Solving Job Shop Scheduling Problem Using Cellular Learning Automata Masoud Abdolzadeh Computer Engineering Department Islamic Azad University Qazvin, IRAN Ms.abdolzadeh@gmail.com Hassan Rashidi Computer Engineering Department Islamic Azad University Qazvin, IRAN hrashi@gmail.com Abstract— Cellular Learning Automata (CLA) is one of the newest optimization methods for solving NP-hard problems. The Job Shop Scheduling Problem (JSSP) is one of these problems. This paper, proposes a new approach for solving the JSSP using CLA with two kinds of actions' set. By generating actions based on received responses from the problem environment, appropriate position for operations of jobs is chosen in execution sequence. The goal in the problem is to minimize maximum completion time of jobs, known as makespan. We present our approach in an algorithmic form after problem definition and a brief description of cellular learning automata. The algorithm is tested on several instances of verity of benchmarks and the experimental results show that it generates nearly optimal solutions, compared with other approaches. Keywords; Job Shop, Scheduling, Makespan, Cellular Learning Automata. I. INTRODUCTION Scheduling in various systems is one of the major challenges to reach high performance. In order to simplify algorithm presentation and real world problems analyzing, scheduling problems classified into different groups. Each real world problem assigned to one of these groups and solved with appropriate solutions. One of these problems is called Job Shop Scheduling Problem. This problem includes resource assigning to set of operations in their given time [1]. JSSP is one of the famous NP-hard scheduling Problems. Only small groups of them can be solved by searching all problem space [2]. A typical problem of JSSP with m machines and n Jobs has (n!) m states in its search space. Thus for problem with 10 jobs and 10 machines there are 7.2651 * 10 183 possible states [3]. There are many approaches for solving JSSP. The main advanced approaches in four recent decades are neural networks [4], genetic algorithms, ant colony, simulated annealing and Tabu search, etc [5-15]. These approaches are classified into several classes. One of these classes presents some solutions for JSSP near to optimal with complexity of polynomial order such as enumerative methods and Lagrangian Relaxation. Another class of these approaches is based on optimization such as local search, genetic, constraint satisfaction, Tabu search and simulated annealing algorithms, etc. These algorithms use problem search space and try to optimize the first or the current solutions and repeat optimization to get terminate criterion. At the end of fourth decade of the 20th century, Cellular Automata was proposed as a model to analyze treatments of complex systems. Learning Automata presented at the beginning of 1960s which treats based on learning algorithm. This model learns how to choose its best action from a set of actions. The Cellular Learning Automaton proposed was based on a combination of cellular and learning automata. In this model each cell equips with a learning automaton that determines cell's state. This paper optimizes JSSP using features of CLA and makes possible learning the position of jobs in job sequence. The rest of this paper is organized as follows. In section II, a detailed description of JSSP is given. Section III summarizes cellular learning automata. In section IV, our proposed algorithm is described. Section V is considered for experimental results and comparison with other algorithms. Section VI is the conclusion. II. JOB SHOP SCHEDULING PROBLEM This section defines JSSP and describes problem and solution representation methods. A. Problem Definition A JSSP can be defined by (n) jobs and (m) machines. Each job consists of several operations. Each operation should be processed by specified machine. Processing time for each operation is fixed and predefined. In other words, there is a sequel of machines proportionate to each job that must be processed. We suppose all jobs are ready at the beginning time. Initialization time of operations set to zero or as a part of processing time. There is no precedence between jobs. Each machine can process just one operation of a job and each job can be processed by one machine at a time. There is no permission to interrupt for operation processing. We can define Construction of JSSP as follows:  A set of N independent Jobs. {J j } 1≤j≤N  Each J j has a sequence of operations. (G j )  Each G j is ordered series of operations and O i,j determines the position of an operation in the job sequence. There is precedence between the 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.68 49 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.68 49 2009 Third UKSim European Symposium on Computer Modeling and Simulation 978-0-7695-3886-0/09 $26.00 © 2009 IEEE DOI 10.1109/EMS.2009.68 49