Maximum-entropy principle approach to the multiple travelling salesman problem and related problems

Abstract

This thesis presents an investigation into the applications of the maximum-entropy principle as a heuristic for the multiple travelling salesman problem. This is a computationally complex problem which requires special treatment by conventional optimization techniques. Specific focus is given to developing a generalized framework for this problem that can be applied to any number of variants on the basic formulation. Additional consideration is given to the applications of this generalized framework to other variants on the travelling salesman problems such as the close enough travelling salesman problem. The heuristic framework developed here is shown to provide flexibility in addressing the multiple salesman variation on the travelling salesman problem as well as a several other variants on the travelling salesman problem. Additionally, this framework is shown to be effective in determining solutions to this class of problems, and it is especially effective for the close-enough travelling salesman problems which is particularly challenging for most conventional combinatorial algorithms. Concrete steps are presented by which to further extend and improve this framework to become both more widely applicable to variants on the travelling salesman problem, and more computationally efficient in solving such problems.