Modeling of Fuzzy Rule-base Algorithm for the Time Dependent Traveling Salesman Problem

Abstract

The Traveling Salesman Problem (TSP) is one of the most extensively studied NP-hard graph search problems. In the literature, there have been numerous published attempts, applying various approaches in order to find the optimum (least cost) or semi optimum solution. Time Dependent Traveling Salesman Problem (TD TSP) is one of the most sufficient extensions and modifications of the original TSP problem. In TD TSP the costs of edges between nodes varies, they are assigned higher cost in the traffic jam region, such as city center or during the rush hour periods. In this paper, we introduce an even more realistic approach, the 3FTD TSP (Triple Fuzzy Time Dependent Traveling Salesman Problem); a fuzzified model of the original TD TSP. The 3FTD TSP presents a variation of the TD TSP utilizing fuzzy values in the cost between two nodes (shops, cities, etc.), the geographical areas of the traffic jam region, and also the rush hour period. The goal is to give a practically useful and realistic alternative of the basic TD TSP problem. In order to calculate the (quasi-) optimum solution, the Discrete Bacterial Memetic Evolutionary Algorithm was used, since it has been proven to be rather efficient (and predictably) in a wide range of NP-hard problems, including the original TSP and the TD TSP as well. The results from the runs based on the extensions of the family of benchmarks generated from the original TD TSP benchmark data set showed rather good and credible initial results.