Dynamic Multi-objective Optimization of the Travelling Thief Problem

Abstract

Investigation of detailed and complex optimisation problem formulations that reflect realistic scenarios is a burgeoning field of research. A growing body of work exists for the Travelling Thief Problem, including multi-objective formulations and comparisons of exact and approximate methods to solve it. However, as many realistic scenarios are non-static in time, dynamic formulations have yet to be considered for the TTP. Definition of dynamics within three areas of the TTP problem are addressed; in the city locations, availability map and item values. Based on the elucidation of solution conservation between initial sets and obtained non-dominated sets, we define a range of initialisation mechanisms using solutions generated via solvers, greedily and randomly. These are then deployed to seed the population after a change and the performance in terms of hypervolume and spread is presented for comparison. Across a range of problems with varying TSP-component and KP-component sizes, we observe interesting trends in line with existing conclusions; there is little benefit to using randomisation as a strategy for initialisation of solution populations when the optimal TSP and KP component solutions can be exploited. Whilst these separate optima don't guarantee good TTP solutions, when combined, provide better initial performance and therefore in some examined instances, provides the best response to dynamic changes. A combined approach that mixes solution generation methods to provide a composite population in response to dynamic changes provides improved performance in some instances for the different dynamic TTP formulations. Potential for further development of a more cooperative combined method are realised to more cohesively exploit known information about the problems.