biobjective Variable Neighborhood Search

Adaptive Selection Strategy

Computational Experiments

Conclusions