Transfer Optimisation in Genetic Programming for Solving Uncertain Capacitated Arc Routing Problem
Authors:   , Ansari Ardeh Mazhar 
Published: July 2022

<p><b>Uncertain Capacitated Arc Routing Problem (UCARP) is a combinatorial optimisation problem with many important real-world applications. Genetic programming (GP) is a powerful machine learning technique that has been successfully used to automatically evolve routing policies for UCARP. Reusability is an open issue in the field of UCARP and in this direction, an open challenge is the case of scenario changes, e.g. change in the number of vehicles and probability distributions of random demands, which typically requires new training procedures to be initiated. Considering the expensive training cost of evolving routing policies for UCARP, a promising strategy is to learn and reuse knowledge from a previous problem-solving process to improve the effectiveness and efficiency of solving a new related problem, i.e. transfer learning. </b></p>
<p>The overall goal of this thesis is to develop novel knowledge transfer algorithms for GP for solving UCARP to handle environment changes more effectively and efficiently. To fulfil this goal, a plethora of machine learning techniques, i.e. surrogate models, feature selection, searching and specialised genetic operators, are utilised in this thesis. </p>
<p>	First, this thesis explores the effectiveness of the existing transfer optimisation methods for solving UCARP. Accordingly, one of the main directions of this thesis is towards identifying the nature of transferable knowledge, which can impact the quality of knowledge transfer for GP to solve UCARP. For this purpose, a collection of the state-of-the-art transfer optimisation GP algorithms are evaluated for UCARP. After identifying some potential gaps in the literature, a number of preliminary transfer optimisation algorithms are proposed that supplement the literature. To evaluate the algorithms, a large set of knowledge transfer scenarios with various source and target problems were designed based on real-world datasets. According to the results, none of the methods showed significant improvement in the effectiveness of the trained UCARP routing policies. These results revealed the need for more effective transfer optimisation methods specifically designed for UCARP. Furthermore, our investigations revealed that the presence of duplicates in knowledge sources is one of the main challenges for effective transfer optimisation in solving UCARP.</p>
<p>	Second, we propose approaches to handling the presence of duplicates in the transferred knowledge. The first approach increases population diversity after knowledge transfer to counteract the loss of diversity that is introduced by the presence of duplicates in the transferred knowledge. In the second approach, the duplicates are removed from the transferred knowledge. Then, the transferred knowledge is utilised to create a diverse initial GP population of high-quality individuals. Both approaches are investigated through detailed experimental studies. The results indicate that, while the first approach did not perform better than GP with knowledge transfer, the second can improve the effectiveness of training routing policies with GP significantly. </p>
<p>	Third, this thesis proposes a novel algorithm that transfers the phenotypic characteristics of the routing policies for solving the source problem. In the new algorithm, the most fit and unique source routing policies are utilised for initialising GP for solving the target problem. Then, a tabu list is placed on the source routing policies and the GP process is prohibited from recreating any of the source routing policies. The motivation for this approach is that, due to the existence of similarity between the source and target problems, source routing policies are unlikely to have a good performance for the target problem. Our experimental studies confirmed that by prohibiting GP from recreating source policies, and the computational resources will be spent on searching and evaluating new regions of the search space, which can lead to discovering better solutions. </p>
<p>	Fourth, this thesis proposes a novel knowledge transfer algorithm based on the idea of maintaining the transferred knowledge as an auxiliary population. In this approach, first, the best individuals of the duplicate-free knowledge source are used to initialise GP. Additionally, these transferred individuals are also maintained as an auxiliary population and are evolved alongside the main population. To save the computational cost, the auxiliary population is evolved with a surrogate method. Additionally, an elaborate knowledge exchange mechanism between the two populations is devised that emphasises transferring high-quality and unique individuals, the transfer of which can improve the diversity of the receiving population. This allows GP to overcome the problem of losing its population diversity during the evolutionary process. Our detailed experimental results confirmed the superior performance of the proposed algorithm and confirmed that the proposed method improved the phenotypic diversity of GP population.</p>