AIS-SFHM APPROACH FOR OPTIMIZATION OF MULTI OBJECTIVE JOB SHOP PROBLEMS

The n-job, m-machine Job shop scheduling (JSP) problem is one of the general production scheduling problems. The JSP problem is a scheduling problem, where a set of ‘n’ jobs must be processed or assembled on a set of ‘m’ dedicated machines. Each job consists of a specific set of operations, which have to be processed according to a given technical precedence order. Job shop scheduling problem is a NP-hard combinatorial optimization problem. In this paper, optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered. The hybrid approach of Sheep Flocks Heredity Model Algorithm (SFHM) is used for finding optimal makespan, mean flow time, mean tardiness. The hybrid SFHM approach is tested with multi objective job shop scheduling problems. Initial sequences are generated with Artificial Immune System (AIS) algorithm and results are refined using SFHM algorithm. The results show that the hybrid SFHM algorithm is an efficient and effective algorithm that gives better results than SFHM Algorithm, Genetic Algorithm (GA). The proposed hybrid SFHM algorithm is a good problem-solving technique for job shop scheduling problem with multi criteria.


INTRODUCTION
The classical job-shop scheduling problem (JSP) is one of most difficult combinatorial optimization problems. During the last decades a great deal of attention has been paid to solving these problems with many kind of algorithms by considering single objective. But real world scheduling problems naturally involve multiple objectives. There are only few attempts available to tackle the multi-objective JSP.
In a multi-objective context, find as much different schedules as possible, which are non-dominated with regard to two or more objectives. Some frequently used performance measures are makespan, mean flow-time and mean tardiness. Makespan is defined as the maximum completion time of all jobs. Mean flow-time is the average of the flow-times of all jobs. Mean tardiness is defined as the average of tardiness of all jobs. Bruker [1] show that the Job shop Scheduling (JSP) is an NP-hard [2] combinatorial problem. Because of the NPhard characteristics of job shop scheduling, it is usually very hard to find its optimal solution, and an optimal solution in the mathematical sense is not always necessary in practices [3]. Researchers turned to search its near-optimal solutions with all kind of heuristic algorithms [4]. Fortunately, the searched near optimal solutions usually meet requirements of practical problems very well.

LITERATURE REVIEW
In a single-objective context some of the recent approaches have shown quite promising results [5][6]. But real world scheduling problems naturally involve multiple objectives. There are only few attempts to tackle the multi-objective JSP [7].
Additionally, researches on job shop scheduling problems have been concentrated primarily on the optimisation of individual measures of system performance. While a single objective may be justified in certain situations, many scheduling problems are more naturally formulated with multiple, often competing, objectives to obtain a trade-off schedule. Examples of multi-criteria scheduling approaches include those in Daniels [8], Lee and Jung [9], and Murata, Ishibuchi, and Tanaka [10].
The remainder of the paper is organized as follows. Section 3 describes the Problem statement. Section 4 introduces the new hybrid algorithm for JSP problem. Section 5 shows Results and discussion. Finally, section 6 presents the conclusion of this work.

PROBLEM STAREMENT
In a multi-objective context, find as much different schedules as possible, which are non-dominated with regard to two or more objectives. Performance measures are makespan, mean flow-time and mean tardiness. Makespan is defined as the

Representation of solution seed
Consider the three-job three-machine problem Processing time Machine sequence Suppose a seed is given as [3 2 1], where 1 stands for job j1, 2 for job j2, and 3 for job j3. This sequence has to be operated 3 times in the same order because each job has three operations. So that we can consider the initial seed as the following format [ 3 2 1 3 2 1 3 2 1]. There are three 2s in the seed, which stands for the three operations of job j2. The first 2 corresponds to the first operation of job j2 which will be processed on machine 1, the second 2 corresponds to the second operation of job j2 which will be processed on machine 3, and the third 2 corresponds to the third operation of job j2 which will be processed on machine 2. We can see that all operations for job j2 are given the same symbol 2 and then interpreted according to their orders of occurrence in the sequence of this seed. The corresponding relationships of the operations of jobs and processing machines are shown in Figure 1.

Figure.1. Feasible schedule
This concept is used to find the makespan for the sequences of the problems where the generated seed (job sequence) is operated equal to the number of machines represented in the particular problem.

Proposed hybrid Algorithm for Multi Objective JSP Problem
Generate a population of P antibodies (job sequences)

Stage 1(AIS Algorithm)
For each iteration Select the sequence in the antibody population; Find out the affinity of each antibody; Cloning process (generate copies of the antibodies) Steps in Mutation process (for each clone)

RESULTS AND DISCUSSION
The Hybrid algorithm is implemented in C language on personal computer Pentium IV 2.4 GHz. The maximum number of iterations has been set to 100 X n, where n is the number of jobs.
Multi-objective optimization differs from single-objective optimization in many ways [11]. For two or more conflicting objectives, each objective corresponds to a different optimal solution, but none of these trade-off solutions is optimal with respect to all objectives. Thus, multi-objective optimization does not try to find one optimal solution but all trade-off solutions.
For multi-objective scheduling the proposed artificial immune algorithm is used to optimize makespan, mean flow time and mean tardiness of the two JSP given by Bagchi [7] are the basis of the following experiments. The first problem, called JSP1, is a ten job five machine instance. The second problem, called JSP2, is a ten job ten machine instance. Apparently, the hybrid algorithm minimizes all objectives simultaneously. This algorithm is compared with the similar previous work using GA [12] and SFHM algorithm [13] and shown in Table 1 and Table 2. Graph 2-9 shows that the comparison of makespan, mean flow time, mean tardiness and coefficient of function results of JSP1 and JSP2 problems.

CONCLUSION
In this paper, hybrid approach has been used for solving multi objective job shop scheduling problems with the objective of minimization of makespan, mean flow time and mean tardiness. The algorithm uses simple but effective techniques for calculating cloning process, applying mutations, a receptor editing procedure and multi stage genetic operation. This algorithm has been tested on JSP 1 and JSP 2 problem instances given in Bagchi [7]. The findings were compared with Genetic Algorithm [12] and SFHM algorithm [13] that tested the same problems. Hybrid algorithm gives better results than the genetic algorithm and SFHM algorithm. The proposed hybrid algorithm is competent and proves to be a good problemsolving technique for job shop scheduling.