Abstract
The traveling salesman problem (TSP) consists of finding the shortest way between cities, which passes through all cities and returns to the starting point, given the distance between cities. The Vehicle Routing Problem (VRP) is the issue of defining the assumptions and limitations in mapping routes for vehicles performing certain operational activities. It is a major problem in logistics transportation. In specific areas of business, where transportation can be perceived as added value to the product, it is estimated that its optimization can lower costs up to 25% in total. The economic benefits for more open markets are a key point for VRP. This paper discusses the metaheuristics usage for solving the vehicle routing problem with special attention toward Genetic Algorithms (GAs). Metaheuristic algorithms are selected to solve the vehicle routing problem, where GA is implemented as our primary metaheuristic algorithm. GA belongs to the evolutionary algorithm (EA) family, which works on a “survival of the fittest” mechanism. This paper presents the idea of implementing different genetic operators, modified for usage with the VRP, and performs experiments to determine the best combination of genetic operators for solving the VRP and to find optimal solutions for large-scale real-life examples of the VRP.
Highlights
The traveling salesman problem (TSP) consists of the need to visit many places in the shortest, safest, and least expensive way and return to the starting point, so that the route does not take too much time, wasting company resources
How far a solution was from an optimal one could not be analyzed, as traveled distances differ for each instance and are dependent on large amount of constraints written into them, introduced during the generation process
Using edge recombination is considered as a kind of gamble, as luck is a variable in obtaining good results
Summary
The traveling salesman problem (TSP) consists of the need to visit many places in the shortest, safest, and least expensive way and return to the starting point, so that the route does not take too much time, wasting company resources. This problem is presented with the help of a graph or map whose points are expressed by cities and the edges connecting them—roads. In practice (that is, having a limited amount of available time), heuristic methods are used to solve. These methods do not guarantee finding the optimal solution but offer an acceptable approximate solution in a reasonable time. In addition to heuristic methods, which are created to solve one specific problem, there are metaheuristic methods
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