TSP Race: Minimizing completion time in time-sensitive applications

https://doi.org/10.1016/j.ejor.2014.12.022Get rights and content

Highlights

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    Minimizing time from receipt to complete implementation is often the real goal.

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    Parallelizing implementation with computation can significantly speed completion.

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    Break-even speed ratios can be well-estimated.

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    Simple heuristics used with CIP can beat direct application of complex heuristics.

Abstract

In this paper, we present an approach for parallelizing computation and implementation time for problems where the objective is to complete the solution as soon after receiving the problem instance as possible. We demonstrate the approach on the TSP. We define the TSP race problem, present a computation-implementation parallelized (CIP) approach for solving it, and demonstrate CIP’s effectiveness on TSP Race instances. We also demonstrate a method for determining a priori when CIP will be effective. Although in this paper we focus on TSP, our general CIP approach can be effective on other problems and applications with similar time sensitivity.

Section snippets

Introduction to TSP Race and CIP

The classical traveling salesman problem (TSP) is to find the shortest tour through a set of points and back to the start; it is named after the situation of a traveling salesman who needs to visit a set of cities and then return home.

Consider a case where two traveling salesmen are given the same large set of points and are each challenged to finish a tour before the other. The first traveling salesman follows a traditional approach, computing an optimal tour upfront before starting to travel.

Application areas and motivation

Our main motivation to design CIP approaches is to address time-sensitive applications in which total time from obtaining an instance to completing the implementation of a solution is an important objective to optimize. Among such applications, CIP is most appropriate for those where computation time is comparable to implementation time. (Otherwise, if computation time is relatively small then one could quickly compute the best solution and then implement it, and if implementation time is

Literature review

TSP has a rich literature. Applegate et al. (2007) is a comprehensive guide to TSP’s history. Common exact algorithms for TSP and its variants include branch-and-cut, e.g., Ascheuer, Jünger, and Reinelt (2000), Baldacci, Hadjiconstantinou, and Mingozzi (2003), Cordeau, Dell’Amico, and Iori (2010), Jünger and Störmer (1995), Ascheuer, Fischetti, and Grötschel (2001) and branch-and-bound, e.g., Poremba and Toriello (2014), Volgenant and Jonker (1982), Gavish and Srikanth (1986), Carpaneto,

Theoretical approach

Our approach is to decrease the total TSP completion time by making better use of the travel time. The main idea is to embed the computation into travel so as to have less computation-only time. Fig. 1 is a visual summary of our approach. We split the graph into subgraphs. Initially, we do one step of computation to choose a path through the first subgraph. While traveling on this path, we do a second computation to choose a path through the second subgraph, etc. Except for the first

Graph partitioning policies and computational results

The main contribution of the CIP approach is to decrease the total completion time in spite of a possible increase in both computation time and travel time. How we partition the graph plays an important role. We propose and test four different partitioning rules. In the first three partitioning methods, the nodes are partitioned based on their location, before any travel begins. In the last method, the partition is created on the fly by the initial fast algorithm. These methods are discussed in

Time coefficient break-even analysis and parameter selection mechanism

Now that we have shown the CIP approach to be effective for TSP Race, we would like to characterize the break-even point beyond which the CIPBA approach should be used instead of its constituent algorithms A and B. The main factor affecting the performance of the CIP approach is the ratio of computation and travel speeds. In applications where the computation is already extremely fast relative to the travel, the CIP approach may not help. So, we would like to determine the smallest applicable

Conclusion

In this paper, we introduced a computation-implementation parallelization (CIP) approach to solving problems where the goal is to minimize the time from getting the problem instance to completing the implementation of its solution. By embedding computation into the implementation, we can decrease the total completion time. Focusing on a min-completion-time variant of TSP that we name TSP Race, we proposed and evaluated four methods of partitioning the graph for CIP, and verified that CIP is a

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions that improved this paper.

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