A regression analysis of the impact of routing and packing dependencies on the expected runtime

Problems with multiple interdependent components offer a better representation of the real-world situations where globally optimal solutions are preferred over optimal solutions for the individual components. One such model is the Travelling Thief Problem (TTP); while it may offer a better benchmarking alternative to the standard models, only one form of inter-component dependency is investigated. The goal of this paper is to study the impact of different models of dependency on the fitness landscape using performance prediction models (regression analysis). To conduct the analysis, we consider a generalised model of the TTP, where the dependencies between the two components of the problem are tunable through problem features. We use regression trees to predict the instance difficulty using an efficient memetic algorithm that is agnostic to the domain knowledge to avoid any bias. We report all the decision trees resulting from the regression model, which is the core in understanding the relationship between the dependencies (represented by the features) and problem difficulty (represented by the runtime). The regression model was able to predict the expected runtime of the algorithm based on the problem features. Furthermore, the results show that the contribution of the item value drop dependency is significantly higher than the velocity change dependency.