Abstract
Open Shop Scheduling Problem (OSSP) is a combinatorial optimization problem for more than two machines and n jobs. Open Shop Scheduling Problem is another kind of scheduling problem along with flow shop and job shop scheduling problems. The open shop scheduling problem involves scheduling of jobs, where the sequence of the operations of each job can be arbitrarily chosen and need not be same. This means that the operations of the jobs can be performed in any sequence. In the absence of sequences for the jobs, for a given set of jobs, finding different parameters like maximum completion time Cmax becomes highly difficult and complex. One can use complete enumeration method or branch and bound method to solve this problem optimally for small and medium size problems. The large size problems of open shop problem with more than two machines and with n jobs can be solved by either a heuristic or meta-heuristics such as genetic algorithm, simulated annealing algorithm, etc. to obtain very near optimal solution. The performance of the genetic algorithm is affected by crossover operator performed between two parent chromosomes. Hence, this paper explores various crossover operators used, while using evolutionary based genetic algorithm to solve open shop scheduling problems. It further attempts to propose a new crossover operator using three chromosomes.
Highlights
IntroductionJob shop scheduling problem and open shop scheduling problem differed in the way of operations in each job need to be processed on “m” machines [1] [2]
Flow shop scheduling problem, job shop scheduling problem and open shop scheduling problem differed in the way of operations in each job need to be processed on “m” machines [1] [2]
Crossover operator is an important stage in the Genetic Algorithm (GA), which involves mating of the selected chromosomes to produce child chromosomes with better fitness which in turn becomes parent chromosomes in the generation
Summary
Job shop scheduling problem and open shop scheduling problem differed in the way of operations in each job need to be processed on “m” machines [1] [2]. Open shop scheduling problem involves scheduling of jobs, and each of the jobs does not have any sequence. The objective is to complete the processing of all the jobs in such a way that the total time taken to complete all the jobs is minimized This is called as makespan or maximum completion time (Cmax). Crossover operator is an important stage in the Genetic Algorithm (GA), which involves mating of the selected chromosomes to produce child chromosomes with better fitness which in turn becomes parent chromosomes in the generation.
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