THE TRAVELING SALESMAN PROBLEM WITH JOB-TIMES, MULTI-CIRCUIT, AND VARIATIONS

Abstract

The Traveling Salesman Problem (TSP), Assignment Problem (AP), and Scheduling Problems (SP) such as Job-shop or Flow-shop problems are well known in computational mathematics. This dissertation explores four new types of problems that inherit the properties of one or some of the above mentioned problems, each of which will be elaborated as follows: The first problem considered is the Travelling Salesman Problem with Jobtimes (TSPJ) which integrates two factors {distance and job-time in an optimization metric. It is a variant of TSP where the traveler moves through n locations, visiting each location once to initiate one of n jobs, and returns to the first location. After initiation of a job, the traveler moves to the next location immediately and the job continues autonomously. The goal is to minimize the time of completion of the last job, i.e. makespan. By using a mathematical model and the heuristics, the results show that the new adapted nearest neighbor algorithm and a proposed local search improvement heuristics solution has less than 6% relative optimality gap with the optimum solution of the sample sets in acceptable processing time. Also, the gaps between the GAMS solutions and the GA outputs are less than 10%. The second problem considered is the Traveling Salesman Problem with Jobtime, Drop-off, and Pick-up (TSPJDP). It is a variant of TSP where the traveler/ transporter moves through n given locations, visiting each location first to drop an autonomous agent off to execute a preassigned job, and again to pick the agents up after completion of their job. At the end, the traveler returns to the origin. After initiation of the job at each drop-off location, the traveler can either wait to pick up the agent, or move to another location immediately. The agent continues autonomously and waits to be picked up after the job is completed. The goal is to find the sequence of the drop offs and pick-ups that minimizes the completion time of the entire tour. By using a mathematical model and the heuristics, the results show that the heuristics solutions have at most 3% relative optimality gap with the optimum solution in the sample sets. The third problem considered is the Multi Circuit Traveling Salesman Problem(MCTSP). It is a variant of TSP where the traveler makes multiple circuits through a given set of nodes, visiting each node once in each circuit without returning to the depot until visiting all