A Memetic Algorithm for the Generalized Traveling Salesman Problem

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.Comment: 15 pages, to appear in Natural Computing, Springer, available online: http://www.springerlink.com/content/5v4568l492272865/?p=e1779dd02e4d4cbfa49d0d27b19b929f&pi=1

Multi-Stop Routing Optimization: A Genetic Algorithm Approach

In this research, we investigate and propose new operators to improve Genetic Algorithm’s performance to solve the multi-stop routing problem. In a multi-stop route, a user starts at point x, visits all destinations exactly once, and then return to the same starting point. In this thesis, we are interested in two types of this problem. The first type is when the distance among destinations is fixed. In this case, it is called static traveling salesman problem. The second type is when the cost among destinations is affected by traffic congestion. Thus, the time among destinations changes during the day. In this case, it is called time-dependent traveling salesman problem. This research proposes new improvements on genetic algorithm to solve each of these two optimization problems. First, the Travelling Salesman Problem (TSP) is one of the most important and attractive combinatorial optimization problems. There are many meta-heuristic algorithms that can solve this problem. In this paper, we use a Genetic Algorithm (GA) to solve it. GA uses different operators: selection, crossover, and mutation. Sequential Constructive Crossover (SCX) and Bidirectional Circular Constructive Crossover (BCSCX) are efficient to solve TSP. Here, we propose a modification to these crossovers. The experimental results show that our proposed adjustment is superior to SCX and BCSCX as well as to other conventional crossovers (e.g. Order Crossover (OX), Cycle Crossover (CX), and Partially Mapped Crossover (PMX)) in term of solution quality and convergence speed. Furthermore, the GA solver, that is improved by applying inexpensive local search operators, can produce solutions that have much better quality within reasonable computational time. Second, the Time-Dependent Traveling Salesman Problem (TDTSP) is an interesting problem and has an impact on real-life applications such as a delivery system. In this problem, time among destinations fluctuates during the day due to traffic, weather, accidents, or other events. Thus, it is important to recommend a tour that can save driver’s time and resources. In this research, we propose a Multi-Population Genetic Algorithm (MGA) where each population has different crossovers. We compare the proposed MG against Single-Population Genetic Algorithm (SGA) in terms of tour time solution quality. Our finding is that MGA outperforms SGA. Our method is tested against real-world traffic data [1] where there are 200 different instances with different numbers of destinations. For all tested instances, MGA is superior on average by at least 10% (for instances with size less than 50) and 20% (for instances of size 50) better tour time solution compared to SGA with OX and SGA with PMX operators, and at least 4% better tour time compared toga with SCX operator

Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search.Comment: 25 page