Applying designed experiments to optimize the performance of genetic algorithms used for scheduling complex products in the capital goods industry

Conventional optimization approaches, such as Linear Programming, Dynamic Programming and Branch-and-Bound methods are well established for solving relatively simple scheduling problems. Algorithms such as Simulated Annealing, Taboo Search and Genetic Algorithms (GA) have recently been applied to large combinatorial problems. Owing to the complex nature of these problems it is often impossible to search the whole problem space and an optimal solution cannot, therefore, be guaranteed. A Bi-Criteria Genetic Algorithm (BCGA) has been developed for the scheduling of complex products with multiple resource constraints and deep product structure. This GA identifies and corrects infeasible schedules and takes account of the early supply of components and assemblies, late delivery of final products and capacity utilization. The research has used manufacturing data obtained from a capital goods company. Genetic Algorithms include a number of parameters, including the probabilities of crossover and mutation, the population size and the number of generations. The BCGA scheduling tool provides 16 alternative crossover operations and eight different mutation mechanisms. The overall objective of this study was to develop an efficient design-of-experiments approach to identify genetic algorithm operators and parameters that produce solutions with minimum total cost. The case studies were based upon a complex, computationally intensive scheduling problem that was insoluble using conventional approaches. This paper describes an efficient sequential experimental strategy that enabled this work to be performed within a reasonable time. The first stage was a screening experiment, which had a fractional factorial embedded within a half Latin-square design. The second stage was a half-fraction design with a reduced number of GA operators. The results are compared with previous studies. It is demonstrated that, in this case, improved GA performance was achieved using the experimental strategy proposed. The appropriate genetic operators and parameters may be case specific, leading to the view that experimental design may be the best way to proceed when finding the ‘best’ combination of GA operators and parameters.