Optimization Techniques to Solve Travelling Salesman Problem Using Machine Learning Algorithms

Travelling Salesmen problem is a very popular problem in the world of computer programming. It deals with the optimization of algorithms and an ever changing scenario as it gets more and more complex as the number of variables goes on increasing. The solutions which exist for this problem are optimal for a small and definite number of cases. One cannot take into consideration of the various factors which are included when this specific problem is tried to be solved for the real world where things change continuously. There is a need to adapt to these changes and find optimized solutions as the application goes on. The ability to adapt to any kind of data, whether static or ever-changing, understand and solve it is a quality that is shown by Machine Learning algorithms. As advances in Machine Learning take place, there has been quite a good amount of research for how to solve NP-hard problems using Machine Learning. This reportis a survey to understand what types of machine algorithms can be used to solve with TSP. Different types of approaches like Ant Colony Optimization and Q-learning are explored and compared. Ant Colony Optimization uses the concept of ants following pheromone levels which lets them know where the most amount of food is. This is widely used for TSP problems where the path is with the most pheromone is chosen. Q-Learning is supposed to use the concept of awarding an agent when taking the right action for a state it is in and compounding those specific rewards. This is very much based on the exploiting concept where the agent keeps on learning onits own to maximize its own reward. This can be used for TSP where an agentwill be rewarded for having a short path and will be rewarded more if the path chosen is the shortest. Keywords: LINEAR REGRESSION, LASSO REGRESSION, RIDGE REGRESSION, DECISION TREE REGRESSOR, MACHINE LEARNING, HYPERPARAMETER TUNING, DATA ANALYSIS

The New Approaches Based on Ant Colony Optimization and Greedy Search Algorithm for Solving Hierarchical Chinese Postman Problem with Stochastic Travel Times

Hierarchical Chinese postman problem (HCPP), a variant of the Chinese postman problem, aims to find the shortest tour or tours by passing through the arcs classified according to precedence relationship. HCPP, which has a wide application area in real-life problems such as shovel snow and routing patrol vehicles where precedence relations are important, belongs to the NP-hard problem class. In real-life problems, travel time between the two locations in city traffic varies due to reasons such as traffic jam, weather conditions, etc. Therefore travel times are uncertain. In this study, HCPP is handled with the chance-constrained stochastic programming approach, and a new type of problem, hierarchical Chinese postman problem with stochastic travel times, is introduced. Due to the NP-hard nature of the problem, the developed mathematical model with stochastic parameter values cannot find proper solutions in large size problems within the appropriate time interval. Therefore, two new solution approaches, a heuristic method based on the Greedy Search (GSA) algorithm and a meta-heuristic method based on ant colony optimization (ACO) are proposed in this study. These new algorithms were tested on modified benchmark instances and randomly generated problem instances with as many as 817 edges. The performance of algorithms was compared in terms of solution quality and computational time.