Convergence Behaviour of Population Size and Mutation Rate for NSGA-II in the Context of the Traveling Thief Problem

Abstract

The so-called optimization problems are encountered by mathematicians and computer scientists everywhere. The probably simplest optimization problem is finding a minimum or maximum of an analytic one-dimensional function, which is usually accomplished by finding the roots of the first derivative. It is, however, not unusual that no efficient algorithm is known for a particular optimization problem. It gets even harder, when you combine two such problems to a multi-component optimization problem. Such multi-component optimization problems are difficult to solve not only because of the contained hard optimization problems, but in particular, because of the interdependencies between the different components. Interdependence complicates a decision making by forcing each sub-problem to influence the quality and feasibility of solutions of the other sub-problems.

The subject of the investigation of this work is the multi-component optimization problem called “Traveling Thief Problem”, which combines two well-known optimization problems: The Knapsack Problem and the Traveling Salesman Problem. In particular, we want to examine how the mutation rate and population size affect the fitness achieved by the Non-dominated Sorting Genetic Algorithm II when applying it to the Traveling Thief Problem.