MERGING OPTIMALITY CONDITIONS WITH GENETIC ALGORITHM OPERATORS TO SOLVE SINGLE MACHINE TOTAL WEIGHTED TARDINESS PROBLEM

1.Introduction Production sequencing and scheduling is one of the most important activities in production planning and control.Sequencing is defined as the order in which the jobs are processed through the machines.The allocation of machines over time to process a collection of jobs is defined as Scheduling.Several methods have been developed to solve the scheduling problem which can be classified as follows:1)efficient optimal methods,2)implicit and explicit,or complete enumerative methods,a…

Merging optimality conditions with genetic algorithm operators to solve single machine total weighted tardiness problem

In this paper, a constrained genetic algorithm (CGA) is proposed to solve the single machine total weighted tardiness problem. The proposed CGA incorporates dominance rules for the problem under consideration into the GA operators. This incorporation should enable the proposed CGA to obtain close to optimal solutions with much less deviation and much less computational effort than the conventional GA (UGA). Several experiments were performed to compare the quality of solutions obtained by the three versions of both the CGA and the UGA with the results obtained by a dynamic programming approach. The computational results showed that the CGA was better than the UGA in both quality of solutions obtained and the CPU time needed to obtain the close to optimal solutions. The three versions of the CGA reduced the percentage deviation by 15.6%, 61.95%, and 25% respectively and obtained close to optimal solutions with 59% lower CPU time than what the three versions of the UGA demanded. The CGA performed better than the UGA in terms of quality of solutions and computational effort when the population size and the number of generations are smaller.