Parallel computing for large-scale trans-portation network design problems

Amelia Regan, Dmitri ArkhipovUniversity of California, Irvine

and distrib-uted

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 im-provement (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 engineer-ing (in the dept of civil & environmental engr)

• I mainly worked on freight and logistics and IT adoption across in-dustries

• 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 op-

portunity to participate in three year study of fuel efficiency stan-dards 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 – A number of different objectives can be considered such

as improving system travel times versus improving so-cial 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 sub-ject to randomness or stochastic network disrup-tions, decision-makers may prefer solutions that are resilient against the uncertainty.

• Solutions to optimization problems that are least sensitive to uncertainty are called robust solu-tions.

• 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 Multiobjective Metaheuristic and Network Degradation Simulation Model for Robust Toll Pric-ing, 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 func-tions. Transportation Research Record: Journal of the Transportation Research Board, 2196.

Surrogate models

• Surrogate models have been used for optimiza-tion in addition to functional fitting and approxi-mation. Gutmann (2001) proves that convergence can be achieved with the use of radial basis func-tions (RBFs) as an iterative search algorithm for global optimization.

• Surrogate models such as RBFs can be used for optimization without as much concern for accu-racy 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 imple-mented on only relatively small networks.

• After explaining their methods using 2-4 node ex-amples, researchers typically move to a small (6-10 node) example, and then a medium sized ex-ample.

Transportation Network Design

• The Sioux Falls SD network which was first used in the mid-1970’s is still com-monly 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 cen-troids (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 parallel-ism. 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 per-

formed 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 prob-lems common in combinatorial optimization

• Less well known are advances in navigational programming aka distributed sequential comput-ing

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 Dis-

tributed 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 par-allel portions run on the GPU.

Applications in transportation and lo-gistics

• Parallel and distributed metahuristics have been popular for some time– Especially for logistics problems – using distributed comput-

ing to enhance solution quality with metaheuristics, or com-bining several or many metaheuristics with some informa-tion 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 men-

tions 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 represen-tative of a continuous network design problem.

• Toll pricing under demand or supply uncertainty has been less studied, but has been gaining inter-est 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 sto-chastic 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).

• Sumalee and 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 uncer-tainty as a derivative.

• Wang et al. (2013) extend stochastic congestion pricing to multiple operators that can choose to cooperate or compete in their toll pric-ing 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 op-erational, 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 re-sponsive 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 sus-tainable toll design for congested road networks with uncertain demand. In-ternational 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 Mathemat-ics 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 re-alistic 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 ex-pected social welfare (and minimize its variance) and a lower level which assumes that travelers behave according to Wardrop’s Equilibrium Princi-ple

“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-opti-mized 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 de-mand.

• Our formulation assumes instead that the scenarios reflect stochastic link capacities

• Chow’s primary contributions were to develop an effi-cient 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-indepen-dent 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 mat-lab 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 in-volved 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 im-plementation 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 com-puter 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 transporta-tion models of all sorts as not just “the work of technicians” and not something to be left for oth-ers 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