อัลกอริทึมการแตกกิ่งและกำหนดขอบเขตสำหรับปัญหาการเดินทางของพนักงานขายภายใต้ความน่าจะเป็นที่กลับไปยังจุดเริ่มเดินทาง

Abstract

This paper presents a branch and bound algorithm for the solution of the Probabilistic Traveling Salesman Problem with Return. The algorithm is composed of three main steps. In the first step, branching divides the problem into smaller subproblems that are easier and quicker to handle. All possible solutions are then checked for feasibility by comparing with the boundaries (lower and upper bounds).  The second step, known as bounding, is to find lower and upper bounds for the solution at each node that are continually refined over time. A feasible solution must lie between these bounds.  In the third step, called node selection, the jump-tracking strategy chooses a node with the best result to process.  For obtaining the optimal solution, many iterations are executed until the shortest route is identified.  A computer program was developed based on the algorithm, and number of test cases have been solved in an acceptable time; a 15 city problem took less than a second, and a 800 city problem required about 30 minutes.