Predicting Parallel TSP Performance: a Computational Approach

Abstract

Faced with a scientific force and a critical need to solve large-scale and/or time-constrained problems, the industry reports that access to high-performance computing (HPC) capability is required now more than ever. Continued hardware and software advances, such as more powerful and lower-cost processors, have made it easier for scientists and engineers to install and use clusters / multi-cores and complete high-performance computing jobs. In particular, the Traveling Salesman Problem (TSP) is one of the most famous problems (and the best one perhaps studied) in the field of the combinatorial optimization. In spite of the apparent simplicity of their formulation, the TSP is a complex solving problem and the complexity of its solution has been a continue challenge to the mathematicians for centuries. Not only the study of this problem has attracted people from mathematics but also many researchers of other fields like operations research, physics, biology, or artificial intelligence, and accordingly there is a vast amount of literature on it. On the other hand, not yet an effective polynomial-time algorithm is known for the general case. Many aspects of the problem still need to be considered and questions are still left to be answered satisfactorily. A significant challenge is being able to predict TSP performance order. It is important to bear in mind, that the TSP conclusions drawn could eventually be applied to any TSP family problem. There are important cases of practical problems that can be formulated as TSP problems and many other problems are generalizations of this problem. Therefore, there is a tremendous need for predicting the performance order of TSP algorithms. Measuring the execution time (performance) of a TSP parallel algorithm for all possible input values would allow answering any question about how the algorithm will respond under any set of conditions. Unfortunately, it is impossible to make all of these measurements. TSP performance depends on the number of cores used, the data size, as well as other parameters. Detecting the main other parameters that affect performance order is the real clue to obtain a good estimation. The issue of measuring performance for the TSP problem in practice and how to relate practical results to the theoretical analysis is addressed in this chapter as a knowledge discovery methodology. The defined methodology for performance modelling begins by generating a representative sample of the full population of TSP instances and measuring their execution times. An interactive and iterative process explores data in search of patterns and/or relationships detecting the main parameters that affect performance. Knowing the main parameters which characterise time complexity, it becomes possible to suspect new hypotheses to