A Hybrid Genetic Algorithm for the min-max Multiple Traveling Salesman Problem

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min-max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets

Integrating forecasting in metaheuristic methods to solve dynamic routing problems: evidence from the logistic processes of tuna vessels

The multiple Traveling Salesman Problem (mTSP) is a widespread phenomenon in real-life scenarios, and in fact it has been addressed from multiple perspectives in recent decades. However, mTSP in dynamic circumstances entails a greater complexity that recent approaches are still trying to grasp. Beyond time windows, capacity and other parameters that characterize the dynamics of each scenario, moving targets is one of the underdeveloped issues in the field of mTSP. The approach of this paper harnesses a simple prediction method to prove that integrating forecasting within a metaheuristic evolutionary-based method, such as genetic algorithms, can yield better results in a dynamic scenario than their simple non-predictive version. Real data is used from the retrieval of Fish Aggregating Devices (FADs) by tuna vessels in the Indian Ocean. Based on historical data registered by the GPS system of the buoys attached to the devices, their trajectory is firstly forecast to feed subsequently the functioning of a genetic algorithm that searches for the optimal route of tuna vessels in terms of total distance traveled. Thus, although valid for static cases and for the Vehicle Routing Problem (VRP), the main contribution of this method over existing literature lies in its application as a global search method to solve the multiple TSP with moving targets in many dynamic real-life optimization problems.Ministerio de Economía y Competitividad | Ref. ECO2016-76625-RXunta de Galicia | Ref. GRC2014/02

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Application of Genetic Algorithms to Solve MTSP Problems with Priority (Case Study at the Jakarta Street Lighting Service)

Transportation is one thing that is very important and is the highest cost in the supply chain. One way to reduce these costs is to optimize vehicle routes. The Multiple Traveling Salesman Problem (MTSP) and Capacitated Vehicle Routing Problem (CVRP) are models that have been extensively researched to optimize vehicle routes. In its development based on actual events in the real world, some priorities must be visited first in optimizing vehicle routes. Several studies on MTSP and CVRP models have been conducted with exact solutions and algorithms. In a real case in the Jakarta City Street Lighting Section, the problem of determining the route in three shifts is a crucial problem that must be resolved to increase worker productivity to improve services. Services in MCB (Miniature Circuit Breaker) installation and maintenance activities for general street lights and priority is given to light points that require replacement. Because, in this case, the delivery capacity is not taken into account, the priority of the lights visited is random, and the number of street light points is enormous, in this study, we use the MTSP method with priority and solve by a genetic algorithm assisted by the nearest neighbor algorithm. From the resolution of this problem, it was found that the travel time reduction was 32 % for shift 1, 24 % for shift 2, and 23 % for shift 3. Of course, this time reduction will impact worker productivity so that MCB installation can be done faster for all lights and replace a dead lamp

Makespan minimizing on multiple travel salesman problem with a learning effect of visiting time

-The multiple traveling salesman problem (MTSP) involves the assignment and sequencing procedure simultaneously. The assignment of a set of nodes to each visitors and determining the sequence of visiting of nodes for each visitor. Since specific range of process is needed to be carried out in nodes in commercial environment, several factors associated with routing problem are required to be taken into account. This research considers visitors’ skill and category of customers which can affect visiting time of visitors in nodes. With regard to learning-by-doing, visiting time in nodes can be reduced. And different class of customers which are determined based on their potential purchasing of power specifies that required time for nodes can be vary. So, a novel optimization model is presented to formulate MTSP, which attempts to ascertain the optimum routes for salesmen by minimizing the makespan to ensure the balance of workload of visitors. Since this problem is an NP-hard problem, for overcoming the restriction of exact methods for solving practical large-scale instances within acceptable computational times. So, Artificial Immune System (AIS) and the Firefly (FA) metaheuristic algorithm are implemented in this paper and algorithms parameters are calibrated by applying Taguchi technique. The solution methodology is assessed by an array of numerical examples and the overall performances of these metaheuristic methods are evaluated by analyzing their results with the optimum solutions to suggested problems. The results of statistical analysis by considering 95% confidence interval for calculating average relative percentage of deviation (ARPD) reveal that the solutions of proposed AIS algorithm has less variation and Its’ confidence interval of closer than to zero with no overlapping with that of FA. Although both proposed meta-heuristics are effective and efficient in solving small-scale problems, in medium and large scales problems, AIS had a better performance in a shorter average time. Finally, the applicability of the suggested pattern is implemented in a case study in a specific company, namely Kalleh