An official website of the United States government
We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation-based linear-programming relaxation for this VRP. Specifically, we focus on algorithms for the “pricing problem,” which corresponds to the resource-constrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2% optimality gaps for most VRP benchmark instances and less than 1% optimality gaps for the medical home care delivery instances, both under a 30-minute computational time limit. The use of cutting planes (e.g., robust cuts) can further reduce optimality gaps on some hard instances, without much increase in the run time. Summary of Contribution: The vehicle routing problem (VRP) is a fundamental combinatorial problem, and its variants have been studied extensively in the literature of operations research and computer science. In this paper, we consider general-purpose algorithms for solving VRPs, including the column-generation approach for the linear programming relaxations of the integer programs of VRPs and the column-enumeration approach for seeking improved integer solutions. We revise the pulse algorithm and also propose a random-coloring algorithm that can be used for solving the elementary shortest path problem that formulates the pricing problem in the column-generation approach. We show that the parallel implementation of both algorithms can significantly improve the performance of column generation and the random coloring algorithm can improve the solution time and quality of the VRP integer solutions produced by the column-enumeration approach. We focus on algorithmic design for VRPs and conduct extensive computational tests to demonstrate the performance of various approaches.
more »
« less
Brief Announcement: A Parallel (Δ, Γ)-Stepping Algorithm for the Constrained Shortest Path Problem
We design a parallel algorithm for the Constrained Shortest Path (CSP) problem. The CSP problem is known to be NP-hard and there exists a pseudo-polynomial time sequential algorithm that solves it. To design the parallel algorithm, we extend the techniques used in the design of the Δ-stepping algorithm for the single-source shortest paths problem.
more »
« less
- Award ID(s):
- 1724227
- PAR ID:
- 10349904
- Date Published:
- Journal Name:
- SPAA '22: Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
- Page Range / eLocation ID:
- 287 to 289
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The multi objective shortest path (MOSP) problem, crucial in various practical domains, seeks paths that optimize multiple objectives. Due to its high computational complexity, numerous parallel heuristics have been developed for static networks. However, real-world networks are often dynamic where the network topology changes with time. Efficiently updating the shortest path in such networks is challenging, and existing algorithms for static graphs are inadequate for these dynamic conditions, necessitating novel approaches. Here, we first develop a parallel algorithm to efficiently update a single objective shortest path (SOSP) in fully dynamic networks, capable of accommodating both edge insertions and deletions. Building on this, we propose DynaMOSP, a parallel heuristic for Dynamic Multi Objective Shortest Path searches in large, fully dynamic networks. We provide a theoretical analysis of the conditions to achieve Pareto optimality. Furthermore, we devise a dedicated shared memory CPU implementation along with a version for heterogeneous computing environments. Empirical analysis on eight real-world graphs demonstrates that our method scales effectively. The shared memory CPU implementation achieves an average speedup of 12.74× and a maximum of 57.22×, while on an Nvidia GPU, it attains an average speedup of 69.19×, reaching up to 105.39× when compared to state-of-the-art techniques.more » « less
-
In recent years, Internet of Things (IoT) devices have been extensively deployed in edge networks, including smart homes and offices. Despite the exciting opportunities afforded by the advancements in the IoT, it also introduces new attack vectors and vulnerabilities in the system. Existing studies have shown that the attack graph is an effective model for performing system-level analysis of IoT security. In this paper, we study IoT system vulnerability analysis and network hardening. We first extend the concept of attack graph to weighted attack graph and design a novel algorithm for computing a shortest attack trace in a weighted attack graph. We then formulate the network hardening problem. We prove that this problem is NP-hard, and then design an exact algorithm and a heuristic algorithm to solve it. Extensive experiments on 9 synthetic IoT systems and 2 real-world smart home IoT testbeds demonstrate that our shortest attack trace algorithm is robust and fast, and our heuristic network hardening algorithm is efficient in producing near optimal results compared to the exact algorithm.more » « less
-
null (Ed.)Efficient provisioning of 5G network slices is a major challenge for 5G network slicing technology. Previous slice provisioning methods have only considered network resource attributes and ignored network topology attributes. These methods may result in a decrease in the slice acceptance ratio and the slice provisioning revenue. To address these issues, we propose a two-stage heuristic slice provisioning algorithm, called RT-CSP, for the 5G core network by jointly considering network resource attributes and topology attributes in this paper. The first stage of our method is called the slice node provisioning stage, in which we propose an approach to scoring and ranking nodes using network resource attributes (i.e., CPU capacity and bandwidth) and topology attributes (i.e., degree centrality and closeness centrality). Slice nodes are then provisioned according to the node ranking results. In the second stage, called the slice link provisioning stage, the k-shortest path algorithm is implemented to provision slice links. To further improve the performance of RT-CSP, we propose RT-CSP+, which uses our designed strategy, called minMaxBWUtilHops, to select the best physical path to host the slice link. The strategy minimizes the product of the maximum link bandwidth utilization of the candidate physical path and the number of hops in it to avoid creating bottlenecks in the physical path and reduce the bandwidth cost. Using extensive simulations, we compared our results with those of the state-of-the-art algorithms. The experimental results show that our algorithms increase slice acceptance ratio and improve the provisioning revenue-to-cost ratio.more » « less
-
null (Ed.)This paper revisits the k-mismatch shortest unique substring finding problem and demonstrates that a technique recently presented in the context of solving the k-mismatch average common substring problem can be adapted and combined with parts of the existing solution, resulting in a new algorithm which has expected time complexity of O(n log^k n), while maintaining a practical space complexity at O(kn), where n is the string length. When , which is the hard case, our new proposal significantly improves the any-case O(n^2) time complexity of the prior best method for k-mismatch shortest unique substring finding. Experimental study shows that our new algorithm is practical to implement and demonstrates significant improvements in processing time compared to the prior best solution's implementation when k is small relative to n. For example, our method processes a 200 KB sample DNA sequence with k=1 in just 0.18 seconds compared to 174.37 seconds with the prior best solution. Further, it is observed that significant portions of the adapted technique can be executed in parallel, using two different simple concurrency models, resulting in further significant practical performance improvement. As an example, when using 8 cores, the parallel implementations both achieved processing times that are less than 1/4 of the serial implementation's time cost, when processing a 10 MB sample DNA sequence with k=2. In an age where instances with thousands of gigabytes of RAM are readily available for use through Cloud infrastructure providers, it is likely that the trade-off of additional memory usage for significantly improved processing times will be desirable and needed by many users. For example, the best prior solution may spend years to finish a DNA sample of 200MB for any , while this new proposal, using 24 cores, can finish processing a sample of this size with k=1 in 206.376 seconds with a peak memory usage of 46 GB, which is both easily available and affordable on Cloud. It is expected that this new efficient and practical algorithm for k-mismatch shortest unique substring finding will prove useful to those using the measure on long sequences in fields such as computational biology. We also give a theoretical bound that the k-mismatch shortest unique substring finding problem can be solved using O(n log^k n) time and O(n) space, asymptotically much better than the one we implemented, serving as a new discovery of interest.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3490148.3538555
