and distributed Parallel computing for large-scale transportation network design problems Amelia Regan, Dmitri Arkhipov University of California, Irvine
Transportation Network Design • Network design in transportation covers a wide range of strategies and operations, including road expansion, road improvement, signal control, ramp metering, and toll pricing • Most problems however are related to link improvement (generally continuous problems), link addition (generally discrete problems), or transit network design (also generally discrete problems)
My work and interests • I joined UC Irvine in 1997 as an assistant professor of civil engineering (in the dept of civil & environmental engr) • I mainly worked on freight and logistics and IT adoption across industries • I was very interested in combinatorial auctions (contracting) and other contracting methods • I switched half time to computer science in 2003 and full time in 2007 • My interests remain in transportation but mainly in computational issues • I teach classes in discrete math, optimization, and technical writing • Lately I have gotten interested in technology policy due to an opportunity to participate in three year study of fuel efficiency standards for trucks (which means studying the CAFÉ standards as well)
Transportation Network Design • Network design in transportation covers a wide range of strategies and operations, including road expansion, road improvement, signal control, ramp metering, and toll pricing • Anumber of different objectives can be considered such as improving system travel times versus improving social equity • More complex solutions that include sustainability and performance under disruptions are needed. • This leads to multiobjective network design formulations which explicitly consider uncertainty
Robust Transportation Network Design • When operating or planning a network that is subject to randomness or stochastic network disruptions, decision-makers may prefer solutions that are resilient against the uncertainty. • Solutions to optimization problems that are least sensitive to uncertainty are called robust solutions. • Whether they are discrete or continuous problems – these variations tend to be much more complex than the already complex underlying problems.
We got interested in these problems as a result of Joe Chow’s dissertation research at UCI (2007-2010) • Chow, J.Y.J. and A.C. Regan (2013), A Surrogate-Based MultiobjectiveMetaheuristic and Network Degradation Simulation Model for Robust Toll Pricing, Optimization and Engineering, in press. • Chow, J.Y.J., A.C. Regan and D.I. Arkhipov (2010), Fast converging global heuristic for continuous network design problem using radial basis functions. Transportation Research Record: Journal of the Transportation Research Board, 2196.
Surrogate models • Surrogate models have been used for optimization in addition to functional fitting and approximation. Gutmann (2001) proves that convergence can be achieved with the use of radial basis functions (RBFs) as an iterative search algorithm for global optimization. • Surrogate models such as RBFs can be used for optimization without as much concern for accuracy if they are used as part of an iterative search algorithm instead of a direct approximation of the true function.
Transportation Network Design • Most network design research has continued to develop models that can be tested and implemented on only relatively small networks. • After explaining their methods using 2-4 node examples, researchers typically move to a small (6-10 node) example, and then a medium sized example.
Transportation Network Design • The Sioux Falls SD network which was first used in the mid-1970’s is still commonly referred to as a “medium sized” network by researchers (24 nodes, 76 links)
Transportation Network Design • To be fair – some problems are tested on more realistic problems (in Chow, Regan and Arkhipov, we tested our method vs a GA based method on the Anaheim California Network with, 38 centroids (OD nodes), 416 total nodes, and 914 links and 31 links chosen as potential candidates for capacity expansion.
Some key terms • multi-core, many-core processors • A processor system containing multiple cores per chip. A many-core processor is one in which the number of cores is large enough that traditional multi-processor techniques are no longer efficient. • parallelism vs. concurrency • Parallelism involves multiple computer actions physically taking place at the same time. Concurrency involves programming in order to take advantage of parallelism. Thus, parallelism takes place in hardware, whereas concurrency takes place in software. • concurrent programming • Programming for multiple cores or multiple computers. • cluster • Multiple networked computers managed as a single resource and designed for working together on large computational problems. • data parallelism • A form of parallel computing in which the same processing is applied to multiple subsets of a large data set in parallel. • task parallelism • A form of parallel computing in which different stages of a computation are performed in parallel.
Recent important advances in parallel and distributed computing • Cluster and cloud computing resources are widely available and inexpensive • Inexpensive multi-core computers • Significant advances have been made on using GPUs in sophisticated ways for local search problems common in combinatorial optimization • Less well known are advances in navigational programming aka distributed sequential computing
Recent important advances in parallel computing • Significant advances have been made on using GPUs in sophisticated ways for local search problems • See for example a special issue of the Journal of Parallel and Distributed Computing (2013), Edited by E. Talbi and G. Hasle • Brodtkorb, A. R., Hagen, T. R., Schulz, C., & Hasle, G. (2013). GPU computing in discrete optimization. Part I: Introduction to the GPU. EURO Journal on Transportation and Logistics • Schulz, C., Hasle, G., Brodtkorb, A. R., & Hagen, T. R. (2013). GPU computing in discrete optimization. Part II: Survey focused on routing problems, EURO Journal on Transportation and Logistics. • CPU + GPU is a powerful combination because CPUs consist of a few cores optimized for serial processing, while GPUs consist of thousands of smaller, more efficient cores designed for parallel performance. Serial portions of the code run on the CPU while parallel portions run on the GPU.
Applications in transportation and logistics • Parallel and distributed metahuristics have been popular for some time • Especially for logistics problems – using distributed computing to enhance solution quality with metaheuristics, or combining several or many metaheuristics with some information sharing • See Potvin and Gendreau (2010) (eds) Handbook of Metaheurstics (2nd edition – first the edition was published in 2003 and was edited by Glover and Kochenberg.) • These have be applied much less often in other transportation network design problems • A recent review of research on these problems barely mentions parallel implementations, though they do mention these as promising for future work • See Farahani, R. Z., Miandoabchi, E., Szeto, W. Y., & Rashidi, H. (2013). A review of urban transportation network design problems. European Journal of Operational Research.
Getting back to our problem • We are using model in Chow and Regan (2013) as a representative CNDP problem and as a starting point for our research. • The toll pricing problem is discussed as representative of a continuous network design problem. • Toll pricing under demand or supply uncertainty has been less studied, but has been gaining interest in recent years.
Some related work • Li et al. (2007) are one of the first to propose using toll pricing as a strategy to manage uncertainty in a network with stationary stochastic OD demand and link capacity. • Boyles et al. (2010) propose that toll prices that respond to changes in network capacities can be useful if the information is provided to travelers, and further break down that value into its components (Gardner et al., 2011). • Sumaleeand Xu (2011) present a closed form marginal cost pricing formulation under stochastic demand. • Li et al. (2012) consider robust toll pricing with stochastic demand using a linear measure of variance to avoid the nonconvex mean-variance objective. • Yao et al. (2012) represent congestion pricing with departure time choice using Vickrey’s bottleneck model under travel time uncertainty as a derivative. • Wang et al. (2013) extend stochastic congestion pricing to multiple operators that can choose to cooperate or compete in their toll pricing strategies.
Some related work • Li, H., Bliemer, M.C.J., Bovy, P.H.L., 2007. Optimal toll design from reliability perspective. Proc., 6th Triennnial Conference on Transportation Analysis, Phuket, Thailand. • Boyles, S., Kockelman, K.M., Waller, T.S., 2010. Congestion pricing under operational, supply-side uncertainty. Transportation Research Part C 18(4), 519-535. • Gardner, L.M., Boyles, S.D., Waller, S.T., 2011. Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem. Transportation Research Part A 45(3), 204-218. • Sumalee, A., Xu, W., 2011. First-best marginal cost toll for a traffic network with stochastic demand. Transportation Research Part B 45(1), 41-59. • Li, Z.C., Lam, W.H.K., Wong, S.C., Sumalee, A., 2012. Environmentally sustainable toll design for congested road networks with uncertain demand. International Journal of Sustainable Transportation 6(3), 127-155. • Yao, T., Wei, M.M., Zhang, B., Friesz, T., 2012. Congestion derivatives for a traffic bottleneck with heterogeneous commuters. Transportation Research Part B 46(10), 1454-1473. • Wang, H., Mao, W., Shao, H., 2013. Stochastic congestion pricing among multiple regions: competition and cooperation. Journal of Applied Mathematics 2013, 1-12.
Getting back to our problem • Chow had developed a model and a computational scheme which significantly reduced the time needed to find a solution – rendering his method feasible for small networks. • However it is far from tractable for networks of realistic sizes. • The formulation is a variation of that found in: • Chen, A., Subprasom, K., Ji, Z., 2006. A simulation-based multi-objective genetic algorithm (SMOGA) procedure for BOT network design problem. Optimization Engineering 7 (3), 225-247.
The formulation • The model has the standard bi-level formulation with an upper level in which we maximize expected social welfare (and minimize its variance) and a lower level which assumes that travelers behave according to Wardrop’s Equilibrium Principle “The journey times in all routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route. Each user non-cooperatively seeks to minimize his cost of transportation. …. A user-optimized equilibrium is reached when no user may lower his transportation cost through unilateral action.”
The formulation • Chen’s formulation assumes that |S| scenarios are generated in which the stochastic element is OD demand. • Our formulation assumes instead that the scenarios reflect stochastic link capacities • Chow’s primary contributions were to develop an efficient solution method based on a radial basis function approximation (a multi-objective radial basis function approximation) to find solutions for this formulation, and to demonstrate that even if tolls do not improve social welfare in the deterministic case, that when like failures (due to snow or other weather) are likely then tolls can improve social welfare • Show model….
The formulation • Chow’s other major contribution was to propose a way to generate the scenarios with non-independent link failures. • Show model….
Our current research • To see how the model might be improved by simple parallelization techniques and more complicated ones which necessitate re-designing the solution strategy • Using very simple techniques easily found in the matlab toolkit, Arkhipov obtained a 3X speed up (intel i7 quad core machine). • The matlab toolkit proved very easy to implement on our existing matlab code most of the changes involved only identifying opportunities to insert parallel loops (parfor’s). • We might be able to squeeze a 4-5X speed up with a bit of additional work, but this means little given the combinatorial nature of the problem and our goal of attacking toll setting on networks in California
Our current research • Now we are re-working the solution technique from scratch to find opportunities for significant parallelization • Scenario generation can clearly be parceled out to separate processors • The scenario generation relies on monte-carlo simulation so it’s and ideal place to start • Moreover, the scenario generation is by no means well determined • We need to consider alternative angles as well
Putting this project in context • Over the last few years much of my transportation related research has been related to communication in VANETs • Until very recently the likelihood of near term implementation of useful V2V and V2I networks seems slim…. That might be changing due to automation brought on by the possibility of autonomous vehicles • Still privacy, security and liability concerns are a considerable hurdle to implementation • See Regan, A. C. (2013), Vehicular ad hoc Networks: Storms on the Horizon, Access Magazine, in press. • And two longer book chapters “Vehicular ad hoc Networks and Broadcasting in Vehicular ad hoc Networks” with Rex Chen coming out in 2014. (Woodhead publishing).
Putting this project in context • I find myself searching for opportunities to see our work implemented, or leading to implementations • Ideally academic work in engineering and computer science both helps to train researchers and engineers who will later do interesting and useful implementable work and leads to breakthroughs in practice. • I view some of the work that needs to be done in terms of parallel implementations of transportation models of all sorts as not just “the work of technicians” and not something to be left for others to figure out but a core part of our work as academic researchers….
Thanks for listening • Questions? • Comments? • Special thanks to my friend Elise for inviting me today • Special thanks to you all for attending