Augmented tour construction heuristics for the travelling salesman problem

Tour construction heuristics serve as fundamental techniques in optimizing the routes of a traveling salesman. These heuristics remain significant as foundational methods for generating initial solutions to the Traveling Salesman Problem (TSP), facilitating subsequent applications of tour improvement heuristics. These heuristics effectively comprise the iterative application of city node selection and insertion. However, thus far, no attempts have been made to enhance the basic structure of tour construction heuristics to bring a better initial solution for the advanced heuristics. This study aims to enhance tour construction heuristics without compromising their theoretical complexity. Specifically, an iterative step of partial tour deconstruction has been introduced to the existing heuristics. This additional step has been implemented and evaluated with three highly performing tour construction heuristics: the farthest insertion heuristic, the max difference insertion heuristic, and the fast max difference insertion heuristic. The results demonstrate that augmenting these heuristics with the partial tour deconstruction step improves the best, worst, and average solutions while preserving their theoretical complexit

Introducing Complexity Curtailing Techniques for the Tour Construction Heuristics for the Travelling Salesperson Problem

In this paper, complexity curtailing techniques are introduced to create faster version of insertion heuristics, that is, cheapest insertion heuristic (CIH) and largest insertion heuristic (LIH), effectively reducing their complexities from O(n3) to O(n2) with no significant effect on quality of solution. This paper also examines relatively not very known heuristic concept of max difference and shows that it can be culminated into a full-fledged max difference insertion heuristic (MDIH) by defining its missing steps. Further to this the paper extends the complexity curtailing techniques to MDIH to create its faster version. The resultant heuristic, that is, fast max difference insertion heuristic (FMDIH), outperforms the “farthest insertion” heuristic (FIH) across a wide spectrum of popular datasets with statistical significance, even though both the heuristics have the same worst case complexity of O(n2). It should be noted that FIH is considered best among lowest order complexity heuristics. The complexity curtailing techniques presented here open up the new area of research for their possible extension to other heuristics

Localized genetic algorithm for the vehicle routing problem

This thesis identifies some problems, the genetic algorithm (GA) is facing in the area of vehicle routing and proposes various methods to address those problems. Those problems arise from the unavailability of suitable chromosomal representation and evaluation schemes of GA for the Vehicle Routing Problem (VRP). The representation and evaluation schemes already in use have problems of high computational cost, illegal chromosomes (chromosomes not representing a legal tour) and wrong fitness assignment (fitness not truly representing chromosome genetic makeup). These problems are addressed by several proposed new schemes, namely the Self Imposed Constraints Evaluation scheme, the Contour and Reverse Contour Evaluation schemes and the Order Skipping Evaluation scheme, which are specifically tailored for various objectives, problems and situations. Apart from this, a methodology, which has previously being used in other meta-heuristics, is incorporated into GA i.e., the independent application of GA on various sub-localities of the problem. We call this GA, a Localized Genetic Algorithm (LGA). LGA is an iterative procedure between optimization and controlled de-optimization. The procedure of controlled de-optimization is also novel. It brings the solution into a new search space while controlling its cost effectively. LGA is introduced with various search techniques, i.e. intensive, extensive and selective, the use of which depends on the problem size and the availability of computational resources. Furthermore, search reduction techniques (Fitness Approximation Methods) are also introduced into the LGA, which has enabled the LGA to be applied to large scale problems. Due to the implementation of those proposals, LGA is the first GA-driven approach to be applied to very large scale CVRP problems of up to 1200 customers, i.e. datasets presented by Feiyue in 2005 and large scale VRPTW problems of up to 1000 customers, datasets presented by Gehring and Homberger in 1999. Lastly, a standard unit for computational comparison, i.e., Bellman's Evaluation Units BEUs, is also introduced to facilitate computational comparisons for future researchers. LGA has shown promising results on CVRP and VRPTW problems. It is flexible and also has the potential to be extended to not only other vehicle routing problems, but also to other ordering problems