Abstract

No-wait job-shop scheduling (NWJSS) problem is one of the classical scheduling problems that exist on many kinds of industry with no-wait constraint, such as metal working, plastic, chemical, and food industries. Several methods have been proposed to solve this problem, both exact (i.e. integer programming) and metaheuristic methods. Cross entropy (CE), as a new metaheuristic, can be an alternative method to solve NWJSS problem. This method has been used in combinatorial optimization, as well as multi-external optimization and rare-event simulation. On these problems, CE implementation results an optimal value with less computational time in average. However, using original CE to solve large scale NWJSS requires high computational time. Considering this shortcoming, this paper proposed a hybrid of cross entropy with genetic algorithm (GA), called CEGA, on m-machines NWJSS. The results are compared with other metaheuritics: Genetic Algorithm-Simulated Annealing (GASA) and hybrid tabu search. The results showed that CEGA providing better or at least equal makespans in comparison with the other two methods.

Highlights

  • No-wait job-shop scheduling problem (NWJJS) is a problem categorized to non-polynomial hard (NP-Hard) problem, especially for m-machines [1]

  • Using original Cross entropy (CE) to solve large scale No-wait job-shop scheduling (NWJSS) requires high computational time. Considering this shortcoming, this paper proposed a hybrid of cross entropy with genetic algorithm (GA), called CEGA, on m-machines NWJSS

  • This paper proposed a new algorithm of hybridized cross entropy with genetic algorithm (CEGA)

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Summary

Introduction

No-wait job-shop scheduling problem (NWJJS) is a problem categorized to non-polynomial hard (NP-Hard) problem, especially for m-machines [1]. Because the continuity of operation in each job must be kept to avoid operation reworking or job redoing, the use of incorrect method for scheduling purpose may make the makespan significantly longer. Genetic Algorithm-Simulated Annealing (GASA) [2] and Hybrid Tabu Search [3] are examples of methods used to solve this problem. As a relatively new metaheuristic, has been widely used in broad applications, such as combinatorial optimization, continuous optimization, noisy optimization, and rare event simulation [4]. On these problems, cross entropy can find optimal or near optimal solution with less computational time. The proposed method is new in solving NWJSS problem. Using the hybrid of CE and GA the computational time can be reduced significantly while maintaining better makespan

Problem Overview
Problem Formulation
Basic Idea of Cross Entropy
I i 1 S Zl ˆt N
Cross Entropy for Combinatorial Optimization
Example
Proposed Algorithm
Experiments
Conclusions

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