# A population-based approach to sequential ordering problems

Thesis (MScEng (Industrial Engineering))--University of Stellenbosch, 2007.

Thesis

This project was initiated to develop a new and novel approach to address complex sequencing problems, in particular, an alternative method was developed to find solutions to the sequential ordering problem. The sequential ordering problem is concerned with the arrangement of a number of elements in a sequence that respects a number of precedence constraints and results in the lowest overall cost. A precedence constraint requires that some element will occur before another in the solution sequence, and the cost of a solution is determined by summing the independent individual costs that are incurred when progressing from one specific element in the solution sequence to another. Instances of this problem are regularly found in the practice of industrial engineering in problems such as the routing of a delivery vehicle, the scheduling of jobs on a machine and the preparation of project plans with limited resources. The sequential ordering problem is known to be complex in the sense that as the size of problem instances increases, the best-known time required to find a guaranteed optimal solution increases exponentially.